SAS/Genetics User/'s Guide

SAS/Genetics®
User’s Guide

SAS/Genetics®
User’s Guide
References to this documentation being online with the
software should be ignored. The documentation is actually
online at www.sas.com/service/library/onlinedoc/genetics.

The correct bibliographic citation for this manual is as follows: SAS Institute Inc.,
SAS/Genetics® User’s Guide, Cary, NC: SAS Institute Inc., 2002.
SAS/Genetics® User’s Guide
Copyright © 2002 SAS Institute Inc., Cary, NC, USA.
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51223_0502

Contents
Chapter 1. Introduction
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
Chapter 2. The ALLELE Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Chapter 3. The CASECONTROL Procedure . . . . . . . . . . . . . . . . . . . . . . . 33
Chapter 4. The FAMILY Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
Chapter 5. The HAPLOTYPE Procedure . . . . . . . . . . . . . . . . . . . . . . . . . 61
Chapter 6. The PSMOOTH Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Chapter 7. The TPLOT Macro . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
Syntax Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

Credits
Documentation
Writing
Wendy Czika and Xiang Yu
Editing
Virginia Clark and Rob Pratt
Technical Review
Russell D. Wolﬁnger and Robert N. Rodriguez
Documentation Production
Tim Arnold
Software
Procedures
Wendy Czika and Xiang Yu
TPLOT Results
Art Barnes and Susan R. Edwards
Support Groups
Quality Assurance
Ming-Chun Chang, Bruce Elsheimer, Gregory D. Goodwin,
Kelly M. Graham, Gerardo I. Hurtado, Bob Overby,
Greg Weier, and Charlotte Zinkus
Technical Support
Rob Agnelli and Kathleen Kiernan

ii
Credits

Acknowledgments
Many people make signiﬁcant and continuing contributions to the development of
SAS software products. The following are some of those who have contributed sig-
niﬁcant amounts of their time to help us make improvements to SAS/Genetics soft-
ware. This includes research and consulting, testing, or reviewing documentation.
We are grateful for the involvement of these members of the statistical community
and the many others who are not mentioned here for their feedback, suggestions, and
consulting.
Margaret G. Ehm
GlaxoSmithKline
Greg Gibson
North Carolina State University
Shizue Izumi
Radiation Effects Research Foundation
Dahlia Nielsen
North Carolina State University
Bruce S. Weir
North Carolina State University
Dmitri Zaykin
GlaxoSmithKline
The simulated GAW12 data used in this book are supported by NIGMS grant
GM31575.
The ﬁnal responsibility for the SAS System lies with SAS alone. We hope that you
will always let us know your opinions about the SAS System and its documentation.
It is through your participation that SAS Software is continuously improved.
Please send your comments to suggest@sas.com.

iv
Acknowledgments

Chapter 1
Introduction
Chapter Contents
OVERVIEW OF SAS/GENETICS SOFTWARE . . . . . . . . . . . . . . .
3
ABOUT THIS BOOK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
Chapter Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
Typographical Conventions . . . . . . . . . . . . . . . . . . . . . . . . . .
5
Options Used in Examples
. . . . . . . . . . . . . . . . . . . . . . . . . .
5
WHERE TO TURN FOR MORE INFORMATION . . . . . . . . . . . . .
7
Online Help System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
SAS Institute Technical Support Services . . . . . . . . . . . . . . . . . . .
7
RELATED SAS SOFTWARE . . . . . . . . . . . . . . . . . . . . . . . . . .
7
Base SAS Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
SAS/GRAPH Software . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
SAS/IML Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
SAS/INSIGHT Software
. . . . . . . . . . . . . . . . . . . . . . . . . . .
8
SAS/STAT Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9

2
Chapter 1. Introduction

Chapter 1
Introduction
Overview of SAS/Genetics Software
Statistical analyses of genetic data are now central to medicine, agriculture, evolu-
tionary biology, and forensic science. The inherent variation in genetic data, together
with the substantial increase in the scale of genetic data following the human genome
project, has created a need for reliable computer software to perform these analy-
ses. The procedures offered by SAS/Genetics and described here represent an initial
response of SAS Institute to this need.
Although many of the statistical techniques used in the new procedures are standard,
others have had to be developed to reﬂect the genetic nature of the data. All the proce-
dures are designed to operate on data sets that have a familiar structure to geneticists,
and that mirror those used in existing software. The syntax for these genetic anal-
yses follows that familiar to SAS users, and the output can be tabular or graphical.
The objective of the procedures is to bring the full power of SAS analyses to bear on
the characterization of fundamental genetic parameters, and most importantly on the
detection of associations between genetic markers and disease status.
Most of the analyses in SAS/Genetics are concerned with detecting patterns of co-
variation in genetic marker data. These data generally consist of pairs of discrete cate-
gories; this pairing derives from the underlying biology, namely the fact that complex
organisms have pairs of chromosomes. Each marker refers to the genetic status of a
locus, each marker type is called an allele, and each pair of alleles in an individual is
called a genotype. A set of alleles present on a single chromosome is called a hap-
lotype. Genetic markers may be single nucleotide polymorphisms (SNPs), which are
sites in the DNA where the nucleotide varies among individuals, usually with only
two alleles possible; microsatellites, which are simple sequence repeats that generate
usually between 2 and 20 categories; and other classes of DNA variation.
Two of the procedures in SAS/Genetics are concerned solely with the analysis of ge-
netic marker data. The ALLELE procedure calculates descriptive statistics such as
the frequency and variance of alleles and genotypes, as well as estimating measures
of marker informativeness, and testing whether genotype frequencies are consistent
with Hardy-Weinberg equilibrium (HWE). This procedure also supports three meth-
ods for calculation of the degree and signiﬁcance of linkage disequilibrium (LD)
among markers at pairs of loci, where LD refers to the propensity of alleles to co-
segregate. The HAPLOTYPE procedure is used to infer the most likely multilocus
haplotype frequencies in a set of genotypes. Since genetic markers are usually mea-
sured independently of one another, there is no direct way to determine which two
alleles were on the same chromosome. The algorithm implemented in this procedure
converges on the haplotype frequencies that have the highest probability of generating
the observed genotypes.

4
Chapter 1. Introduction
Many genetic data sets are now used to study the relationship between genetic mark-
ers and complex phenotypes, particularly disease susceptibility. In general terms,
traits can be measured as continuous variables (for example, weight or serum glucose
concentration), as discrete numerical categories (for example, meristic measures or
psychological class), or as affected/unaffected indicator variables. The two proce-
dures CASECONTROL and FAMILY both take simple dichotomous indicators of
disease status and use standard genetic algorithms to compute statistics of associa-
tion between these indicators and the genetic markers. The CASECONTROL pro-
cedure is designed to contrast allele and genotype frequencies between affected and
unaffected populations, using three types of chi-square tests and options for con-
trolling correlation of allele frequencies among members of the same subpopula-
tion. Signiﬁcant associations may indicate that the marker is linked to a locus that
contributes to disease susceptibility, though population structure in conjunction with
environmental or cultural variables can also lead to associations, and the statistical
results must be interpreted with caution. The FAMILY procedure employs several
transmission/disequilibrium tests of nonrandom association between disease status
and linkage to markers transmitted from heterozygous parents to affected offspring
(TDT) or pairs of affected and unaffected siblings (S-TDT and SDT). A joint anal-
ysis known as the reconstruction-combined TDT (RC-TDT) can also accommodate
missing parental genotypes and families lacking unaffected children under some cir-
cumstances.
The output of these procedures can be further explored by using the PSMOOTH
procedure to adjust p-values from association tests performed on large numbers of
markers obtained in a genome scan, or by creating a graphical representation of the
procedures’ output, namely p-values from tests for LD, HWE, and marker-disease
associations, using the %TPLOT macro.
About This Book
Since SAS/Genetics software is a part of the SAS System, this book assumes that you
are familiar with base SAS software and with the books SAS Language Reference:
Dictionary, SAS Language Reference: Concepts, and the SAS Procedures Guide. It
also assumes that you are familiar with basic SAS System concepts such as creating
SAS data sets with the DATA step and manipulating SAS data sets with the proce-
dures in base SAS software (for example, the PRINT and SORT procedures).
Chapter Organization
This book is organized as follows.
Chapter 1, this chapter, provides an overview of SAS/Genetics software and sum-
marizes related information, products, and services. The next ﬁve chapters describe
the SAS procedures that make up SAS/Genetics software. These chapters appear in
alphabetical order by procedure name. They are followed by a chapter documenting
a SAS macro provided with SAS/Genetics software.
The chapters documenting the SAS/Genetics procedures are organized as follows:

Options Used in Examples
5
• The Overview section provides a brief description of the analysis provided by
the procedure.
• The Getting Started section provides a quick introduction to the procedure
through a simple example.
• The Syntax section describes the SAS statements and options that control the
procedure.
• The Details section discusses methodology and miscellaneous details.
• The Examples section contains examples using the procedure.
• The References section contains references for the methodology and examples
for the procedure.
Typographical Conventions
This book uses several type styles for presenting information. The following list
explains the meaning of the typographical conventions used in this book:
roman
is the standard type style used for most text.
UPPERCASE ROMAN
is used for SAS statements, options, and other SAS lan-
guage elements when they appear in the text. However,
you can enter these elements in your own SAS programs
in lowercase, uppercase, or a mixture of the two.
UPPERCASE BOLD
is used in the “Syntax” sections’ initial lists of SAS state-
ments and options.
oblique
is used for user-supplied values for options in the syntax
deﬁnitions. In the text, these values are written in italic.
helvetica
is used for the names of variables and data sets when they
appear in the text.
bold
is used to refer to matrices and vectors.
italic
is used for terms that are deﬁned in the text, for emphasis,
and for references to publications.
monospace
is used for example code. In most cases, this book uses
lowercase type for SAS code.
Options Used in Examples
Output of Examples
For each example, the procedure output is numbered consecutively starting with 1,
and each output is given a title. Each page of output produced by a procedure is en-
closed in a box. Most of the output shown in this book is produced with the following
SAS System options:
options linesize=80 pagesize=200 nonumber nodate;

6
Chapter 1. Introduction
In some cases, if you run the examples, you will get slightly different output de-
pending on the SAS system options you use and the precision used for ﬂoating-point
calculations by your computer. This does not indicate a problem with the software.
In all situations, any differences should be very small.
Graphics Options
The examples that contain graphical output are created with a speciﬁc set of options
and symbol statements. The code you see in the examples creates the color graphics
that appear in the online (CD) version of this book. A slightly different set of op-
tions and statements is used to create the black-and-white graphics that appear in the
printed version of the book.
If you run the examples, you may get slightly different results. This may occur be-
cause not all graphic options for color devices translate directly to black-and-white
output formats. For complete information on SAS/GRAPH software and graphics
options, refer to SAS/GRAPH Software: Reference.
The following GOPTIONS statement is used to create the online (color) version of
the graphic output.
filename GSASFILE
’<file-specification>’;
goptions gsfname=GSASFILE
gsfmode =replace
fileonly
transparency
dev
= gif
ftext
= swiss
lfactor = 1
htext
= 4.0pct
htitle
= 4.5pct
hsize
= 5.625in
vsize
= 3.5in
noborder
cback
= white
horigin = 0in
vorigin = 0in ;
The following GOPTIONS statement is used to create the black-and-white version of
the graphic output, which appears in the printed version of the manual.
filename GSASFILE
’<file-specification>’;
goptions gsfname=GSASFILE
gsfmode =replace
gaccess = sasgaedt fileonly
dev
= pslepsf
ftext
= swiss
lfactor = 1
htext
= 3.0pct
htitle
= 3.5pct
hsize
= 5.625in
vsize
= 3.5in
border
cback
= white
horigin = 0in
vorigin = 0in ;
In most of the online examples, the plot symbols are speciﬁed as follows:
symbol1 value=dot color=white height=3.5pct;

Base SAS Software
7
The SYMBOLn statements used in online examples order the symbol colors as fol-
lows: white, yellow, cyan, green, orange, blue, and black.
In the examples appearing in the printed manual, symbol statements specify
COLOR=BLACK and order the plot symbols as follows: dot, square, triangle, circle,
plus, x, diamond, and star.
Where to Turn for More Information
This section describes other sources of information about SAS/Genetics software.
Online Help System
You can access online help information about SAS/Genetics software in two ways.
You can select SAS System Help from the Help pull-down menu and then select
SAS/Genetics Software from the list of available topics. Or, you can bring up a
command line and issue the command help Genetics to bring up an index to the
statistical procedures, or issue the command help ALLELE (or another procedure
name) to bring up the help for that particular procedure. Note that the online help
includes syntax and some essential overview and detail material.
SAS Institute Technical Support Services
As with all SAS Institute products, the SAS Institute Technical Support staff is avail-
able to respond to problems and answer technical questions regarding the use of
SAS/Genetics software.
Related SAS Software
Many features not found in SAS/Genetics software are available in other parts of the
SAS System. If you do not ﬁnd something you need in SAS/Genetics software, try
looking for the feature in the following SAS software products.
Base SAS Software
The features provided by SAS/Genetics software are in addition to the features pro-
vided by Base SAS software. Many data management and reporting capabilities
you will need are part of Base SAS software. Refer to SAS Language Reference:
Concepts, SAS Language Reference: Dictionary, and the SAS Procedures Guide for
documentation of Base SAS software.
SAS DATA Step
The DATA step is your primary tool for reading and processing data in the SAS
System. The DATA step provides a powerful general-purpose programming language
that enables you to perform all kinds of data processing tasks. The DATA step is
documented in SAS Language Reference: Concepts.

8
Chapter 1. Introduction
Base SAS Procedures
Base SAS software includes many useful SAS procedures. Base SAS procedures
are documented in the SAS Procedures Guide. The following is a list of Base SAS
procedures you may ﬁnd useful:
CHART
for printing charts and histograms
CONTENTS
for displaying the contents of SAS data sets
CORR
for computing correlations
FREQ
for computing frequency crosstabulations
MEANS
for computing descriptive statistics and summarizing or collapsing
data over cross sections
PRINT
for printing SAS data sets
SORT
for sorting SAS data sets
TABULATE
for printing descriptive statistics in tabular format
TRANSPOSE
for transposing SAS data sets
UNIVARIATE
for computing descriptive statistics
SAS/GRAPH Software
SAS/GRAPH software includes procedures that create two- and three-dimensional
high-resolution color graphics plots and charts. You can generate output that graphs
the relationship of data values to one another, enhance existing graphs, or simply
create graphics output that is not tied to data.
SAS/IML Software
SAS/IML software gives you access to a powerful and ﬂexible programming lan-
guage (Interactive Matrix Language) in a dynamic, interactive environment. The
fundamental object of the language is a data matrix. You can use SAS/IML soft-
ware interactively (at the statement level) to see results immediately, or you can store
statements in a module and execute them later. The programming is dynamic be-
cause necessary activities such as memory allocation and dimensioning of matrices
are done automatically. SAS/IML software is of interest to users of SAS/Genetics
software because it enables you to program your own methods in the SAS System.
SAS/INSIGHT Software
SAS/INSIGHT software is a highly interactive tool for data analysis. You can ex-
plore data through a variety of interactive graphs including bar charts, scatter plots,
box plots, and three-dimensional rotating plots. You can examine distributions and
perform parametric and nonparametric regression, analyze general linear models and
generalized linear models, examine correlation matrices, and perform principal com-
ponent analyses. Any changes you make to your data show immediately in all graphs

SAS/STAT Software
9
and analyses. You can also conﬁgure SAS/INSIGHT software to produce graphs and
analyses tailored to the way you work.
SAS/INSIGHT software may be of interest to users of SAS/Genetics software for
interactive graphical viewing of data, editing data, exploratory data analysis, and
checking distributional assumptions.
SAS/STAT Software
SAS/STAT software includes procedures for a wide range of statistical methodologies
including
• logistic and linear regression
• censored regression
• principal component analysis
• variance component analysis
• cluster analysis
• contingency table analysis
• categorical data analysis: log-linear and conditional logistic models
• general linear models
• linear and nonlinear mixed models
• generalized linear models
• multiple hypothesis testing
SAS/STAT software is of interest to users of SAS/Genetics software because many
statistical methods for analyzing genetics data not included in SAS/Genetics software
are provided in SAS/STAT software.

10
Chapter 1. Introduction

Chapter 2
The ALLELE Procedure
Chapter Contents
OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
GETTING STARTED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
SYNTAX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
PROC ALLELE Statement . . . . . . . . . . . . . . . . . . . . . . . . . . 17
BY Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
VAR Statement
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
DETAILS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Statistical Computations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Frequency Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Measures of Marker Informativeness . . . . . . . . . . . . . . . . . . . 21
Testing for Hardy-Weinberg Equilibrium . . . . . . . . . . . . . . . . . 21
Linkage Disequilibrium (LD) . . . . . . . . . . . . . . . . . . . . . . . 22
Missing Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
OUTSTAT= Data Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Displayed Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
ODS Table Names . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
EXAMPLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Example 2.1. Using the NDATA= Option with Microsatellites . . . . . . . . 27
Example 2.2. Computing Linkage Disequilibrium Measures for SNP Data . 29
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

12
Chapter 2. The ALLELE Procedure

Chapter 2
The ALLELE Procedure
Overview
The ALLELE procedure performs preliminary analyses on genetic marker data.
These analyses serve to characterize the markers themselves or the population from
which they were sampled, and can also serve as the basis for joint analyses on mark-
ers and traits. A genetic marker is any heritable unit that obeys the laws of trans-
mission genetics, and the analyses presented here assume the marker genotypes are
determined without error. With an underlying assumption of random sampling, the
analyses rest on the multinomial distribution of marker alleles, and many standard
statistical techniques can be invoked with little modiﬁcation. The ALLELE proce-
dure uses the notation and concepts described by Weir (1996); this is the reference
for all equations and methods not otherwise cited.
Data are usually collected at the genotypic level but interest is likely to be centered
on the constituent alleles, so the ﬁrst step is to construct tables of allele and genotype
frequencies. When alleles are independent within individuals, that is when there is
Hardy-Weinberg equilibrium (HWE), analyses can be conducted at the allelic level.
For this reason the ALLELE procedure allows for Hardy-Weinberg testing, although
testing is also recommended as a means for detecting possible errors in data.
PROC ALLELE calculates the PIC, heterozygosity, and allelic diversity measures
that serve to give an indication of marker informativeness. Such measures can be
useful in determining which markers to use for further linkage or association testing
with a trait. High values of these measures are a sign of marker informativeness,
which is a desirable property in linkage and association tests.
Associations between markers may also be of interest. PROC ALLELE provides tests
and various statistics for the association, also called the linkage disequilibrium, be-
tween each pair of markers. These statistics can be formed either by using haplotypes
that are given in the data, by estimating the haplotype frequencies, or by using only
genotypic information.
Getting Started
Example
Suppose you have genotyped 25 individuals at ﬁve markers. You want to examine
some basic properties of these markers, such as whether they are in HWE, how many
alleles each has, what genotypes appear in the data, and if there is linkage disequi-
librium between any pairs of markers. You have ten columns of data, with the ﬁrst
two columns containing the set of alleles at the ﬁrst marker, the next two columns
containing the set of alleles for the second marker, and so on. There is one row per
each individual. You input your data as follows:

14
Chapter 2. The ALLELE Procedure
data markers;
input (m1-m10) ($);
datalines;
B
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;
You can now use PROC ALLELE to examine the frequencies of alleles and genotypes
in your data, and see if these frequencies are occurring in proportions you would
expect. The following statements will perform the analysis you want:
proc allele data=markers outstat=ld
prefix=Marker
exact=10000 boot=1000 seed=123;
var m1-m10;
run;
proc print data=ld;
run;
This analysis is using 10,000 permutations to approximate an exact p-value for
the HWE test as well as 1,000 bootstrap samples to obtain the conﬁdence inter-
val for the allele frequencies and one-locus Hardy-Weinberg disequilibrium (HWD)
coefﬁcients.
The starting seed for the random number generator is 123.
The
PREFIX= option requests that the ﬁve markers be named Marker1–Marker5. Since
the BOOTSTRAP= option is speciﬁed but the ALPHA= option is omitted, a 95%
conﬁdence interval is calculated by default.

Example
15
All ﬁve markers are included in the analysis since the ten variables containing the
alleles for those ﬁve markers were speciﬁed in the VAR statement.
The results from the analysis are as follows.
The ALLELE Procedure
Marker Summary
----------Test for HWE---------
Number
Number
of
of
Hetero-
Allelic
Chi-
Pr >
Prob
Locus
Indiv Alleles
PIC zygosity Diversity
Square
DF
ChiSq
Exact
Marker1
25
2 0.3714
0.4800
0.4928
0.0169
1 0.8967 1.0000
Marker2
25
2 0.3685
0.3600
0.4872
1.7041
1 0.1918 0.2262
Marker3
25
2 0.3546
0.4800
0.4608
0.0434
1 0.8350 1.0000
Marker4
25
2 0.3648
0.4800
0.4800
0.0000
1 1.0000 1.0000
Marker5
25
3 0.5817
0.4400
0.6552
9.3537
3 0.0249 0.0106
Figure 2.1.
Marker Summary for the ALLELE Procedure
Figure 2.1 displays information about the ﬁve markers. From this output, you can
conclude that Marker5 is the only one showing signiﬁcant departure from HWE.
Allele Frequencies
Standard
95% Confidence
Locus
Allele
Frequency
Error
Limits
Marker1
A
0.4400
0.0711
0.3000
0.5800
Marker1
B
0.5600
0.0711
0.4200
0.7000
Marker2
A
0.5800
0.0784
0.4200
0.7400
Marker2
B
0.4200
0.0784
0.2600
0.5800
Marker3
A
0.6400
0.0665
0.5200
0.7600
Marker3
B
0.3600
0.0665
0.2400
0.4800
Marker4
A
0.6000
0.0693
0.4600
0.7400
Marker4
B
0.4000
0.0693
0.2600
0.5400
Marker5
A
0.2800
0.0637
0.1400
0.4200
Marker5
B
0.3000
0.0800
0.1600
0.4600
Marker5
C
0.4200
0.0833
0.2800
0.6000
Figure 2.2.
Allele Frequencies for the ALLELE Procedure
Figure 2.2 displays the allele frequencies for each marker with their standard errors
and the lower and upper limits of the 95% conﬁdence interval.

16
Chapter 2. The ALLELE Procedure
Genotype Frequencies
HWD
Standard
95% Confidence
Locus
Genotype
Frequency
Coeff
Error
Limits
Marker1
A/A
0.2000
0.006
0.0493
-0.092
0.096
Marker1
A/B
0.4800
0.006
0.0493
-0.092
0.096
Marker1
B/B
0.3200
0.006
0.0493
-0.092
0.096
Marker2
A/A
0.4000
0.064
0.0477
-0.034
0.148
Marker2
A/B
0.3600
0.064
0.0477
-0.034
0.148
Marker2
B/B
0.2400
0.064
0.0477
-0.034
0.148
Marker3
A/A
0.4000
-0.010
0.0457
-0.104
0.080
Marker3
A/B
0.4800
-0.010
0.0457
-0.104
0.080
Marker3
B/B
0.1200
-0.010
0.0457
-0.104
0.080
Marker4
A/A
0.3600
0.000
0.0480
-0.092
0.086
Marker4
A/B
0.4800
0.000
0.0480
-0.092
0.086
Marker4
B/B
0.1600
0.000
0.0480
-0.092
0.086
Marker5
A/A
0.0800
0.002
0.0405
-0.076
0.082
Marker5
A/B
0.1600
0.004
0.0337
-0.066
0.064
Marker5
A/C
0.2400
-0.002
0.0380
-0.074
0.068
Marker5
B/B
0.2000
0.110
0.0445
0.014
0.188
Marker5
B/C
0.0400
0.106
0.0282
0.044
0.156
Marker5
C/C
0.2800
0.104
0.0453
0.010
0.188
Figure 2.3.
Genotype Frequencies for the ALLELE Procedure
Figure 2.3 displays the genotype frequencies for each marker with the associated
disequilibrium coefﬁcient, its standard error, and the 95% conﬁdence limits.
Obs
Locus1
Locus2
NIndiv
Test
ChiSq
DF
ProbChi
ProbEx
1
Marker1
Marker1
25
HWE
0.01687
1
0.89667
1.0000
2
Marker1
Marker2
25
LD
1.05799
1
0.30367
0.6707
3
Marker1
Marker3
25
LD
1.42074
1
0.23328
0.6524
4
Marker1
Marker4
25
LD
0.33144
1
0.56481
0.9668
5
Marker1
Marker5
25
LD
2.29785
2
0.31698
0.8398
6
Marker2
Marker2
25
HWE
1.70412
1
0.19175
0.2262
7
Marker2
Marker3
25
LD
0.13798
1
0.71030
0.7242
8
Marker2
Marker4
25
LD
1.34100
1
0.24686
0.9015
9
Marker2
Marker5
25
LD
1.13574
2
0.56673
0.5503
10
Marker3
Marker3
25
HWE
0.04340
1
0.83497
1.0000
11
Marker3
Marker4
25
LD
0.46296
1
0.49624
0.9323
12
Marker3
Marker5
25
LD
0.95899
2
0.61909
0.2624
13
Marker4
Marker4
25
HWE
0.00000
1
1.00000
1.0000
14
Marker4
Marker5
25
LD
6.16071
2
0.04594
0.9235
15
Marker5
Marker5
25
HWE
9.35374
3
0.02494
0.0106
Figure 2.4.
Testing for Disequilibrium Using the ALLELE Procedure
Figure 2.4 displays the output data set created using the OUTSTAT= option of the
PROC ALLELE statement. This data set contains the statistics for testing individual
markers for HWE and marker pairs for linkage disequilibrium.

PROC ALLELE Statement
17
Syntax
The following statements are available in PROC ALLELE.
PROC ALLELE < options > ;
BY variables ;
VAR variables ;
Items within angle brackets (< >) are optional, and statements following the PROC
ALLELE statement can appear in any order. The VAR statement is required. The
syntax of each statement is described in the following section in alphabetical order
after the description of the PROC ALLELE statement.
PROC ALLELE Statement
PROC ALLELE < options > ;
You can specify the following options in the PROC ALLELE statement.
ALPHA=number
speciﬁes that a conﬁdence level of 100(1−number)% is to be used in forming boot-
strap conﬁdence intervals for estimates of allele frequencies and disequilibrium coef-
ﬁcients. The value of number must be between 0 and 1, and is set to 0.05 by default.
BOOTSTRAP=number
BOOT=number
indicates that bootstrap conﬁdence intervals should be formed for the estimates of
allele frequencies and one-locus disequilibrium coefﬁcients using number random
samples. One thousand samples are usually recommended to form conﬁdence inter-
vals. If this statement is omitted, no conﬁdence limits are reported.
CORRCOEFF
requests that the “Linkage Disequilibrium Measures” table be displayed and contain
the correlation coefﬁcient r, a linkage disequilibrium measure.
DATA=SAS-data-set
names the input SAS data set to be used by PROC ALLELE. The default is to use the
most recently created data set.
DELTA
requests that the “Linkage Disequilibrium Measures” table be displayed and contain
the population attributable risk δ, a linkage disequilibrium measure. This option is
ignored if HAPLO=NONE.
DPRIME
requests that the “Linkage Disequilibrium Measures” table be displayed and contain
Lewontin’s D , a linkage disequilibrium measure.

18
Chapter 2. The ALLELE Procedure
EXACT=number
indicates that the exact p-values for the disequilibrium tests should be calculated us-
ing number permutations. Large values of number (10,000 or more) are usually rec-
ommended for accuracy, but long execution times may result, particularly with large
data sets. When this option is omitted, no exact tests are performed. If HAPLO=EST,
then only the exact tests for Hardy-Weinberg equilibrium are performed; the exact
tests for linkage disequilibrium cannot be performed since haplotypes are unknown.
HAPLO=NONE | EST | GIVEN
indicates whether haplotypes frequencies should not be used, haplotype frequencies
should be estimated, or observed haplotype frequencies in the data should be used.
This option affects all linkage disequilibrium tests and measures. By default or when
HAPLO=NONE is speciﬁed, the composite linkage disequilibrium (CLD) coefﬁcient
is used in place of the usual linkage disequilibrium (LD) coefﬁcient. In addition, the
composite haplotype frequencies are used to form the linkage disequilibrium mea-
sures indicated by the options CORRCOEFF and DPRIME. When HAPLO=EST,
the maximum likelihood estimates of the haplotype frequencies are used to calcu-
late the LD test statistic as well as the LD measures. The HAPLO=GIVEN option
indicates that the haplotypes have been observed, and thus the observed haplotype
frequencies are used in the LD test statistic and measures.
When HAPLO=GIVEN, haplotypes are denoted in the data with all alleles compris-
ing one of an individual’s two haplotypes in the ﬁrst of the two variables listed for
each marker, and alleles of the other haplotype in the second of the two variables
listed for each marker.
MAXDIST=number
speciﬁes the maximum number of markers apart that a pair of markers can be in order
to perform any linkage disequilibrium calculations. For example, if MAXDIST=1 is
speciﬁed, linkage disequilibrium measures and statistics are calculated only for pairs
of markers that are one apart, such as M1 and M2, M2 and M3, and so on. The
number speciﬁed must be an integer and is set to 50 markers by default. This option
assumes that markers are speciﬁed in the VAR statement in the physical order in
which they appear on a chromosome or across the genome.
NDATA=SAS-data-set
names the input SAS data set containing names, or identiﬁers, for the markers used
in the output. There must be a NAME variable in this data set, which should contain
the same number of rows as there are markers in the input data set speciﬁed in the
DATA= option. When there are fewer rows than there are markers, markers without
a name are named using the PREFIX= option. Likewise, if there is no NDATA= data
set speciﬁed, the PREFIX= option is used.
NOFREQ
suppresses the display of the “Allele Frequencies” and the “Genotype Frequencies”
tables. See the section “Displayed Output” on page 26 for a detailed description of
these tables.

BY Statement
19
NOPRINT
suppresses the normal display of results. Note that this option temporarily disables
the Output Delivery System (ODS).
OUTSTAT=SAS-data-set
names the output SAS data set containing the disequilibrium statistics, for both
within-marker and between-marker disequilibria.
PREFIX=preﬁx
speciﬁes a preﬁx to use in constructing names for marker variables in all output. For
example, if PREFIX=VAR, the names of the variables are VAR1, VAR2, ..., VARn.
Note that this option is ignored when the NDATA= option is speciﬁed, unless there
are fewer names in the NDATA data set than there are markers. If this option is
omitted, PREFIX=M is the default.
PROPDIFF
requests that the “Linkage Disequilibrium Measures” table be displayed and contain
the proportional difference d, a linkage disequilibrium measure. This option is ig-
nored if HAPLO=NONE.
SEED=number
speciﬁes the initial seed for the random number generator used for permuting the
data in the exact tests and for the bootstrap samples. The value for number must be a
positive integer; the computer clock time is the default. For more details about seed
values, refer to SAS Language Reference: Concepts.
YULESQ
requests that the “Linkage Disequilibrium Measures” table be displayed and con-
tain Yule’s Q, a linkage disequilibrium measure.
This option is ignored if
HAPLO=NONE.
BY Statement
BY variables ;
You can specify a BY statement with PROC ALLELE to obtain separate analyses on
observations in groups deﬁned by the BY variables. When a BY statement appears,
the procedure expects the input data set to be sorted in the order of the BY variables.
The variables are one or more variables in the input data set.
If your input data set is not sorted in ascending order, use one of the following alter-
natives:
• Sort the data using the SORT procedure with a similar BY statement.
• Specify the BY statement option NOTSORTED or DESCENDING in the BY
statement for the ALLELE procedure. The NOTSORTED option does not
mean that the data are unsorted but rather that the data are arranged in groups
(according to values of the BY variables) and that these groups are not neces-
sarily in alphabetical or increasing numeric order.
• Create an index on the BY variables using the DATASETS procedure (in Base
SAS software).

20
Chapter 2. The ALLELE Procedure
For more information on the BY statement, refer to the discussion in SAS Language
Reference: Concepts. For more information on the DATASETS procedure, refer to
the discussion in the SAS Procedures Guide.
VAR Statement
VAR variables ;
The VAR statement identiﬁes the variables containing the marker alleles. The VAR
statement should contain 2m variable names, where m is the number of markers in
the data set. Note that alleles for the same marker should be listed consecutively.
Details
Statistical Computations
Frequency Estimates
A marker locus M may have a series of alleles Mu, u = 1, ..., k. A sample of n
individuals may therefore have several different genotypes at the locus, with nuv
copies of type Mu/Mv. The number nu of copies of allele Mu can be found directly
by summation: nu = 2nuu +
n
v=u
uv .
The sample frequencies are written as
˜
pu = nu/(2n) and ˜
Puv = nuv/n. The ˜
Puv’s are unbiased maximum likelihood
estimates (MLEs) of the population proportions Puv.
The variance of the sample allele frequency ˜
pu is calculated as
1
Var(˜
pu) =
(pu + Puu − 2p2
2n
u)
and can be estimated by replacing pu and Puu with their sample values ˜
pu and ˜
Puu.
The variance of the sample genotype frequency ˜
Puv is not generally calculated; in-
stead, an MLE of the HWD coefﬁcient Duv for alleles Mu and Mv is calculated as
˜
ˆ
P
D
uv − ˜
pu ˜
pv, u = v
uv =
˜
p
˜
u ˜
pv − 1 P
2
uv ,
u = v
and the MLE’s variance is estimated using one of the following formulas, depending
on whether the two alleles are the same or different:
1
Var( ˆ
Duu) =
˜
p2
n
u(1 − ˜
pu)2 + (1 − 2˜
pu)2 ˆ
Duu − ˆ
D2uu
1
Var( ˆ
D
ˆ
ˆ
uv )
=
˜
pu ˜
pv(1 − ˜
pu)(1 − ˜
pv) +
(˜
p2 Dvw + ˜
p2Duw)
2n
u
v
w=u,v
− (1 − ˜
pu − ˜
pv)2 − 2(˜
pu − ˜
pv)2 ˆ
Duv + ˜
p2
−
u ˜
p2v
2 ˆ
D2uv
The standard error, the square root of the variance, is reported for the sample allele
frequencies and the disequilibrium coefﬁcient estimates. When the BOOTSTRAP=

Statistical Computations
21
option of the PROC ALLELE statement is speciﬁed, bootstrap conﬁdence intervals
are formed by resampling individuals from the data set and are reported for these
estimates, with the 100(1 − α)% conﬁdence level given by the ALPHA=α option (or
α = 0.05 by default).
Measures of Marker Informativeness
Polymorphism Information Content
The polymorphism information content (PIC) measures the probability of differenti-
ating the allele transmitted by a given parent to its child given the marker genotype
of father, mother, and child (Botstein et al. 1980). It is computed as
k
k−1
k
PIC = 1 −
˜
p2 −
u
2˜
p2u ˜
p2v
u=1
u=1 v=u+1
Heterozygosity
The heterozygosity, sometimes called the observed heterozygosity, is simply the pro-
portion of heterozygous individuals in the data set and is calculated as
k
Het = 1 −
˜
Puu
u=1
Allelic Diversity
The allelic diversity, sometimes called the expected heterozygosity, is the expected
proportion of heterozygous individuals in the data set when HWE holds and is calcu-
lated as
k
Div = 1 −
˜
p2u
u=1
Testing for Hardy-Weinberg Equilibrium
Under ideal population conditions, the two alleles an individual receives, one from
each parent, are independent so that Puu = p2u and Puv = 2pupv, u = v. The factor
of 2 for heterozygotes recognizes the fact that Mu/Mv and Mv/Mu genotypes are
generally indistinguishable. This statement about allelic independence within loci is
called Hardy-Weinberg equilibrium (HWE). Forces such as selection, mutation, and
migration in a population or nonrandom mating can cause departures from HWE. Two
methods are used here for testing a marker for HWE, both of which can accommodate
any number of alleles. Both methods are testing the hypothesis that Puu = p2u and
Puv = 2pupv, u = v for all u, v = 1, ..., k.

22
Chapter 2. The ALLELE Procedure
Chi-Square Goodness-of-Fit Test
The chi-square goodness-of-ﬁt test can be used to test markers for HWE. The chi-
square statistic
(nuu − n˜
p2
(nuv − 2n˜
pu ˜
pv)2
X2
u)2
T =
+
n˜
p2
2n˜
p
u
u
u
u ˜
pv
v=u
has k(k − 1)/2 degrees of freedom where k is the number of alleles at the marker
locus.
Permutation Version of Exact Test
The exact test given by Guo and Thompson (1992) is based on the conditional prob-
ability of genotype counts given allelic counts and the hypothesis of allelic indepen-
dence. The test statistic is
n! 2h
nu!
T =
u
(2n)!
n
u,v
uv !
where h =
n
u
v=u
uv is the number of heterozygous individuals. Signiﬁcance
levels are calculated by the permutation procedure. The 2n alleles are randomly
permuted the number of times indicated in the EXACT= option to form new sets of
n genotypes. The signiﬁcance level is then calculated as the proportion of times the
value of T for each set of permuted data exceeds the value of T for the actual data.
You can indicate the random seed used to randomly permute the data in the SEED=
option of the PROC ALLELE statement.
Linkage Disequilibrium (LD)
The set of genetic material an individual receives from each parent contains an al-
lele at every locus, and statements can be made about these allelic combinations,
or haplotypes. The probability puv (called the gametic or haplotype frequency) that
an individual receives the haplotype MuNv for marker loci M and N can be com-
pared to the product of the probabilities that each allele is received. The difference
is the linkage, or gametic, disequilibrium (LD) coefﬁcient Duv for those two alleles:
Duv = puv − pupv. There is a general expectation that the amount of linkage disequi-
librium is inversely related to the distance between the two loci, but there are many
other factors that may affect disequilibrium. There may even be disequilibrium be-
tween alleles at loci that are located on different chromosomes. Note that these tests
and measures will be calculated only for pairs of markers at most d markers apart,
where d is the integer speciﬁed in the MAXDIST= option of the PROC ALLELE
statement, or 50 by default.
Table 2.1 displays how the HAPLO= option of the PROC ALLELE statement inter-
acts with the linkage disequilibrium calculations. These calculations are discussed in
more detail in the following two sections.

Statistical Computations
23
Table 2.1.
Interaction of HAPLO= option with LD calculations
HAPLO=
LD Test
Estimate of
Option
Statistic
LD Exact Test
Haplotype Freq
GIVEN
˜
D
Permutes alleles to form
uv
Observed freq, ˜
puv
new 2-locus haplotypes
EST
ˆ
Duv
Not performed
Estimated freq, ˆ
puv
NONE
˜
∆
Permutes genotypes to form
uv
Composite freq, ˜
p∗uv
new 2-locus genotypes
Tests
When haplotypes are known, the HAPLO=GIVEN option should be included in the
PROC ALLELE statement so that the linkage disequilibrium can be computed di-
rectly by substituting the observed frequencies ˜
puv, ˜
pu, and ˜
pv into the equation in
the preceding section for Duv. This creates the MLE, ˜
Duv, of the LD coefﬁcient
between a pair of alleles at different markers. PROC ALLELE calculates an over-
all chi-square statistic to test that all of the Duv’s between two markers are zero as
follows:
k
l
(2n) ˜
D2
X2
uv
T =
˜
pu ˜
pv
u=1 v=1
which has (k − 1)(l − 1) degrees of freedom for markers with k and l alleles, respec-
tively.
There is also an exact test available when haplotypes are known. An exact p-value for
testing the hypothesis in the preceding paragraph can be calculated by conditioning
on the allele counts as with the exact test for HWE. The conditional probability of the
haplotype counts is then
nu!
nv!
T =
u
v
(2n)!
n
u,v
uv !
and the signiﬁcance level is obtained again by permuting the alleles at one locus
to form 2n new two-locus haplotypes. You can indicate the number of permutations
that are used in the EXACT= option of the PROC ALLELE statement and the random
seed used to randomly permute the data in the SEED= option of the PROC ALLELE
statement.
When it is requested that haplotype frequencies be estimated with the HAPLO=EST
option, Duv is estimated using ˆ
Duv = ˆ
puv − ˜
pu ˜
pv, where ˆ
puv is the MLE of puv
assuming HWE. The estimate ˆ
puv is calculated according to the method described by
Weir and Cockerham (1979). Again, a chi-square test statistic can be calculated to
test that all of the Duv’s between a pair of markers are zero as
k
l
n ˆ
D2
X2
uv
T =
˜
pu ˜
pv
u=1 v=1

24
Chapter 2. The ALLELE Procedure
which has (k − 1)(l − 1) degrees of freedom for markers with k and l alleles, respec-
tively. No exact test is available when haplotype frequencies are estimated.
The HAPLO=NONE option indicates that haplotypes are unknown and ˆ
Duv should
not be used in the tests for LD between pairs of markers. Instead of using the es-
timated haplotype frequencies which assumes HWE, a test can be formed using the
composite linkage disequilibrium (CLD) coefﬁcient ∆uv that does not require this
assumption and uses only allele and two-locus genotype frequencies. The MLE ˜
∆uv
of ∆uv can be calculated as described by Weir (1979), and a chi-square statistic that
tests all ∆uv’s between a pair of markers are zero can be formed as follows:
k
l
n ˜
∆2
X2
uv
T =
˜
pu ˜
pv
u=1 v=1
which has (k − 1)(l − 1) degrees of freedom for markers with k and l alleles, respec-
tively.
An exact test for CLD is also available, where the conditional probability of the two-
locus genotypes given the one-locus genotypes is
n
n
r,s
rs!
u,v
uv !
T = n!
n
r,s,u,v
rsuv !
where nrsuv is the count of MrMsNuNv genotypes, nrs is the count of Mr/Ms
genotypes, and nuv is the count of Nu/Nv genotypes. The exact signiﬁcance level is
obtained by permuting the genotypes at one of the loci to create a distribution of the
T ’s (Zaykin, Zhivotovsky, and Weir 1995). Note that this procedure is also testing
for nonzero trigenic and quadrigenic disequilibrium terms, so signiﬁcance may not
necessarily imply the presence of CLD.
Measures
PROC ALLELE offers ﬁve linkage disequilibrium measures to be calculated for each
pair of alleles Mu and Nv located at loci M and N respectively: the correlation coefﬁ-
cient r, the population attributable risk δ, Lewontin’s D , the proportional difference
d, and Yule’s Q. The ﬁve measures are discussed in Devlin and Risch (1995). Since
these measures are designed for biallelic markers, the measures are calculated for
each allele at locus M with each allele at locus N, where all other alleles at each loci
are combined to represent one allele. Thus for each allele Mu in turn, ˜
p1 is used as
the frequency of allele Mu, and ˜
p2 represents the frequency of “not Mu”; similarly
for each Nv in turn, ˜
q1 represents the frequency of allele Nv, and ˜
q2 the frequency
of “not Nv.” All measures have the same numerator, D = p11p22 − p12p21, the LD
coefﬁcient, which can be directly estimated using the observed haplotype frequencies
˜
puv when HAPLO=GIVEN, or estimated using the MLEs of the haplotype frequen-
cies ˆ
puv assuming HWE when HAPLO=EST. The computations for the measures are
as follows:
D
r
=
(p1p2q1q2)1/2

OUTSTAT= Data Set
25
D
δ
=
q1p22
D
min(p
D
=
, D
1q2, q1p2),
D > 0
max =
Dmax
min(p1q1, q2p2), D < 0
D
d
=
q1q2
D
Q
=
p11p22 + p12p21
with estimates of measures calculated by replacing parameters with their appropri-
ate estimates. Under the default option HAPLO=NONE, the numerator D can be
replaced by the CLD coefﬁcient ∆, described in the preceding section, for measures
r and D . This statistic has bounds twice as large as D so the denominator for D
must be multiplied by a factor of 2. However, δ, d, and Q cannot be calculated when
HAPLO=NONE.
Missing Values
An individual’s genotype for a marker is considered missing if at least one of the
alleles at the marker is missing. Any missing genotypes are excluded from all cal-
culations, including the linkage disequilibrium statistics for all pairs that include the
marker. However, the individual’s nonmissing genotypes at other markers can be
used as part of the calculations.
If the BOOTSTRAP= option is speciﬁed, any individuals with missing genotypes for
all markers are excluded from resampling. All other individuals are included, which
could result in different numbers of individuals with nonmissing genotypes for the
same marker across different samples.
OUTSTAT= Data Set
The OUTSTAT= data set contains the following variables:
• the BY variables, if any
• Locus1 and Locus2, which contain the pair of markers for which the disequi-
librium statistics are calculated
• NIndiv, which contains the number of individuals that have been genotyped at
both the markers listed in Locus1 and Locus2 (that is, the number of individ-
uals that have no missing alleles for the two loci)
• Test, which indicates which disequilibrium test is performed, HWE for indi-
vidual markers (when Locus1 and Locus2 contain the same value) or LD for
marker pairs
• ChiSq, which contains the chi-square statistic for testing for disequilibrium. If
Locus1 and Locus2 contain the same marker, the test is for HWE within that
locus. Otherwise, it is a test for linkage disequilibrium between the two loci.
• DF, which contains the degrees of freedom for the chi-square test

26
Chapter 2. The ALLELE Procedure
• ProbChi, which contains the p-value for the chi-square test
• ProbEx, which contains the exact p-value for testing the pair of markers in
Locus1 and Locus2 for disequilibrium. This variable is included in the
OUTSTAT= data set only when the EXACT= parameter in the PROC ALLELE
statement is a positive integer and HAPLO=NONE or HAPLO=GIVEN.
Displayed Output
This section describes the displayed output from PROC ALLELE. See the section
“ODS Table Names” on page 27 for details about how this output interfaces with the
Output Delivery System.
Marker Summary
The “Marker Summary” table lists information on each of the markers, including
• NIndiv, the number of individuals genotyped at the marker
• NAllele, the number of alleles at the marker
• PIC, the polymorphism information content (PIC) measure
• Het, the heterozygosity measure
• Div, the allelic diversity measure
as well as the following columns for the test for HWE:
• ChiSq, the chi-square statistic
• DF, the degrees of freedom for the chi-square test
• ProbChiSq, the p-value for the chi-square test
• ProbExact, the exact p-value for the HWE test (only if the EXACT= option is
speciﬁed in the PROC ALLELE statement)
Allele Frequencies
The “Allele Frequencies” table lists all the observed alleles for each marker, with
an estimate of the allele frequency, the standard error of the frequency, and when
the BOOTSTRAP= option is speciﬁed, the bootstrap lower and upper limits of the
conﬁdence interval for the frequency based on the conﬁdence level determined by
the ALPHA= option of the PROC ALLELE statement (0.95 by default).
Genotype Frequencies
The “Genotype Frequencies” table lists all the observed genotypes (denoted by the
two alleles separated by a “/”) for each marker, with the observed genotype frequency,
an estimate of the disequilibrium coefﬁcient D, the standard error of the estimate,
and when the BOOTSTRAP= option is speciﬁed, the lower and upper limits of the
bootstrap conﬁdence interval for D based on the conﬁdence level determined by the
ALPHA= option of the PROC ALLELE statement (0.95 by default).

Example 2.1. Using the NDATA= Option with Microsatellites
27
Linkage Disequilibrium Measures
The “Linkage Disequilibrium Measures” table lists the frequency of each haplotype
at each marker pair (observed frequency when HAPLO=GIVEN and estimated fre-
quency otherwise), an estimate of the LD coefﬁcient Duv, and whichever linkage dis-
equilibrium measures are included in the PROC ALLELE statement (CORRCOEFF,
DELTA, DPRIME, PROPDIFF, and YULESQ). Haplotypes are represented by the
allele at the marker locus listed in Locus1 and the allele at the marker locus listed
in Locus2 separated by a “-.” Note that this table can be quite large when there are
many markers or markers with many alleles. For a data set with m markers, each hav-
ing k
m
i alleles, i = 1, ..., m, the number of rows in the table is
m−1
k
i=1
j=i+1
ikj .
The MAXDIST= option of the PROC ALLELE statement can be used to keep this
table to a manageable size.
ODS Table Names
PROC ALLELE assigns a name to each table it creates, and you must use this name
to reference the table when using the Output Delivery System (ODS). These names
are listed in the following table.
Table 2.2.
ODS Tables Created by the ALLELE Procedure
ODS Table Name
Description
PROC ALLELE option
MarkerSumm
Marker summary
default
AlleleFreq
Allele frequencies
default
GenotypeFreq
Genotype frequencies
default
LDMeasures
Linkage disequilibrium measures
CORRCOEFF, DELTA, DPRIME,
PROPDIFF, or YULESQ
Examples
Example 2.1. Using the NDATA= Option with Microsatellites
The following is a subset of data from GAW12 (Wijsman et al. 2001) and contains
17 individuals’ genotypes at 14 microsatellite markers.
data gaw;
input id m1-m28;
datalines;
1 11 14
6
8
2
5
9
4
6
1
9
9
9
7
3
5 10
1
4
6
5
9
1
1
3
5
6
2
2
2 12
1
4
6
6
3
3
2
1 11 11
4 11
2
2 13 11
2
1
9
9
1
5
6
1
2
5
3
2 10
4
8
4
9
2
7
7
1
9
2
7 10
2
2
7
7
6
8
9
4
5
1
7
2
6
2
4
5 14
7
3
9 13
4
2
2
4 11
5
4
7
4
5
7
6
8
2
9
9
1
6
4
1
8
9
5 12 12
3
8
6
2
1
7
3
5
6 11
6
9
5
2 13 16
7
1
9
4
1
1
7
1
1
2
6
4
7
7
8
7 12
4
2
6
5
5 11
5 11
2
4 15 11
1
1
9
2
6
5
7
6
1
5
7
2 10
6
8
7
1
2
3
6
2
5
8
5
6
5
6 13 10
1
8
9
3
1
6
7
7
2
6
8
2 11
6
2
7
1
2
3
6
6 10 11 11
6
4
2 11 11
4
5 11
2
3
2
1
4
1
2
9
2
7
1
1
3
1
5
7
2
5
5 11 11 11
2
6 11
2
1
6
4
9
5
5
4
2
5
9

28
Chapter 2. The ALLELE Procedure
10 11 12
2
4 13
3
1
2
4
9
5 10
7
5
4
4
1
6
8
1
6 10
1
1
2
5
1
1
11 11
2
7
8
1
5
4
6
4
7
5 11 11
6
5
4 16 13
7
4
5
6
6
1
1
4
1
1
12
2 12
6
8
2
7
3
2
7
5
2
8
9
6
2
4
7 16
7
1 10
9
5
1
1
4
9
1
13 13 14
8
3 12 13
7
4
3
2
6 10
9
5
4
4
2 14
8
8
3
6
5
1
1
6
6
2
14
7 10
6
5 10 13
8
3
5
5
9
9 11
6
5
4 13 14
1
1
6
9
2
1
5
3
1
2
15 10 11
4
3
9
7
6
3
4
6 10
1
7
9
2
2
2 14
6
1
9
2
1
1
6
7
5
2
16
2
5
2
7
7
2
2
9
2
2
2
6
9
5
2
2
7
1
1
2
6
2
1
1
1
1
9
6
17 11
4
4
4
9
1
7
8
5
3
5
1 11
5
6
5
2 12
1
5
9
9
1
5
7
7
6
1
;
Note that you can input the same data directly using the statement:
infile ’Genmrk22.1’ delimiter="/ ";
in place of the DATALINES statement.
The actual names of the markers can be used, by creating a data set with the variable
NAME containing these names.
data map;
input name $ location;
datalines;
D22G001
0.50
D22G002
0.79
D22G003
0.88
D22G004
1.02
D22G005
1.24
D22G006
2.20
D22G007
4.27
D22G008
5.85
D22G009
6.70
D22G010
9.36
D22G011
10.87
D22G012
11.67
D22G013
12.66
D22G014
15.89
;
Now an analysis using PROC ALLELE can be performed as follows:
proc allele data=gaw ndata=map nofreq exact=10000 seed=456;
var m1-m28;
run;
This analysis produces summary statistics of the 14 markers and is using 10,000
permutations to get an exact p-value for the HWE test. The allele and genotype
frequency output tables are suppressed with the NOFREQ option.
The results from the analysis are as follows. Note the names of the markers that are
used.

Example 2.2. Computing Linkage Disequilibrium Measures for SNP Data
29
Output 2.1.1.
Summary of Microsatellites for the ALLELE Procedure
The ALLELE Procedure
Marker Summary
Number
Number
of
of
Hetero-
Allelic
Locus
Indiv
Alleles
PIC
zygosity
Diversity
D22G001
17
9
0.8384
0.9412
0.8547
D22G002
17
8
0.8296
0.8824
0.8478
D22G003
17
11
0.8749
0.9412
0.8858
D22G004
17
9
0.8259
0.9412
0.8443
D22G005
17
8
0.8272
0.8235
0.8460
D22G006
17
8
0.8257
0.8235
0.8443
D22G007
17
7
0.8012
0.9412
0.8253
D22G008
17
5
0.6665
0.6471
0.7163
D22G009
17
11
0.8788
0.8824
0.8893
D22G010
17
7
0.7572
0.8235
0.7820
D22G011
17
8
0.7274
0.8235
0.7509
D22G012
17
5
0.5661
0.6471
0.6142
D22G013
17
7
0.7965
0.8235
0.8201
D22G014
17
6
0.7507
0.8824
0.7837
Marker Summary
--------------Test for HWE--------------
Chi-
Pr >
Prob
Locus
Square
DF
ChiSq
Exact
D22G001
32.5172
36
0.6350
0.8581
D22G002
28.5222
28
0.4370
0.3868
D22G003
48.2139
55
0.7295
0.7050
D22G004
24.9692
36
0.9166
0.8361
D22G005
20.9416
28
0.8278
0.9413
D22G006
32.0018
28
0.2744
0.1102
D22G007
19.7625
21
0.5363
0.5745
D22G008
11.4619
10
0.3227
0.2525
D22G009
52.1333
55
0.5849
0.3866
D22G010
14.7227
21
0.8366
0.8624
D22G011
19.0400
28
0.8969
0.8898
D22G012
17.3473
10
0.0670
0.5122
D22G013
38.8062
21
0.0104
0.0390
D22G014
17.2802
15
0.3024
0.4651
Example 2.2. Computing Linkage Disequilibrium Measures
for SNP Data
The following data set contains 44 individuals’ genotypes at ﬁve SNPs.
data snps;
input s1-s10;
datalines;
2 2 2 1 2 1 1 1 2 2
2 2 2 2 2 1 1 1 2 2
2 2 2 2 2 1 2 1 2 2
2 2 2 2 . . 1 1 2 2
2 2 2 2 1 2 1 2 2 2
2 2 2 2 . . 2 1 2 2

30
Chapter 2. The ALLELE Procedure
2 2 2 2 2 1 2 1 2 2
2 2 2 2 . . 2 1 2 2
2 2 2 2 1 1 1 1 2 2
2 2 1 1 2 2 2 1 2 2
2 2 2 1 2 2 2 1 2 2
2 2 2 2 1 1 1 1 2 2
2 2 2 1 2 2 2 2 2 2
2 2 2 2 2 2 1 1 2 2
2 2 2 2 2 1 2 1 2 2
2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 1 2 2
2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 1 1 1 2 2
2 2 2 2 1 1 2 1 2 2
2 2 2 2 2 1 1 1 2 2
2 2 2 2 2 1 2 2 2 2
2 2 2 2 2 1 2 1 2 2
2 2 2 2 2 1 2 1 2 2
2 2 2 2 2 1 2 2 2 2
2 2 2 2 2 1 2 2 2 2
2 2 2 2 2 2 1 1 2 2
2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 1 1 2 2
2 2 2 2 2 2 1 1 2 2
2 2 2 2 2 1 2 1 2 2
2 2 2 2 2 1 2 1 2 2
2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 1 2 2
2 2 2 2 2 1 2 1 2 2
2 2 2 2 2 2 . . 2 2
2 2 2 1 2 2 2 1 2 2
2 2 2 2 2 2 2 1 2 2
2 2 2 2 2 1 1 1 2 2
2 2 2 2 2 2 1 1 2 2
2 2 2 2 2 1 2 1 2 2
2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 1 2 2
2 2 2 2 2 2 2 1 2 2
;
Now an analysis using PROC ALLELE can be performed as follows:
proc allele data=snps prefix=SNP nofreq haplo=est corrcoeff dprime yulesq;
var s1-s10;
run;
This analysis produces summary statistics of the ﬁve SNPs as well as the Linkage
Disequilibrium Measures table, which contains estimated two-locus haplotype fre-
quencies and disequilibrium coefﬁcients, and the linkage disequilibrium measures r,
D , and Q. The allele and genotype frequency output tables are suppressed with the
NOFREQ option.

Example 2.2. Computing Linkage Disequilibrium Measures for SNP Data
31
The results from the analysis are as follows. Note the names of the markers that are
used.
Output 2.2.1.
Summary of SNPs for the ALLELE Procedure
The ALLELE Procedure
Marker Summary
-------Test for HWE-------
Number
Number
of
of
Hetero-
Allelic
Chi-
Pr >
Locus
Indiv
Alleles
PIC
zygosity
Diversity
Square
DF
ChiSq
SNP1
44
1
0.0000
0.0000
0.0000
0.0000
0
.
SNP2
44
2
0.1190
0.0909
0.1271
3.5627
1
0.0591
SNP3
41
2
0.3283
0.4390
0.4140
0.1493
1
0.6992
SNP4
43
2
0.3728
0.4884
0.4957
0.0093
1
0.9231
SNP5
44
1
0.0000
0.0000
0.0000
0.0000
0
.
There are two SNPs that have only one allele appearing in the data.
Output 2.2.2.
Linkage Disequilibrium Measures for SNPs Using the ALLELE
Procedure
Linkage Disequilibrium Measures
LD
Corr
Lewontin’s
Yule’s
Locus1
Locus2
Haplotype
Frequency
Coeff
Coeff
D’
Q
SNP1
SNP2
2-1
0.0682
-0.000
.
.
.
SNP1
SNP2
2-2
0.9318
-0.000
.
.
.
SNP1
SNP3
2-1
0.2927
-0.000
.
.
.
SNP1
SNP3
2-2
0.7073
-0.000
.
.
.
SNP1
SNP4
2-1
0.5465
-0.000
.
.
.
SNP1
SNP4
2-2
0.4535
-0.000
.
.
.
SNP1
SNP5
2-2
1.0000
0.000
.
.
.
SNP2
SNP3
1-1
0.0000
-0.021
-0.181
-1.000
-1.000
SNP2
SNP3
1-2
0.0732
0.021
0.181
1.000
1.000
SNP2
SNP3
2-1
0.2927
0.021
0.181
1.000
1.000
SNP2
SNP3
2-2
0.6341
-0.021
-0.181
-1.000
-1.000
SNP2
SNP4
1-1
0.0331
-0.005
-0.040
-0.132
-0.155
SNP2
SNP4
1-2
0.0367
0.005
0.040
0.132
0.155
SNP2
SNP4
2-1
0.5134
0.005
0.040
0.132
0.155
SNP2
SNP4
2-2
0.4168
-0.005
-0.040
-0.132
-0.155
SNP2
SNP5
1-2
0.0682
-0.000
.
.
.
SNP2
SNP5
2-2
0.9318
-0.000
.
.
.
SNP3
SNP4
1-1
0.2221
0.061
0.266
0.438
0.553
SNP3
SNP4
1-2
0.0779
-0.061
-0.266
-0.438
-0.553
SNP3
SNP4
2-1
0.3154
-0.061
-0.266
-0.438
-0.553
SNP3
SNP4
2-2
0.3846
0.061
0.266
0.438
0.553
SNP3
SNP5
1-2
0.2927
-0.000
.
.
.
SNP3
SNP5
2-2
0.7073
-0.000
.
.
.
SNP4
SNP5
1-2
0.5465
-0.000
.
.
.
SNP4
SNP5
2-2
0.4535
-0.000
.
.
.
In the preceding table, the values for the linkage disequilibrium measures are missing
for several haplotypes; this occurs when there is only one allele at one of the markers
contained in the haplotype, and thus the denominators for these measures are zero.

32
Chapter 2. The ALLELE Procedure
Also note that when the markers are biallelic, the gametic disequilibria have the same
absolute values for all four possible haplotypes.
References
Botstein, D., White, R.L., Skolnick, M., and Davis, R.W. (1980), “Construction
of a Genetic Linkage Map in Man Using Restriction Fragment Length
Polymorphisms,” American Journal of Human Genetics, 32, 314–331.
Devlin, B. and Risch, N. (1995), “A Comparison of Linkage Disequilibrium
Measures for Fine-Scale Mapping,” Genomics, 29, 311–322.
Guo, S.W. and Thompson, E.A. (1992), “Performing the Exact Test of Hardy-
Weinberg Proportion for Multiple Alleles,” Biometrics, 48, 361–372.
Weir, B.S. (1979), “Inferences about Linkage Disequilibrium,” Biometrics, 35,
235–254.
Weir, B.S. (1996), Genetic Data Analysis II, Sunderland, MA: Sinauer Associates,
Inc.
Weir, B.S. and Cockerham, C.C. (1979), “Estimation of Linkage Disequilibrium in
Randomly Mating Populations,” Heredity, 42, 105–111.
Wijsman, E.M., Almasy, L., Amos, C.I., Borecki, I., Falk, C.T., King, T.M.,
Martinez, M.M., Meyers, D., Neuman, R., Olson, J.M., Rich, S., Spence, M.A.,
Thomas, D.C., Vieland, V.J., Witte, J.S., and MacCluer, J.W. (2001), “Analysis of
Complex Genetic Traits: Applications to Asthma and Simulated Data,” Genetic
Epidemiology, 21, S1–S853.
Zaykin, D., Zhivotovsky, L., and Weir, B.S. (1995), “Exact Tests for Association
between Alleles at Arbitrary Numbers of Loci,” Genetica, 96, 169–178.

Chapter 3
The CASECONTROL Procedure
Chapter Contents
OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
GETTING STARTED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
SYNTAX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
PROC CASECONTROL Statement . . . . . . . . . . . . . . . . . . . . . . 37
BY Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
TRAIT Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
VAR Statement
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
DETAILS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Statistical Computations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Missing Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
OUTSTAT= Data Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
EXAMPLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Example 3.1. Performing Case-Control Tests on Multiallelic Markers . . . . 41
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

34
Chapter 3. The CASECONTROL Procedure

Chapter 3
The CASECONTROL Procedure
Overview
Marker information can be used to help locate the genes that affect susceptibility to a
disease. The CASECONTROL procedure is designed for the interpretation of marker
data when random samples are available from the populations of unrelated individ-
uals who are either affected or unaffected by the disease. Several tests are available
in PROC CASECONTROL that compare marker allele and/or genotype frequencies
in the two populations, with frequency differences indicating an association of the
marker with the disease. Although such an association may point to the proximity of
the marker and disease genes in the genome, it may also reﬂect population structure,
so care is needed in interpreting the results; association does not necessarily imply
linkage.
The three chi-square tests available for testing case-control genotypic data are the
genotype case-control test, which tests for dominant allele effects on the disease pen-
etrance, and the allele case-control test and linear trend test, which test for additive
allele effects on the disease penetrance. Since the allele case-control test requires
the assumption of Hardy-Weinberg equilibrium (HWE), it may be desirable to run
the ALLELE procedure on the data to perform the HWE test on each marker (see
Chapter 2, “The ALLELE Procedure,” for more information) prior to applying PROC
CASECONTROL.
Getting Started
Example
Here are some sample SNP data on which the three case-control tests can be per-
formed using PROC CASECONTROL:
data cc;
input affected $ m1-m16;
datalines;
N
1 1 2 2 2 2 2 1 2 1 2 2 1 1 2 2
N
1 1 1 1 2 2 1 1 2 1 2 1 1 1 1 1
N
2 1 1 1 2 1 1 1 2 2 1 1 1 1 1 1
N
2 2 2 1 2 2 1 1 2 2 2 1 1 1 2 2
N
1 1 1 1 2 2 2 1 1 1 1 1 2 1 . .
N
2 1 1 1 2 1 1 1 2 1 2 1 1 1 2 1
N
1 1 1 1 2 2 1 1 2 2 2 2 2 1 2 2
N
2 2 1 1 2 1 2 1 2 2 2 1 1 1 2 1
N
2 1 1 1 2 2 2 1 2 1 . . 1 1 2 1
N
2 1 1 1 2 1 1 1 2 2 1 1 1 1 1 1
N
2 1 2 2 . . 1 1 2 1 1 1 1 1 1 1

36
Chapter 3. The CASECONTROL Procedure
N
2 2 . . 2 1 1 1 2 1 2 1 1 1 2 1
N
2 1 . . 2 2 1 1 2 2 1 1 1 1 2 1
N
2 1 . . 2 2 1 1 2 1 . . 2 1 1 1
N
2 2 . . 2 2 1 1 . . 2 1 1 1 2 1
N
1 1 . . 2 2 1 1 1 1 2 1 1 1 2 1
N
1 1 . . 2 2 1 1 1 1 . . 1 1 2 1
N
2 1 . . 2 2 1 1 1 1 . . 2 1 2 1
A
2 1 2 1 2 1 1 1 1 1 2 1 . . 2 1
A
2 1 2 1 2 2 1 1 2 1 1 1 . . 1 1
A
2 2 2 1 2 2 1 1 2 2 . . . . 2 1
A
2 1 2 2 2 1 1 1 2 1 2 1 . . 2 2
A
. . 2 2 2 1 . . 1 1 2 2 . . 2 1
A
1 1 1 1 2 1 1 1 2 1 1 1 . . 2 2
A
2 1 1 1 2 2 1 1 1 1 2 1 . . 2 1
A
2 1 2 2 2 2 1 1 2 2 . . . . 2 2
A
2 1 1 1 2 2 1 1 2 1 2 1 . . 1 1
A
2 1 2 2 2 1 1 1 2 1 2 1 . . 2 2
A
1 1 1 1 2 2 1 1 2 1 2 1 . . 2 2
A
2 1 2 1 2 1 1 1 2 1 2 2 . . 2 1
A
2 2 2 2 1 1 1 1 2 1 2 1 . . 2 2
A
1 1 1 1 2 1 . . 2 1 2 2 . . 2 2
A
1 1 2 1 2 1 1 1 2 1 2 1 . . 2 2
A
2 2 1 1 2 2 1 1 2 1 1 1 . . 2 1
;
The following SAS code can be used to perform the analysis:
proc casecontrol data=cc prefix=Marker;
var m1-m16;
trait affected;
run;
proc print;
run;
All three case-control tests are performed by default. The output data set created by
default appears as follows:
Chi
ChiSq
ChiSq
Sq
df
df
df
Prob
Prob
Prob
Obs
Locus
Genotype Allele Trend Genotype Allele Trend Genotype Allele Trend
1
Marker1
0.272
0.033
0.032
2
1
1
0.873
0.857
0.858
2
Marker2
3.430
3.260
2.140
2
1
1
0.180
0.071
0.144
3
Marker3
2.981
2.569
2.925
2
1
1
0.225
0.109
0.087
4
Marker4
3.556
3.319
3.556
2
1
1
0.169
0.069
0.059
5
Marker5
3.004
0.535
0.590
2
1
1
0.223
0.464
0.443
6
Marker6
0.767
0.650
0.710
2
1
1
0.682
0.420
0.399
7
Marker7
0.000
0.000
0.000
0
0
0
.
.
.
8
Marker8
4.132
4.061
3.769
2
1
1
0.127
0.044
0.052
Figure 3.1.
Statistics for Case-Control Tests

PROC CASECONTROL Statement
37
Figure 3.1 displays the statistics for the three tests. The genotype case-control statistic
has more degrees of freedom than the other two because it is testing for both domi-
nance genotypic effects and additive effects, while the other statistics are testing for
the signiﬁcant additive effects alone. The p-values for Marker7 are missing because
the genotypes of all the affected individuals are missing at that marker.
Syntax
The following statements are available in PROC CASECONTROL.
PROC CASECONTROL < options > ;
BY variables ;
TRAIT variable ;
VAR variables ;
Items within angle brackets (< >) are optional, and statements following the PROC
CASECONTROL statement can appear in any order. The TRAIT and VAR state-
ments are required. The syntax of each statement is described in the following section
in alphabetical order after the description of the PROC CASECONTROL statement.
PROC CASECONTROL Statement
PROC CASECONTROL < options > ;
You can specify the following options in the PROC CASECONTROL statement.
ALLELE
requests that the allele case-control test be performed. If none of the three test options
(ALLELE, GENOTYPE, or TREND) are speciﬁed, then all three tests are performed
by default.
DATA=SAS-data-set
names the input SAS data set to be used by PROC CASECONTROL. The default is
to use the most recently created data set.
GENOTYPE
requests that the genotype case-control test be performed. If none of the three test
options (ALLELE, GENOTYPE, or TREND) are speciﬁed, then all three tests are
performed by default.
NDATA=SAS-data-set
names the input SAS data set containing names, or identiﬁers, for the markers used
in the output. There must be a NAME variable in this data set, which should contain
the same number of rows as there are markers in the input data set speciﬁed in the
DATA= option. When there are fewer rows than there are markers, markers without
a name are named using the PREFIX= option. Likewise, if there is no NDATA= data
set speciﬁed, the PREFIX= option is used.

38
Chapter 3. The CASECONTROL Procedure
OUTSTAT=SAS-data-set
names the output SAS data set containing the chi-square statistics, degrees of free-
dom, and p-values for the tests performed. When this option is omitted, an output
data set is created by default and named according to the DATAn convention.
PREFIX=preﬁx
speciﬁes a preﬁx to use in constructing names for marker variables in all output. For
example, if PREFIX=VAR, the names of the variables are VAR1, VAR2, ..., VARn.
Note that this option is ignored when the NDATA= option is speciﬁed, unless there
are fewer names in the NDATA data set than there are markers. If this option is
omitted, PREFIX=M is the default.
TREND
requests that the linear trend test be performed. If none of the three test options
(ALLELE, GENOTYPE, or TREND) are speciﬁed, then all three tests are performed
by default.
VIF
speciﬁes that the variance inﬂation factor λ should be applied to the trend chi-square
statistic for genomic control. This adjustment is applied only when the trend test is
performed and all markers in the VAR statement are biallelic.
BY Statement
BY variables ;
You can specify a BY statement with PROC CASECONTROL to obtain separate
analyses on observations in groups deﬁned by the BY variables. When a BY state-
ment appears, the procedure expects the input data set to be sorted in order of the BY
variables. The variables are one or more variables in the input data set.
If your input data set is not sorted in ascending order, use one of the following alter-
natives:
• Sort the data using the SORT procedure with a similar BY statement.
• Specify the BY statement option NOTSORTED or DESCENDING in the BY
statement for the CASECONTROL procedure. The NOTSORTED option does
not mean that the data are unsorted but rather that the data are arranged in
groups (according to values of the BY variables) and that these groups are not
necessarily in alphabetical or increasing numeric order.
• Create an index on the BY variables using the DATASETS procedure (in Base
SAS software).
For more information on the BY statement, refer to the discussion in SAS Language
Reference: Concepts. For more information on the DATASETS procedure, refer to
the discussion in the SAS Procedures Guide.

Statistical Computations
39
TRAIT Statement
TRAIT variable ;
The TRAIT statement identiﬁes a binary variable indicating which individuals are
cases and which are controls or a binary variable representing a dichotomous trait.
This variable can be character or numeric, but must have only two nonmissing levels.
VAR Statement
VAR variables ;
The VAR statement identiﬁes the variables containing the marker alleles. The VAR
statement should contain 2m variable names, where m is the number of markers in
the data set. Note that alleles for the same marker should be listed consecutively.
Details
Statistical Computations
Biallelic Markers
PROC CASECONTROL offers three statistics to test for an association between a
biallelic marker and a binary variable, typically affection status of a particular dis-
ease. Table 3.1 displays the quantities that are used for the three case-control tests for
biallelic markers (Sasieni 1997).
Table 3.1.
Genotype Distribution for Case-Control Sample
Number of M1 alleles
0
1
2
Total
Case
r0
r1
r2
R
Control
s0
s1
s2
S
Total
n0
n1
n2
N
The three statistical methods for testing a marker for association with a disease locus
are Armitage’s trend test (1955), the allele case-control test, and the genotype case-
control test. The trend test and allele case-control test are most useful when there is
an additive allele effect on the disease susceptibility. When Hardy-Weinberg equi-
librium (HWE) holds in the combined sample of cases and controls, these statistics
are approximately equal and have an asymptotic χ21 distribution. However, if the as-
sumption of HWE in the combined sample is violated, then the variance for the allele
case-control statistic is incorrect; only the trend test remains valid under this viola-
tion. The statistics for the trend and allele case-control test, respectively, are given by
Sasieni (1997) as
N [N (r1 + 2r2) − R(n1 + 2n2)]2
X2
T
=
R(N − R)[N (n1 + 2n2) − (n1 + 2n2)2]
2N [2N (r1 + 2r2) − 2R(n1 + 2n2)]2
X2
A
=
(2R)2(N − R)[2N (n1 + 2n2) − (n1 + 2n2)2]

40
Chapter 3. The CASECONTROL Procedure
Devlin and Roeder (1999) describe a genomic control method that adjusts the
trend test statistic for correlation between alleles from members of the same sub-
population. Assuming the variance inﬂation factor λ is constant across the genome,
it can be estimated by ˆ
λ = [median(X1, ..., Xm)/0.675]2, where Xi = XT for the
ith marker, i = 1, ..., m. The adjusted trend statistic, X2 = X2 /ˆ
λ, is approximately
Ta
T
distributed as χ21. This variance correction is made when the VIF option is speciﬁed
in the PROC statement and all markers are biallelic.
If dominance effects of alleles are also suspected to contribute to disease susceptibil-
ity, the genotype case-control test can be used. The standard 2×3 contingency table
analysis is used to form the χ22 statistic for the genotype case-control test as
2
(N ri − Rni)2
(N si − Sni)2
X2
G =
+
N Rni
N Sni
i=0
which tests for both additive and dominance (non-additive) allelic effects (Nielsen
and Weir 1999). Note that this test can be broken into two 1 df chi-square tests: the
trend test mentioned above, and a test for dominance effects alone. This test can be
performed by taking the difference X2 − X2 = X2 to form a new test statistic
G
T
D
asymptotically distributed as χ21.
Multiallelic Markers
When there are multiple alleles of interest at a marker, the same three tests can be per-
formed, except that Devlin and Roeder’s genomic control adjustment is not applied
when there are any markers with more than two alleles. To construct the test statistic
for the multiallelic trend test for a marker with k alleles (Slager and Schaid 2001),
the p × (k − 1) matrix X is created such that each element Xiu represents the number
of times the Mu allele appears in the ith genotype, i = 1, ..., p and u = 1, ..., k − 1,
where p = k(k + 1)/2, the number of possible genotypes. Vectors r and s of length
p contain the genotype counts for the cases and controls respectively, and φ = R/N ,
the proportion of cases in the sample. The multiallelic trend test statistic can then be
expressed as U [Var(U)]−1U, where the vector U = X [(1 − φ)r − φs]. Var(U) is
calculated under the assumption of independent (or unrelated) subjects in the sample
using Var(r) and Var(s). These matrices contain elements σii = Rni(N − ni)/N 2
and σij = −Rninj/N 2, where i, j = 1, ..., p (the R is replaced by S for Var(s)).
This statistic has an asymptotic χ2
distribution.
k−1
Another way to test for additive allele effects at the disease or trait locus is the allele
case-control test, executed using a contingency table analysis similar to the genotype
case-control test described in the preceding section, assuming HWE (Nielsen and
Weir 1999). For a marker with k alleles, a 2×k contingency table is formed with one
row for cases, one for controls, and a column for each allele. The χ2
statistic is
k−1
formed by summing (O − E)2/E over all cells in the table, where O is the observed
count for the cell and E is the expected count, the cell’s column total multiplied by
R/N (or S/N ) for a cell in the case (or control) row.
The genotypic case-control test statistic is calculated in a similar manner, with
columns now representing the p = k(k + 1)/2 genotype classes instead of alle-

Example 3.1. Performing Case-Control Tests on Multiallelic Markers
41
les. Signiﬁcance of this test statistic using the χ2p−1 distribution indicates dominance
and/or additive allelic effects on the disease or trait (Nielsen and Weir 1999).
Missing Values
An individual’s genotype for a marker is considered missing if at least one of the
alleles at the marker is missing. Any missing genotypes are excluded from all calcu-
lations. However, the individual’s nonmissing genotypes at other loci can be used as
part of the calculations. If an individual has a missing trait value, then that individual
is excluded from all calculations.
OUTSTAT= Data Set
The output data set speciﬁed in the OUTSTAT= option of the PROC
CASECONTROL statement contains the following variables:
• the BY variables, if any
• Locus
• the
chi-square
statistic
for
each
test
performed:
ChiSqAllele,
ChiSqGenotype, and ChiSqTrend
• the degrees of freedom for each test performed: dfAllele, dfGenotype, and
dfTrend
• the p-value for each test performed:
ProbAllele, ProbGenotype, and
ProbTrend
Example
Example 3.1. Performing Case-Control Tests on Multiallelic
Markers
The following data are taken from GAW9 (Hodge 1995). A sample of 60 founders
was taken from 200 nuclear families, 30 affected with a disease and 30 unaffected.
Each founder was genotyped at two marker loci.
data founders;
input id disease a1-a4 @@;
datalines;
4
1 6 4 3 7
17
2 4 7 2 7
39
2 6 8 7 7
41
2 4 4 4 7
46
1 8 4 1 5
50
2 4 2 3 7
54
2 4 8 7 6
56
2 7 4 7 7
62
2 4 1 7 3
69
2 6 8 2 7
79
1 6 6 8 7
80
2 6 4 7 3
83
2 8 4 2 7
85
1 5 6 6 2
95
1 3 2 3 7
101 1 4 6 7 7
106 1 2 1 7 2
107 1 1 2 7 7
115 2 4 2 7 5
116 1 4 1 7 3

42
Chapter 3. The CASECONTROL Procedure
120 2 1 6 2 7
123 2 4 4 7 2
130 1 5 2 3 7
133 1 8 6 3 6
134 1 8 4 2 2
139 2 6 4 7 6
142 2 3 6 7 7
151 1 4 6 4 3
152 1 6 7 6 7
153 1 5 1 7 6
154 1 4 6 6 6
168 1 1 4 3 7
178 2 4 1 7 1
187 1 1 8 1 2
189 2 6 4 5 7
190 2 4 4 3 7
195 2 4 4 7 2
207 2 1 6 7 7
216 1 7 4 1 5
222 2 4 2 7 3
225 2 8 7 7 6
234 1 6 4 2 2
244 1 4 4 7 6
249 2 6 8 7 2
263 1 8 2 3 7
267 2 2 2 2 7
276 2 1 6 7 1
284 2 4 8 2 2
286 1 8 8 2 1
289 1 2 6 6 3
290 1 2 4 5 7
294 2 1 8 6 7
297 2 5 4 7 6
313 1 1 7 7 2
337 1 2 6 7 6
366 2 2 2 7 7
368 2 3 1 7 2
381 1 6 4 5 3
384 1 6 2 2 7
396 1 4 5 7 2
;
The multiallelic versions of the association tests are performed since each marker
has more than two alleles. The following code invokes the three case-control tests
to ﬁnd out whether there is a signiﬁcant association between either of the markers
and disease status. Note that the same output could be produced by omitting the
three tests, ALLELE, GENOTYPE, and TREND, from the PROC CASECONTROL
statement.
proc casecontrol data=founders genotype allele trend;
trait disease;
var a1-a4;
run;
proc print noobs;
run;
An output data set is created by default, and the output from the PRINT procedure is
displayed in Output 3.1.1.
Output 3.1.1.
Output Data Set from PROC CASECONTROL for Multiallelic
Markers
ChiSq
ChiSq
ChiSq
df
df
df
Prob
Prob
Prob
Locus Genotype Allele
Trend Genotype Allele Trend Genotype Allele
Trend
M1
27.333
4.441
5.039
35
7
7
0.8191
0.7278 0.6552
M2
18.077
8.772 13.244
35
7
7
0.9920
0.2694 0.0664
This analysis ﬁnds no signiﬁcant association between disease status and either of the
markers. Suppose, however, that allele 7 of the second marker had been identiﬁed

Example 3.1. Performing Case-Control Tests on Multiallelic Markers
43
by previous studies as an allele of interest for this particular disease, and thus there
is concern that its effect is swamped by the other seven alleles. The data set can be
modiﬁed so that the second marker is considered a biallelic marker with alleles 7 and
“not 7.”
data marker2;
set founders;
if a3 ne 7 then a3=1;
if a4 ne 7 then a4=1;
keep id a3 a4 disease;
Now all three tests can be performed on the marker in the new data set.
proc casecontrol data=marker2;
trait disease;
var a3 a4;
run;
proc print noobs;
run;
PROC CASECONTROL performs all three tests by default since none were speciﬁed.
The output data set for this analysis is displayed in Output 3.1.2.
Output 3.1.2.
Output Data Set from PROC CASECONTROL for a Biallelic Marker
ChiSq
ChiSq
ChiSq
df
df
df
Prob
Prob
Prob
Locus Genotype Allele
Trend Genotype Allele Trend Genotype Allele
Trend
M1
12.193
6.599 10.103
2
1
1
0.0023
0.0102 0.0015
With just the single allele of interest, there is now a signiﬁcant association (using a
signiﬁcance level of α = 0.05) according to all three case-control tests between the
marker (speciﬁcally, allele 7) and disease status. Note that the allele and trend tests,
both of which are testing for additive allele effects, produce quite different p-values,
which could be an indication that HWE does not hold for allele 7. This is in fact the
case, which can be checked by running the ALLELE procedure on data set marker2
to test for HWE (see Chapter 2, “The ALLELE Procedure,” for more information).
The excess of heterozygotes forces X2 to be smaller than X2 , and only X2 remains
A
T
T
a valid chi-square statistic under the HWE violation.

44
Chapter 3. The CASECONTROL Procedure
References
Armitage, P. (1955), “Tests for Linear Trends in Proportions and Frequencies,”
Biometrics, 11, 375–386.
Devlin, B. and Roeder, K. (1999), “Genomic Control for Association Studies,”
Biometrics, 55, 997–1004.
Hodge, S.E. (1995), “An Oligogenic Disease Displaying Weak Marker Associations:
A Summary of Contributions to Problem 1 of GAW9,” Genetic Epidemiology,
12, 545–554.
Nielsen, D.M. and Weir, B.S. (1999), “A Classical Setting for Associations between
Markers and Loci Affecting Quantitative Traits,” Genetic Research, 74, 271–277.
Sasieni, P.D. (1997), “From Genotypes to Genes: Doubling the Sample Size,”
Biometrics, 53, 1253–1261.
Slager, S.L. and Schaid, D.J. (2001), “Evaluation of Candidate Genes in Case-Control
Studies: A Statistical Method to Account for Related Subjects,” American
Journal of Human Genetics, 68, 1457–1462.

Chapter 4
The FAMILY Procedure
Chapter Contents
OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
GETTING STARTED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
SYNTAX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
PROC FAMILY Statement
. . . . . . . . . . . . . . . . . . . . . . . . . . 49
BY Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
ID Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
TRAIT Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
VAR Statement
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
DETAILS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
Statistical Computations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
Missing Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
DATA= Data Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
OUTSTAT= Data Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
EXAMPLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
Example 4.1. Performing Tests with Missing Parental Data . . . . . . . . . 56
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

46
Chapter 4. The FAMILY Procedure

Chapter 4
The FAMILY Procedure
Overview
Family genotype data, though more difﬁcult to collect, often provide a more effec-
tive way of testing markers for association with disease status than case-control data.
Case-control data may uncover signiﬁcant associations between markers and a dis-
ease that could be caused by factors other than linkage, such as population struc-
ture. Analyzing family data using the FAMILY procedure ensures that any signiﬁ-
cant associations found between a marker and disease status are due to linkage be-
tween the marker and disease locus. This is accomplished by using the transmis-
sion/disequilibrium test (TDT) and several variations of it that can accommodate
different types of family data. One type of family consists of parents, at least one
heterozygous, and an affected child who have all been genotyped. This family struc-
ture is suitable for the original TDT. Families containing at least one affected and
one unaffected sibling from a sibship that have both been genotyped can be analyzed
using the sibling tests: the sib TDT (S-TDT) or the nonparametric sibling disequilib-
rium test (SDT). Both types of families can be jointly analyzed using the combined
versions of the S-TDT and SDT and the reconstruction-combined TDT (RC-TDT).
The RC-TDT can additionally accommodate families with no unaffected children and
missing parental genotypes in certain situations.
Getting Started
Example
The following example demonstrates how you can use PROC FAMILY to perform
one of several family-based tests, the TDT. You have collected the following family
genotypic data that you input into a SAS data set:
data example;
input ped indiv father mother disease (a1-a4)($);
datalines;
1
1
0
0 1 a b a c
1
2
0
0 1 c c a d
1 101
1
2 1 a c a d
1 102
1
2 1 b c a d
1 103
1
2 1 a c c a
1 104
1
2 2 b c a a
2
3
0
0 1 e e f g
2
4
0
0 1 d e g a
2 105
3
4 1 e d f a
2 106
3
4 2 e e g a
3
5
0
0 1 d a a c

48
Chapter 4. The FAMILY Procedure
3
6
0
0 1 e e c a
3 107
5
6 2 a e a a
4
7
0
0 1 f b a g
4
8
0
0 1 c e h g
4 108
7
8 2 b e a g
4 109
7
8 1 f c g g
4 110
7
8 1 b c a g
4 111
7
8 1 b c a h
5
9
0
0 1 a f d c
5
10
0
0 1 h d c h
5 112
9 10 2 a d d c
5 113
9 10 1 f d d c
6
11
0
0 1 b e c g
6
12
0
0 1 d f a g
6 114 11 12 2 b f c a
6 115 11 12 1 b d g a
7
13
0
0 1 e d c c
7
14
0
0 1 e h d a
7 116 13 14 1 e h c a
7 117 13 14 2 d e c a
7 118 13 14 1 d h c d
7 119 13 14 1 d h c d
;
The ﬁrst column of the data set contains the pedigree ID, followed by an individual
ID, and the two parental IDs. The ﬁfth column is a variable representing affection
status of a disease. The last four columns of this data set contain the two alleles at
each of two markers for each individual. Since there are no missing parental geno-
types in this data set, the TDT is a reasonable test to perform in order to determine if
either of the two markers is signiﬁcantly linked to the disease locus whose location
you are trying to pinpoint. Furthermore, close inspection of the data reveals that there
is only one affected child (which corresponds to a value of “2” for the disease affec-
tion variable) per each family. Thus, the TDT is also a valid test for association with
the disease locus. To perform the analysis, you would use the following statements:
proc family data=example prefix=Marker outstat=stats tdt contcorr;
id ped indiv father mother;
trait disease / affected=2;
var a1-a4;
run;
proc print data=stats;
format ProbTDT pvalue6.5;
run;
This code creates an output data set stats, which contains the chi-square statistic,
degrees of freedom, and p-value for testing each marker for linkage and association
with the disease locus using the TDT. The PREFIX= option in the PROC FAMILY
statement speciﬁes that the two markers be named Marker1 and Marker2 in the out-
put data set. The CONTCORR option indicates that the continuity correction of 0.5
should be used in calculating the chi-square statistic. The AFFECTED= option of the

PROC FAMILY Statement
49
TRAIT statement speciﬁes which value of the variable disease should be considered
“affected.” Note that the pedigree ID variable is listed in the ID statement; however,
it is not necessary for this data set, since all the individual IDs are unique. The same
results would be obtained if this variable were omitted.
Here is the output data set that is produced:
ChiSq
df
Prob
Obs
Locus
TDT
TDT
TDT
1
Marker1
1.57143
6
0.9546
2
Marker2
5.79861
5
0.3263
Figure 4.1.
Statistics for the TDT
Figure 4.1 displays the statistics for the TDT. Since both markers are multiallelic, a
joint test of all alleles at each marker is performed by default. The degrees of freedom
(in the dfTDT column) indicate that there are seven alleles at Marker1 and six alleles
at Marker2, since df= k − 1 where k is the number of marker alleles. The ProbTDT
column shows that neither of the markers is signiﬁcantly linked and associated with
the disease locus.
Syntax
The following statements are available in PROC FAMILY.
PROC FAMILY < options > ;
BY variables ;
ID variables ;
TRAIT variable </ AFFECTED=value> ;
VAR variables ;
Items within angle brackets (< >) are optional, and statements following the PROC
FAMILY statement can appear in any order. The ID, TRAIT, and VAR statements
are required. The syntax of each statement is described in the following section in
alphabetical order after the description of the PROC FAMILY statement.
PROC FAMILY Statement
PROC FAMILY < options > ;
You can specify the following options in the PROC FAMILY statement.
COMBINE
speciﬁes that the combined versions of the S-TDT and SDT be performed. Thus,
families containing parental genotypes can be analyzed under certain conditions us-
ing the TDT, and otherwise the speciﬁed sibling test is performed. Note that if TDT is
also being performed, the TDT is done independently of any other tests. By default,
the combined versions are not used.

50
Chapter 4. The FAMILY Procedure
CONTCORR
CC
speciﬁes that a continuity correction of 0.5 should be used for the TDT, S-TDT, and
RC-TDT tests in their asymptotic normal approximations. By default, no correction
is used.
DATA=SAS-data-set
names the input SAS data set to be used by PROC FAMILY. The default is to use the
most recently created data set.
MULT= JOINT | MAX
speciﬁes which multiallelic version of the TDT, S-TDT, SDT, and RC-TDT tests
should be performed. The joint version of the multiallelic tests combines the analy-
ses for each allele at a marker into one overall test statistic, with degrees of freedom
(df) corresponding to the number of alleles at the marker. The max version of the
multiallelic tests determines if there is at least one allele with a signiﬁcant test statis-
tic, using the maximum 1 df statistic over all alleles with a multiple testing adjustment
made. By default, the joint version of the multiallelic tests is performed. This option
has no effect on biallelic markers.
NDATA=SAS-data-set
names the input SAS data set containing names, or identiﬁers, for the markers used
in the output. There must be a NAME variable in this data set, which should contain
the same number of rows as there are markers in the input data set speciﬁed in the
DATA= option. When there are fewer rows than there are markers, markers without
a name are named using the PREFIX= option. Likewise, if there is no NDATA= data
set speciﬁed, the PREFIX= option is used.
OUTSTAT=SAS-data-set
names the output SAS data set containing the p-values for the tests speciﬁed in the
PROC FAMILY statement. When this option is omitted, an output data set is created
by default and named according to the DATAn convention.
PREFIX=preﬁx
speciﬁes a preﬁx to use in constructing names for marker variables in all output. For
example, if PREFIX=VAR, the names of the variables are VAR1, VAR2, ..., VARn.
Note that this option is ignored when the NDATA= option is speciﬁed, unless there
are fewer names in the NDATA data set than there are markers. If this option is
omitted, PREFIX=M is the default.
RCTDT
requests that the reconstruction-combined TDT (RC-TDT) be performed. If none of
the four test options (RCTDT, SDT, STDT, or TDT) are speciﬁed, then all four tests
are performed by default.
SDT
requests that the SDT, a nonparametric alternative to the S-TDT, be performed. If
none of the four test options (RCTDT, SDT, STDT, or TDT) are speciﬁed, then all
four tests are performed by default. The COMBINE option can be used with this test
to indicate that the combined version of the SDT should be performed.

TRAIT Statement
51
STDT
requests that the sibling TDT (S-TDT), which analyzes data from sibships, be per-
formed. If none of the four test options (RCTDT, SDT, STDT, or TDT) are speciﬁed,
then all four tests are performed by default. The COMBINE option can be used with
this test to indicate that the combined version of the S-TDT should be performed.
TDT
requests that the original TDT be performed. If none of the four test options (RCTDT,
SDT, STDT, or TDT) are speciﬁed, then all four tests are performed by default.
BY Statement
BY variables ;
You can specify a BY statement with PROC FAMILY to obtain separate analyses on
observations in groups deﬁned by the BY variables. When a BY statement appears,
the procedure expects the input data set to be sorted in order of the BY variables. The
variables are one or more variables in the input data set.
If your input data set is not sorted in ascending order, use one of the following alter-
natives:
• Sort the data using the SORT procedure with a similar BY statement.
• Specify the BY statement option NOTSORTED or DESCENDING in the BY
statement for the FAMILY procedure. The NOTSORTED option does not
mean that the data are unsorted but rather that the data are arranged in groups
(according to values of the BY variables) and that these groups are not neces-
sarily in alphabetical or increasing numeric order.
• Create an index on the BY variables using the DATASETS procedure (in Base
SAS software).
For more information on the BY statement, refer to the discussion in SAS Language
Reference: Concepts. For more information on the DATASETS procedure, refer to
the discussion in the SAS Procedures Guide.
ID Statement
ID variables ;
The ID statement is required and must contain, in the following order, either:
• the pedigree ID, the individual ID, then the two parental ID variables, or
• the individual ID, then the two parental IDs
Thus if only three variables are speciﬁed in the ID statement, it is assumed that the
pedigree identiﬁer has been omitted. The pedigree ID is not necessary if all the
individual identiﬁers are unique. The individual and two parental ID variables can
be either numeric or character, but all three must be of the same type. The pedigree
variable, if speciﬁed, can be either numeric or character regardless of the type of the
other three identiﬁers.

52
Chapter 4. The FAMILY Procedure
TRAIT Statement
TRAIT variable </ AFFECTED=value> ;
The TRAIT statement is required and identiﬁes the trait variable. This variable must
be binary, but may be either character or numeric. By default, the second value of
the TRAIT variable that appears in the input data set is considered to be “affected”
for the tests. If you would like to specify a different value for “affected,” you may do
so by adding the /AFFECTED=value option to the TRAIT statement. For a variable
with a numeric format, the number that corresponds to “affected” should be speciﬁed
(AFFECTED=1); if the variable has a character format, the level that corresponds to
“affected” should be speciﬁed in quotes (AFFECTED=“a”).
VAR Statement
VAR variables ;
The VAR statement identiﬁes the variables containing the marker alleles. The VAR
statement should contain 2m variable names, where m is the number of markers in
the data set. Note that alleles for the same marker must be listed consecutively.
Details
Statistical Computations
For all tests, it is assumed that the marker has two alleles, M1 and M2. Extensions
to multiallelic markers are made by performing the tests on each allele in turn, with
the current allele being considered to be M1 and all other alleles considered to be
M2. When the CONTCORR option is speciﬁed in the PROC FAMILY statement, the
z score statistics of all versions of the TDT, S-TDT, and RC-TDT can be continuity
corrected by subtracting 0.5 from the absolute value of the numerator. The two-sided
p-value for each z score using the normal distribution is equivalent to using the p-
value from the χ21 distribution for the square of the z score, and this chi-square form
of the statistic is reported in the output data set.
TDT
The TDT (Spielman, McGinnis, and Ewens 1993) is implemented using a normal
approximation. This test includes families where both parents have been genotyped
for the marker and at least one is heterozygous. If only one parent has been geno-
typed, that parent is heterozygous, and the affected child is not homozygous and does
not have the same genotype as the typed parent, then the TDT can be applied to this
family as well (Curtis and Sham 1995). The TDT tests for equality between the pro-
portion of times a heterozygous parent transmits the M1 allele to an affected child and
the proportion of times a heterozygous parent transmits the M2 allele to an affected
child. The normal approximation to the binomial is used to form the z score statistic
b − b+c
Z =
2
b+c
4

Statistical Computations
53
where b is the number of M1 alleles in all affected children from heterozygous parents
and c is the number of M2 alleles in affected children from heterozygous parents.
Two extensions to a multiallelic TDT are available. The ﬁrst, which is performed by
default or when MULT=JOINT is speciﬁed in the PROC FAMILY statement, com-
bines the TDT for each of k alleles at a marker into one statistic as follows (Spielman
and Ewens 1996):
k
k − 1
TJ =
Z2
k
v
v=1
where Zv is simply the Z deﬁned in the preceding paragraph, with allele Mv treated
as M1 and all other alleles as M2 for each v = 1, ..., k. TJ and the continuity-
corrected form T have an asymptotic χ2
distribution, and the corresponding p-
J
k−1
value is reported.
Alternatively, if the MULT=MAX option is speciﬁed, either zm or zm (when the
CONTCORR option is speciﬁed) is used, where zm = max1≤v≤k |Zv|. The equiva-
lent one degree of freedom chi-square statistic is reported, and a Bonferroni correc-
tion is applied to its p-value.
Note: The TDT is a valid test of linkage and association only when the data con-
sist of unrelated nuclear families and each family contains only one affected child.
Otherwise, it is a valid test of linkage only.
S-TDT
The z score procedure given by Spielman and Ewens (1998) is used to calculate p-
values for the S-TDT. This test can be applied to families where there are at least
one affected sibling and one unaffected sibling, and not all siblings have the same
genotype. The z score, whose two-sided p-value is approximated using the normal
√
distribution, is calculated as z = (Y − A)/ V . Y represents the total observed
number of M1 alleles in the affected siblings. For t total siblings in the family, a
affected and u unaffected, and r that are M1/M1 and s that are M1/M2, summing
over families gives
A =
(2r + s)a/t
and
V =
au[4r(t − r − s) + s(t − s)]/[t2(t − 1)]
as the expected value and variance of Y respectively.
When the COMBINE option is speciﬁed in the PROC FAMILY statement, the S-TDT
and TDT are combined as follows: the TDT is applied to all families that meet the
requirements described in the preceding section. The S-TDT is then applied to the
remaining families that meet its requirements described in the preceding paragraph.

54
Chapter 4. The FAMILY Procedure
Using the notation already given for these tests, the z score for the combined test can
then be written as
(Y + b) − (A + b+c )
z =
2
V + b+c
4
For multiallelic markers, the same extensions can be made to the S-TDT and com-
bined S-TDT that were made to the TDT (Monks, Kaplan, and Weir 1998); that is,
either a joint test over all alleles, or the maximum z score of all the alleles with the
p-value being Bonferroni-corrected.
Note: The S-TDT is a valid test of linkage and association only when the data consist
of unrelated nuclear families and each family contains only one affected and one
unaffected sibling. Otherwise, it is a valid test of linkage only.
SDT
The SDT (Horvath and Laird 1998) is a sign test used on discordant sibling pairs.
As with the S-TDT, one affected sibling and one unaffected sibling are required to
be in each family, but unlike the S-TDT, the SDT remains a valid test of linkage and
association when the sibship is larger.
Continuing the notation from the previous tests, for a affected siblings in a family and
u unaffected siblings in a family, treating each allele Mv in turn as M1 and all other
alleles as M2, v = 1, ..., k, deﬁne for each family in the data the average number of
v alleles among affected siblings and unaffected siblings respectively as
mav = Y /a
mu
v = [(2r + s) − Y ] /u
Then dv = ma −
v
mu
v for each family, and summing over families gives Sv
=
sgn(dv), where sgn(dv) = 1 for dv > 0, 0 for dv = 0, and −1 for dv < 0.
The joint multiallelic SDT statistic is then deﬁned as T = S W−1S where S =
(S1, ..., Sk−1) and Wvw =
sgn(dv)sgn(dw), where v, w = 1, ..., k − 1 (the in-
formation on the kth allele is not needed). This statistic has an asymptotic χ2k−1
distribution, and this distribution is used to obtain p-values for the SDT. When there
are only two alleles at the marker, this joint multiallelic version of the SDT reduces
to the biallelic version of the SDT.
This sibship test is also combined with the TDT when the COMBINE option in the
PROC FAMILY statement is speciﬁed, creating a test which can potentially use more
of the data (Horvath and Laird 1998; Curtis, Miller, and Sham 1999). In order to
maintain the test’s validity as a test of association in families with more than one
affected and one unaffected sibling, a nonparametric multiallelic TDT is used, which
is in the same S W−1S form as the SDT. This test statistic for the joint test also has
an asymptotic χ2
distribution, and the corresponding p-value is reported.
k−1

Missing Values
55
When the MULT=MAX option is speciﬁed in the PROC FAMILY statement, then
the SDT chi-square statistic is simply max1≤v≤k(S2vW −1
vv ) and has one degree of
freedom. This applies to the SDT when used alone or combined with the TDT. As
with the other tests, a Bonferroni correction is made to the p-value.
RC-TDT
The RC-TDT (Knapp 1999) takes the combined S-TDT a step further by reconstruct-
ing missing parental genotypes when possible in order to use more families. The
RC-TDT can be applied to families with at least one affected child that meet one of
the following conditions:
• Both parents are typed with at least one heterozygous for M1.
• One parent is typed, the other can be reconstructed, and at least one parent is
heterozygous for M1.
• Both parents’ genotypes are missing but can be reconstructed, and at least one
parent is heterozygous for M1.
• At least one parental genotype is missing and cannot be reconstructed, but the
conditions for the S-TDT are met.
As with the S-TDT, a z score is created using the statistic Y , but Knapp calculates
a different expected value e and variance v of Y , which takes into account the bias
created by the genotype reconstruction, to form the z score over all families:
√
z = (Y − e)/ v
For multiallelic markers, the same extensions can be made to the RC-TDT that were
made to the TDT and S-TDT; that is, either a joint test over all alleles, or the maxi-
mum z score of all the alleles with the p-value being Bonferroni-corrected.
Note: The RC-TDT is a valid test of linkage and association only when the data
consist of unrelated nuclear families and each family contains only one affected and
one unaffected sibling. Otherwise, it is a valid test of linkage only.
Missing Values
An individual’s genotype for a marker is considered missing if at least one of the
alleles at the marker is missing. Any missing genotypes are excluded from all cal-
culations. However, the individual’s nonmissing genotypes at other loci can be used
as part of the calculations. If a child has a missing trait value, then that individual
is excluded from all calculations. However, missing trait values of individuals used
only as parents do not affect the analysis. See the following section for information
on missing values in the ID variables.

56
Chapter 4. The FAMILY Procedure
DATA= Data Set
The DATA= data set has columns representing markers, ID variables, and a trait, and
rows representing the individuals. There must be one binary trait variable listed in
the TRAIT statement; the three ID variables consisting of the individual’s ID and
the two parental IDs, all of the same type, must be listed in the ID statement, and
optionally the pedigree ID if the individual identiﬁers are not unique. Note that only
individuals with both parents appearing in the data, even if all the parents’ genotypes
are missing, can be used as affected children or in sib-pairs for analysis. However, if
the individual is used only as a parent, then that individual’s parents need not appear
in the data. Also, if a pedigree ID variable is speciﬁed in the ID statement, any
individual with a missing value for that variable is excluded from the analysis, as a
parent and as a child. There are two columns for each marker, representing the two
alleles at that marker carried by the individual. These two columns must be listed
consecutively in the VAR statement. These marker variables must all be of the same
type, but can be either character or numeric variables.
OUTSTAT= Data Set
The OUTSTAT= data set contains the following variables:
• the BY variables, if any
• Locus
• the chi-square statistics for each test performed: ChiSqTDT, ChiSqSTDT,
ChiSqSDT, and ChiSqRCTDT
• the degrees of freedom for each test performed: dfTDT, dfSTDT, dfSDT, and
dfRCTDT
• the p-values for each test performed: ProbTDT, ProbSTDT, ProbSDT, and
ProbRCTDT
Example
Example 4.1. Performing Tests with Missing Parental Data
The following data are from GAW9 (Hodge 1995) and contain 20 nuclear families
that are genotyped at two markers. The data have been modiﬁed so that each mother’s
genotype is missing.
data gaw;
input ped id f_id m_id sex disease m11 m12 m21 m22;
datalines;
1
1
0
0 1 1
7
8
7
2
1
2
0
0 2 1
.
.
.
.
1
401
1
2 1 1
7
2
7
6
1
402
1
2 1 1
8
2
7
6
1
403
1
2 1 1
7
2
2
7
1
404
1
2 2 2
8
2
7
7

Example 4.1. Performing Tests with Missing Parental Data
57
2
3
0
0 1 1
4
4
1
3
2
4
0
0 2 1
.
.
.
.
2
405
3
4 2 1
4
6
1
7
2
406
3
4 2 2
4
4
3
7
3
5
0
0 1 1
6
7
7
2
3
6
0
0 2 1
.
.
.
.
3
407
5
6 2 2
7
4
7
7
4
7
0
0 1 1
1
8
7
3
4
8
0
0 2 1
.
.
.
.
4
408
7
8 2 2
8
4
7
3
4
409
7
8 1 1
1
2
3
3
4
410
7
8 2 1
8
2
7
3
4
411
7
8 1 1
8
2
7
5
5
9
0
0 1 1
7
1
6
2
5
10
0
0 2 1
.
.
.
.
5
412
9
10 2 2
7
6
6
2
5
413
9
10 1 1
1
6
6
2
6
11
0
0 1 1
8
4
2
3
6
12
0
0 2 1
.
.
.
.
6
414
11
12 1 2
8
1
2
7
6
415
11
12 1 1
8
6
3
7
7
13
0
0 1 1
4
6
2
2
7
14
0
0 2 1
.
.
.
.
7
416
13
14 1 1
4
5
2
7
7
417
13
14 2 2
6
4
2
7
7
418
13
14 2 1
6
5
2
6
7
419
13
14 1 1
6
5
2
6
8
15
0
0 1 1
6
8
2
7
8
16
0
0 2 1
.
.
.
.
8
420
15
16 2 1
6
2
7
7
8
421
15
16 2 1
8
6
2
7
8
422
15
16 2 2
6
6
7
7
8
423
15
16 2 1
6
6
7
7
9
17
0
0 1 2
4
7
2
7
9
18
0
0 2 1
.
.
.
.
9
424
17
18 2 2
4
5
7
2
9
425
17
18 2 1
7
4
2
7
9
426
17
18 1 1
4
5
2
2
10
19
0
0 1 1
6
4
2
7
10
20
0
0 2 1
.
.
.
.
10
427
19
20 2 2
4
4
7
2
11
21
0
0 1 1
4
7
7
7
11
22
0
0 2 1
.
.
.
.
11
428
21
22 1 1
7
6
7
2
11
429
21
22 2 2
7
4
7
2
11
430
21
22 2 1
7
6
7
3
12
23
0
0 1 1
7
6
7
5
12
24
0
0 2 1
.
.
.
.
12
431
23
24 1 2
6
4
7
7
13
25
0
0 1 1
4
1
2
8
13
26
0
0 2 1
.
.
.
.
13
432
25
26 1 1
4
8
2
6
13
433
25
26 1 2
1
8
8
6
13
434
25
26 1 1
1
4
2
6

58
Chapter 4. The FAMILY Procedure
14
27
0
0 1 1
7
6
3
2
14
28
0
0 2 1
.
.
.
.
14
435
27
28 1 1
6
2
3
3
14
436
27
28 1 1
7
4
3
7
14
437
27
28 1 1
6
2
2
7
14
438
27
28 1 1
7
4
2
7
14
439
27
28 2 2
6
2
2
7
14
440
27
28 1 1
6
4
3
7
15
29
0
0 1 1
2
4
7
4
15
30
0
0 2 1
.
.
.
.
15
441
29
30 1 1
4
2
7
7
15
442
29
30 2 2
4
8
4
7
15
443
29
30 2 1
4
2
7
5
15
444
29
30 2 1
4
2
7
5
15
445
29
30 1 1
2
8
7
5
;
Since there are missing parental data, the original TDT may not be the best test to
perform on this data set. The following analysis uses the S-TDT, SDT, and RC-TDT
to test markers for linkage with the disease locus.
proc family data=gaw prefix=Marker sdt stdt rctdt;
id id f_id m_id;
var m11 m12 m21 m22;
trait disease / affected=2;
run;
proc print;
run;
The output data set, which is created by default, is displayed in Output 4.1.1.
Output 4.1.1.
Output Data Set from PROC FAMILY
ChiSq
ChiSq
ChiSq
df
df
df
Prob
Prob
Prob
Obs
Locus
STDT
SDT
RCTDT
STDT
SDT
RCTDT
STDT
SDT
RCTDT
1
Marker1
5.6179
3.9668
4.7398
6
6
6
0.467
0.681
0.578
2
Marker2
12.6191
10.6522
11.9388
7
7
7
0.082
0.155
0.103
Since only one parent is missing genotype information in each nuclear family, the
TDT might be applicable to some of the families. The COMBINE option can be
speciﬁed to use the TDT in the appropriate families, and the S-TDT or SDT for all
other families. This option does not apply to the RC-TDT, so that test is omitted from
this analysis.
proc family data=gaw prefix=Marker tdt sdt stdt combine;
id id f_id m_id;
var m11 m12 m21 m22;
trait disease / affected=2;

Example 4.1. Performing Tests with Missing Parental Data
59
run;
proc print;
run;
The output data set is displayed in Output 4.1.2.
Output 4.1.2.
Output Data Set from PROC FAMILY Using COMBINE Option
ChiSq
ChiSq
ChiSq
df
df
df
Prob
Prob
Prob
Obs
Locus
TDT
STDT
SDT
TDT
STDT
SDT
TDT
STDT
SDT
1
Marker1
8.00000
12.0511
5.7200
4
6
6
0.092
0.061
0.455
2
Marker2
2.66667
10.1802
10.6667
2
6
7
0.264
0.117
0.154
Note that the test statistics for the TDT and the S-TDT and SDT are not the same;
this implies that not all families meet the requirements for the TDT. In this case, the
S-TDT, SDT, and RC-TDT use more of the data than the TDT alone. However, since
there is only one affected child in each nuclear family, the TDT is a valid test of
association; since there is at least one occasion when there is more than one unaf-
fected child in a nuclear family, the S-TDT and RC-TDT are not valid for testing for
association of the marker with the disease locus (the SDT is always a valid test of
association when the data consist of unrelated nuclear families). Both of these con-
siderations, the amount of information that can be used and the validity for testing
association, should be taken into account when deciding which test(s) to perform.
Another type of analysis can be performed using the MULT=MAX option in the
PROC FAMILY statement. This option indicates that instead of doing a joint test
over all the alleles at each marker, perform a test to see if any of the alleles at a
marker are signiﬁcantly linked with the disease locus. This analysis is invoked with
the following code, using only the SDT and RC-TDT:
proc family data=gaw prefix=Marker sdt rctdt combine mult=max;
id id f_id m_id;
var m11 m12 m21 m22;
trait disease / affected=2;
run;
proc print;
run;
The output data set produced by this code is displayed in Output 4.1.3.
Output 4.1.3.
Output Data Set from PROC FAMILY Using MULT=MAX Option
ChiSq
ChiSq
df
df
Prob
Prob
Obs
Locus
SDT
RCTDT
SDT
RCTDT
SDT
RCTDT
1
Marker1
2.00000
2.90050
1
1
1.0000
0.6199
2
Marker2
2.66667
3.86422
1
1
0.8198
0.3946

60
Chapter 4. The FAMILY Procedure
The chi-square statistics for the tests always have one degree of freedom when the
MULT=MAX option is used. Note, however, that the p-values are not the cor-
responding right-tailed probabilities for a χ21 statistic; this is because the p-values
are Bonferroni-corrected in order to account for taking the maximum of several chi-
square statistics.
References
Curtis, D., Miller, M.B., and Sham, P.C. (1999), “Combining the Sibling
Disequilibrium Test and Transmission/Disequilibrium Test for Multiallelic
Markers,” American Journal of Human Genetics, 64, 1785–1786.
Curtis, D. and Sham, P.C. (1995), “A Note on the Application of the Transmission
Disequilibrium Test When a Parent is Missing,” American Journal of Human
Genetics, 56, 811–812.
Hodge, S.E. (1995), “An Oligogenic Disease Displaying Weak Marker Associations:
A Summary of Contributions to Problem 1 of GAW9,” Genetic Epidemiology,
12, 545–554.
Horvath, S. and Laird, N.M. (1998), “A Discordant-Sibship Test for Disequilibrium
and Linkage: No Need for Parental Data,” American Journal of Human Genetics,
63, 1886–1897.
Knapp, M. (1999), “The Transmission/Disequilibrium Test and Parental-Genotype
Reconstruction:
The Reconstruction-Combined Transmission/Disequilibrium
Test,” American Journal of Human Genetics, 64, 861–870.
Monks, S.A., Kaplan, N.L., and Weir, B.S. (1998), “A Comparative Study of Sibship
Tests of Linkage and/or Association,” American Journal of Human Genetics, 63,
1507–1516.
Spielman, R.S. and Ewens, W.J. (1996), “The TDT and Other Family-based Tests for
Linkage Disequilibrium and Association,” American Journal of Human Genetics,
59, 983–989.
Spielman, R.S. and Ewens, W.J. (1998), “A Sibship Test for Linkage in the Presence
of Association: The Sib Transmission/Disequilibrium Test,” American Journal
of Human Genetics, 62, 450–458.
Spielman, R.S., McGinnis, R.E., and Ewens, W.J. (1993), “Transmission Test
for Linkage Disequilibrium: The Insulin Gene Region and Insulin-dependent
Diabetes Mellitus (IDDM),” American Journal of Human Genetics, 52, 506–516.

Chapter 5
The HAPLOTYPE Procedure
Chapter Contents
OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
GETTING STARTED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
SYNTAX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
PROC HAPLOTYPE Statement . . . . . . . . . . . . . . . . . . . . . . . . 68
BY Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
TRAIT Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
VAR Statement
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
DETAILS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Statistical Computations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Missing Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
OUT= Data Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
Displayed Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
ODS Table Names . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
EXAMPLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
Example 5.1. Estimating Three-Locus Haplotype Frequencies . . . . . . . . 78
Example 5.2. Using Multiple Runs of the EM Algorithm . . . . . . . . . . . 82
Example 5.3. Testing for Linkage Disequilibrium
. . . . . . . . . . . . . . 83
Example 5.4. Testing for Marker-Trait Associations . . . . . . . . . . . . . 85
Example 5.5. Creating a Data Set for Haplotype Trend Regression (HTR) . . 89
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

62
Chapter 5. The HAPLOTYPE Procedure

Chapter 5
The HAPLOTYPE Procedure
Overview
A haplotype is a combination of alleles at multiple loci on a single chromosome. A
pair of haplotypes constitutes the multilocus genotype. Haplotype information has to
be inferred as data are usually collected at the genotypic, not haplotype pair, level.
For homozygous markers, there is no problem. If one locus has alleles A and a, and
a second locus has alleles B and b, the observed genotype AABB must contain two
haplotypes of type AB; genotype AaBB must contain haplotypes AB and aB, and
so on. Haplotypes and their frequencies can be obtained directly. When both loci are
heterozygous, however, there is ambiguity; a variety of combinations of haplotypes
can generate the genotype, and it is not possible to determine directly which two
haplotypes constitute any individual genotype. For example, the genotype AaBb may
be of type AB/ab with haplotypes AB and ab, or of type Ab/aB with haplotypes
Ab and aB. The HAPLOTYPE procedure uses the expectation-maximization (EM)
algorithm to generate maximum likelihood estimates of haplotype frequencies given
a multilocus sample of genetic marker genotypes under the assumption of Hardy-
Weinberg equilibrium (HWE). These estimates can then in turn be used to assign the
probability that each individual possesses a particular haplotype pair.
Estimation of haplotype frequencies is important for several applications in genetic
data analysis. One application is determining whether there is linkage disequilibrium
(LD), or association, between loci. PROC HAPLOTYPE performs a likelihood ra-
tio test to test the hypothesis of no LD between marker loci. Another application
is association testing of disease susceptibility. Since sites that affect disease status
are embedded in haplotypes, it has been postulated that the power of case-control
studies might be increased by testing for haplotype rather than allele or genotype as-
sociations. One reason is that haplotypes might include two or more causative sites
whose combined effect is measurable, particularly if they show synergistic interac-
tion. Another is that fewer tests need be performed, although if there are a large
number of haplotypes, this advantage is offset by the increased degrees of freedom of
each test. PROC HAPLOTYPE can use case-control data to calculate test statistics
for the hypothesis of no association between alleles comprising the haplotypes and
disease status; such tests are carried out over all haplotypes at the loci speciﬁed, or
for individual haplotypes.

64
Chapter 5. The HAPLOTYPE Procedure
Getting Started
Example
Assume you have a random sample with 25 individuals genotyped at four markers.
You want to infer the gametic phases of the genotypes and estimate their frequencies.
There are eight columns of data, with the ﬁrst two columns containing the pair of
alleles at the ﬁrst marker, and the next two columns containing the pair of alleles for
the second marker, and so on. Each row represents an individual. The data can be
read into a SAS data set as follows:
data markers;
input (m1-m8) ($);
datalines;
B
B
A
B
B
B
A
A
A
A
B
B
A
B
A
B
B
B
A
A
B
B
B
B
A
B
A
B
A
B
A
B
A
A
A
B
A
B
B
B
B
B
A
A
A
B
A
B
A
B
B
B
A
B
A
A
A
B
A
A
A
A
A
A
B
B
A
A
A
A
A
B
A
B
A
B
A
B
B
B
A
B
A
B
A
B
A
A
B
B
A
B
A
B
A
A
A
B
A
A
A
B
A
B
A
B
B
B
B
B
A
B
A
A
A
B
A
A
A
B
B
B
A
B
A
B
A
B
A
B
B
B
A
A
A
B
B
B
B
B
A
A
A
A
A
B
A
A
A
B
A
A
A
B
A
A
A
B
A
B
B
B
A
A
A
A
A
B
A
A
A
B
A
A
A
B
A
B
A
A
A
A
B
B
A
A
A
A
A
A
A
A
A
B
B
B
A
A
A
A
;
You can now use PROC HAPLOTYPE to infer the possible haplotypes and estimate
the four-locus haplotype frequencies in this sample. The following statements will
perform these calculations:
proc haplotype data=markers out=hapout init=random prefix=SNP;
var m1-m8;
run;
proc print data=hapout noobs round;
run;

Example
65
This analysis uses the EM algorithm to estimate the haplotype frequencies from the
sample. The standard errors and a conﬁdence interval are estimated, by default, un-
der a binomial assumption for each haplotype frequency estimate. A more precise
estimate of the standard error can be obtained through the jackknife process by speci-
fying the option SE=JACKKNIFE in the PROC HAPLOTYPE statement, but it takes
considerably more computations (see the “Methods for Estimating Standard Error”
section on page 73 for more information). The option INIT=RANDOM indicates
that initial haplotype frequencies are randomly generated, using a random seed cre-
ated by the system clock since the SEED= option is omitted. The default conﬁdence
level 0.95 is used since the ALPHA= option of the PROC HAPLOTYPE statement
was omitted. Also by default, the convergence criterion of 0.00001 must be satisﬁed
for one iteration, and the maximum number of iterations is set to 100. The PREFIX=
option requests that the four markers, indicated by the eight allele variables in the
VAR statement, be named SNP1-SNP4.
The results from the procedure are as follows.
The HAPLOTYPE Procedure
Analysis Information
Loci Used
SNP1 SNP2 SNP3 SNP4
Number of Individuals
25
Number of Starts
1
Convergence Criterion
0.00001
Iterations Checked for Conv.
1
Maximum Number of Iterations
100
Number of Iterations Used
15
Log Likelihood
-95.94742
Initialization Method
Random
Random Number Seed
51220
Standard Error Method
Binomial
Haplotype Frequency Cutoff
0
Figure 5.1.
Analysis Information for the HAPLOTYPE Procedure
Figure 5.1 displays information on several of the settings used to perform the
HAPLOTYPE procedure as well as information on the EM algorithm. Note that you
can obtain from this table the random seed that was generated by the system clock if
you need to replicate this analysis.

66
Chapter 5. The HAPLOTYPE Procedure
Haplotype Frequencies
Standard
95% Confidence
Number
Haplotype
Freq
Error
Limits
1
A-A-A-A
0.14302
0.05001
0.04500
0.24105
2
A-A-A-B
0.07527
0.03769
0.00140
0.14914
3
A-A-B-A
0.00000
0.00000
0.00000
0.00000
4
A-A-B-B
0.00000
0.00010
0.00000
0.00020
5
A-B-A-A
0.09307
0.04151
0.01173
0.17442
6
A-B-A-B
0.05335
0.03210
0.00000
0.11627
7
A-B-B-A
0.00002
0.00061
0.00000
0.00122
8
A-B-B-B
0.07526
0.03769
0.00140
0.14913
9
B-A-A-A
0.08638
0.04013
0.00772
0.16504
10
B-A-A-B
0.08792
0.04046
0.00863
0.16722
11
B-A-B-A
0.07921
0.03858
0.00359
0.15482
12
B-A-B-B
0.10819
0.04437
0.02122
0.19517
13
B-B-A-A
0.10098
0.04304
0.01662
0.18534
14
B-B-A-B
0.00000
0.00001
0.00000
0.00002
15
B-B-B-A
0.09732
0.04234
0.01433
0.18030
16
B-B-B-B
0.00000
0.00001
0.00000
0.00002
Figure 5.2.
Haplotype Frequencies from the HAPLOTYPE Procedure
Figure 5.2 displays the possible haplotypes in the sample and their estimated fre-
quencies with standard errors and the lower and upper limits of the 95% conﬁdence
interval.

Example
67
ID
m1
m2
m3
m4
m5
m6
m7
m8
HAPLOTYPE1
HAPLOTYPE2
PROB
1
B
B
A
B
B
B
A
A
B-A-B-A
B-B-B-A
1.00
2
A
A
B
B
A
B
A
B
A-B-A-A
A-B-B-B
1.00
2
A
A
B
B
A
B
A
B
A-B-A-B
A-B-B-A
0.00
3
B
B
A
A
B
B
B
B
B-A-B-B
B-A-B-B
1.00
4
A
B
A
B
A
B
A
B
A-A-A-B
B-B-B-A
0.26
4
A
B
A
B
A
B
A
B
A-B-A-A
B-A-B-B
0.36
4
A
B
A
B
A
B
A
B
A-B-A-B
B-A-B-A
0.15
4
A
B
A
B
A
B
A
B
A-B-B-A
B-A-A-B
0.00
4
A
B
A
B
A
B
A
B
A-B-B-B
B-A-A-A
0.23
5
A
A
A
B
A
B
B
B
A-A-A-B
A-B-B-B
1.00
6
B
B
A
A
A
B
A
B
B-A-A-A
B-A-B-B
0.57
6
B
B
A
A
A
B
A
B
B-A-A-B
B-A-B-A
0.43
7
A
B
B
B
A
B
A
A
A-B-A-A
B-B-B-A
1.00
7
A
B
B
B
A
B
A
A
A-B-B-A
B-B-A-A
0.00
8
A
B
A
A
A
A
A
A
A-A-A-A
B-A-A-A
1.00
9
B
B
A
A
A
A
A
B
B-A-A-A
B-A-A-B
1.00
10
A
B
A
B
A
B
B
B
A-B-A-B
B-A-B-B
0.47
10
A
B
A
B
A
B
B
B
A-B-B-B
B-A-A-B
0.53
11
A
B
A
B
A
B
A
A
A-A-A-A
B-B-B-A
0.65
11
A
B
A
B
A
B
A
A
A-B-A-A
B-A-B-A
0.35
11
A
B
A
B
A
B
A
A
A-B-B-A
B-A-A-A
0.00
12
B
B
A
B
A
B
A
A
B-A-A-A
B-B-B-A
0.51
12
B
B
A
B
A
B
A
A
B-A-B-A
B-B-A-A
0.49
13
A
B
A
A
A
B
A
B
A-A-A-A
B-A-B-B
0.72
13
A
B
A
A
A
B
A
B
A-A-A-B
B-A-B-A
0.28
14
A
B
B
B
B
B
A
B
A-B-B-B
B-B-B-A
1.00
15
A
A
A
B
A
A
A
B
A-A-A-A
A-B-A-B
0.52
15
A
A
A
B
A
A
A
B
A-A-A-B
A-B-A-A
0.48
16
B
B
A
B
A
B
A
B
B-A-A-B
B-B-B-A
0.44
16
B
B
A
B
A
B
A
B
B-A-B-B
B-B-A-A
0.56
17
A
B
B
B
A
A
A
B
A-B-A-B
B-B-A-A
1.00
18
B
B
B
B
A
A
A
A
B-B-A-A
B-B-A-A
1.00
19
A
B
A
A
A
B
A
A
A-A-A-A
B-A-B-A
1.00
20
A
B
A
A
A
B
A
B
A-A-A-A
B-A-B-B
0.72
20
A
B
A
A
A
B
A
B
A-A-A-B
B-A-B-A
0.28
21
B
B
A
A
A
A
A
B
B-A-A-A
B-A-A-B
1.00
22
A
A
A
B
A
A
A
B
A-A-A-A
A-B-A-B
0.52
22
A
A
A
B
A
A
A
B
A-A-A-B
A-B-A-A
0.48
23
A
B
A
A
A
A
B
B
A-A-A-B
B-A-A-B
1.00
24
A
A
A
A
A
A
A
A
A-A-A-A
A-A-A-A
1.00
25
A
B
B
B
A
A
A
A
A-B-A-A
B-B-A-A
1.00
Figure 5.3.
Output Data Set from the HAPLOTYPE Procedure
Figure 5.3 displays each individual’s genotype with each of the possible haplotype
pairs that can comprise the genotype, and the probability the genotype can be resolved
into each of the possible haplotype pairs.

68
Chapter 5. The HAPLOTYPE Procedure
Syntax
The following statements are available in PROC HAPLOTYPE.
PROC HAPLOTYPE < options > ;
BY variables ;
TRAIT variable ;
VAR variables ;
Items within angle brackets (< >) are optional, and statements following the PROC
HAPLOTYPE statement can appear in any order. Only the VAR statement is re-
quired. The syntax for each statement is described in the following section in alpha-
betical order after the description of the PROC HAPLOTYPE statement.
PROC HAPLOTYPE Statement
PROC HAPLOTYPE < options > ;
You can specify the following options in the PROC HAPLOTYPE statement.
ALPHA=number
speciﬁes that a conﬁdence level of 100(1−number)% is to be used in forming the
conﬁdence intervals for estimates of haplotype frequencies. The value of number
must be between 0 and 1, inclusive, and 0.05 is used as the default value if it is not
speciﬁed.
CONV=number
speciﬁes the convergence criterion for iterations of the EM algorithm, where 0 <
number ≤ 1. The iteration process is stopped when the ratio of the change in the log
likelihoods to the former log likelihood is less than or equal to number for the number
of consecutive iterations speciﬁed in the NLAG= option (or 1 by default), or after the
number of iterations speciﬁed in the MAXITER= option has been performed. The
default value is 0.00001.
CUTOFF=number
speciﬁes a lower bound on a haplotype’s estimated frequency in order for that haplo-
type to be included in the “Haplotype Frequencies” table. The value of number must
be between 0 and 1, inclusive. By default, all possible haplotypes from the sample
are included in the table.
DATA=SAS-data-set
names the input SAS data set to be used by PROC HAPLOTYPE. The default is to
use the most recently created data set.
INIT=LINKEQ | RANDOM | UNIFORM
indicates the method of initializing haplotype frequencies to be used in the EM al-
gorithm. INIT=LINKEQ initializes haplotype frequencies assuming linkage equilib-
rium by calculating the product of the frequencies of the alleles that comprise the
haplotype. INIT=RANDOM initializes haplotype frequencies with random values

PROC HAPLOTYPE Statement
69
from a Uniform(0,1) distribution, and INIT=UNIFORM assigns equal frequency to
all haplotypes. By default, INIT=LINKEQ.
ITPRINT
requests that the “Iteration History” table be displayed. This option is ignored if the
NOPRINT option is speciﬁed.
LD
requests that haplotype frequencies be calculated under the assumption of no LD, in
addition to being calculated using the EM algorithm. When this option is speciﬁed,
the “Test for Allelic Associations” table is displayed, which contains statistics for the
likelihood ratio test for allelic associations. This option is ignored if the NOPRINT
option is speciﬁed.
MAXITER=number
speciﬁes the maximum number of iterations to be used in the EM algorithm. The
number must be a non-negative integer. Iterations are carried out until convergence
is reached according to the convergence criterion, or number iterations have been
performed. The default is MAXITER=100.
NDATA=SAS-data-set
names the input SAS data set containing names, or identiﬁers, for the markers used
in the output. There must be a NAME variable in this data set, which should contain
the same number of rows as there are markers in the input data set speciﬁed in the
DATA= option. When there are fewer rows than there are markers, markers without
a name are named using the PREFIX= option. Likewise, if there is no NDATA= data
set speciﬁed, the PREFIX= option is used.
NLAG=number
speciﬁes the number of consecutive iterations that must meet the convergence crite-
rion speciﬁed in the CONV= option (0.00001 by default) for the iteration process of
the EM algorithm to stop. The number must be a positive integer. If this option is
omitted, one iteration must satisfy the convergence criterion by default.
NOPRINT
suppresses the display of the “Analysis Information,” “Iteration History,” “Haplotype
Frequencies,” and “Test for Allelic Associations” tables. Either the OUT= option, the
TRAIT statement, or both must be used with the NOPRINT option.
NSTART=number
speciﬁes the number of different starts used for the EM algorithm. When this option is
speciﬁed, PROC HAPLOTYPE starts the iterations with different random initial val-
ues number−2 times as well as once with uniform frequencies for all the haplotypes
and once using haplotype frequencies assuming linkage equilibrium (independence).
Results on the analysis using the initial values that produce the best log likelihood
are then reported. The number must be a positive integer. If this option is omitted or
NSTART=1, only one start with initial frequencies generated according to the INIT=
option is used.

70
Chapter 5. The HAPLOTYPE Procedure
OUT=SAS-data-set
names the output SAS data set containing the probabilities of each genotype being
resolved into all of the possible haplotype pairs.
OUTCUT=number
speciﬁes a lower bound on a haplotype pair’s estimated probability given the in-
dividual’s genotype in order for that haplotype pair to be included in the OUT=
data set. The value of number must be between 0 and 1, inclusive. By default,
number = 0.00001. In order to be able to view all possible haplotype pairs for an
individual’s genotype, OUTCUT=0 can be speciﬁed.
PREFIX=preﬁx
speciﬁes a preﬁx to use in constructing names for marker variables in all output. For
example, if PREFIX=VAR, the names of the variables are VAR1, VAR2, ..., VARn.
Note that this option is ignored when the NDATA= option is speciﬁed, unless there
are fewer names in the NDATA data set than there are markers. If this option is
omitted, PREFIX=M is the default.
SE=BINOMIAL | JACKKNIFE
speciﬁes the standard error estimation method. There are two methods available: the
BINOMIAL option, which gives a standard error estimator from a binomial distribu-
tion and is the default method, and the JACKKNIFE option, which requests that the
jackknife procedure be used to estimate the standard error.
SEED=number
speciﬁes the initial seed for the random number generator used for creating the ini-
tial haplotype frequencies when INIT=RANDOM. The value for number must be a
positive integer; the computer clock time is the default. For more details about seed
values, refer to SAS Language Reference: Concepts.
BY Statement
BY variables ;
You can specify a BY statement with PROC HAPLOTYPE to obtain separate anal-
yses on observations in groups deﬁned by the BY variables. When a BY statement
appears, the procedure expects the input data set to be sorted in order of the BY
variables. The variables are one or more variables in the input data set.
If your input data set is not sorted in ascending order, use one of the following alter-
natives:
• Sort the data using the SORT procedure with a similar BY statement.
• Specify the BY statement option NOTSORTED or DESCENDING in the BY
statement for the HAPLOTYPE procedure. The NOTSORTED option does
not mean that the data are unsorted but rather that the data are arranged in
groups (according to values of the BY variables) and that these groups are not
necessarily in alphabetical or increasing numeric order.
• Create an index on the BY variables using the DATASETS procedure (in Base
SAS software).

Statistical Computations
71
For more information on the BY statement, refer to the discussion in SAS Language
Reference: Concepts. For more information on the DATASETS procedure, refer to
the discussion in the SAS Procedures Guide.
TRAIT Statement
TRAIT variable < / options > ;
The TRAIT statement identiﬁes the binary variable that indicates which individuals
are cases and which are controls, or represents a dichotomous trait. This variable
can be character or numeric, but must have only two nonmissing levels. When this
statement is used, the “Test for Marker-Trait Association” table is included in the
output.
There are two options you can specify in the TRAIT statement:
PERMUTATION= number
PERM=number
speciﬁes the number of permutations to be used to calculate the empirical p-value
of the haplotype case-control tests. This number must be a positive integer. By
default, no permutations are used and the p-value is calculated using the chi-square
test statistic. Note that this option can greatly increase the computation time.
TESTALL
speciﬁes that each individual haplotype should be tested for association with the
TRAIT variable. When this option is included in the TRAIT statement, the “Tests
for Haplotype-Trait Association” table is included in the output.
VAR Statement
VAR variables ;
The VAR statement identiﬁes the variables containing the marker alleles. The VAR
statement should contain 2m variable names, where m is the number of markers in
the data set and m > 1. Note that the two columns containing alleles for the same
marker must be listed consecutively.
Details
Statistical Computations
The EM Algorithm
The EM algorithm (Excofﬁer and Slatkin 1995; Hawley and Kidd 1995; Long,
Williams, and Urbanek 1995) iteratively furnishes the maximum likelihood estimates
(MLEs) of m-locus haplotype frequencies, for any integer m > 1, when a direct solu-
tion for the MLE is not readily feasible. The EM algorithm assumes HWE; it has been
argued (Fallin and Schork 2000) that positive increases in the Hardy-Weinberg dis-
equilibrium coefﬁcient (toward excess heterozygosity) may increase the error of the
EM estimates, but negative increases (toward excess homozygosity) do not demon-
strate a similar increase in the error. The iterations start with assigning initial values

72
Chapter 5. The HAPLOTYPE Procedure
to the haplotype frequencies. When the INIT=RANDOM option is included in the
PROC HAPLOTYPE statement, uniformly distributed random values are assigned to
all haplotype frequencies; when INIT=UNIFORM, each haplotype is given an ini-
tial frequency of 1/h, where h is the number of possible haplotypes in the sample.
Otherwise, the product of the frequencies of the alleles that comprise the haplotype
is used as the initial frequency for the haplotype. Different starting values can lead to
different solutions since a maximum that is found could be a local maximum and not
the global maximum. You can try different starting values for the EM algorithm by
specifying a number greater than 1 in the NSTART= option to get better estimates.
The expectation and maximization steps (E-step and M-step, respectively) are then
carried out until the convergence criterion is met or the number of iterations exceeds
the number speciﬁed in the MAXITER= option of the PROC HAPLOTYPE state-
ment.
For a sample of n individuals, suppose the ith individual has genotype Gi. The
probability of this genotype in the population is Pi, so the log likelihood is
n
log L =
log Pi
i=1
which is calculated after each iteration’s E-step of the EM algorithm, described in the
following paragraphs.
Let hj be the jth possible haplotype and fj its frequency in the population. For geno-
type Gi, the set Hi is the collection of pairs of haplotypes, hj and its “complement”
hci, that constitute that genotype. The haplotype frequencies f
j
j used in the E-step for
iteration 0 of the EM algorithm are given by the initial values; all subsequent itera-
tions use the haplotype frequencies calculated by the M-step of the previous iteration.
The E-step sets the genotype frequencies to be products of these frequencies:
Pi =
fjf ci
j
j∈Hi
When Gi has m heterozygous loci, there are 2m−1 terms in this sum. The number of
times haplotype hj occurs in the sum is written as mij, which is 2 if Gi is completely
homozygous, and either 1 or 0 otherwise.
The M-step sets new haplotype frequencies from the genotype frequencies:
n
1
mijfjf ci
j
fj = 2n
Pi
i=1
The EM algorithm increases the likelihood after each iteration, and multiple starting
points can generally lead to the global maximum.

Statistical Computations
73
Once the EM algorithm has arrived at the MLEs of the haplotype frequencies, each
individual i’s probability of having a particular haplotype pair (hj, hci) given the
j
individual’s genotype Gi is calculated as
fjf ci
j
Pr{hj, hci|
j Gi} =
Pi
for each j ∈ Hi. These probabilities are displayed in the OUT= data set.
Methods for Estimating Standard Error
Typically, an estimate of the variance of a haplotype frequency is obtained by invert-
ing the estimated information matrix from the distribution of genotype frequencies.
However, it often turns out that in a large multilocus system, a certain proportion
of haplotypes have ML frequencies equal or close to zero which makes the sample
information matrix nearly singular (Excofﬁer and Slatkin 1995). Therefore, two ap-
proximation methods are used to estimate the variances, as proposed by Hawley and
Kidd (1995).
The binomial method estimates the standard error by calculating the square root of
the binomial variance, as if the haplotype frequencies are obtained by direct counting:
fj(1 − fj)
VarB(fj) = 2n − 1
The jackknife method is a simulation-based method that can be used to estimate the
standard errors of haplotype frequencies. Each individual is in turn removed from
the sample, and all the haplotype frequencies are recalculated from this “delete-1”
sample. Let Tn−1,i be the haplotype frequency estimator from the ith “delete-1”
sample; then the jackknife variance estimator has the following formula:
n
n
n − 1
1
2
VarJ(fj) =
Tn−1,i −
Tn−1,j
n
n
i=1
j=1
and the square root of this variance estimate is the estimate of standard error. The
jackknife is less dependent on the model assumptions; however, it requires computing
the statistic n times.
Conﬁdence intervals with conﬁdence level 1 − α for the haplotype frequency esti-
mates from the ﬁnal iteration are then calculated using the following formula:
fj ± z1−α/2
Var(fj)
where z1−α/2 is the value from the standard normal distribution that has a right-tail
probability of α/2.

74
Chapter 5. The HAPLOTYPE Procedure
Testing for Allelic Associations
When the LD option is speciﬁed in the PROC HAPLOTYPE statement, haplotype
frequencies are calculated using the EM algorithm as well as by assuming no allelic
associations among loci, that is, no LD. Under the null hypothesis of no LD, hap-
lotype frequencies are simply the product of the individual allele frequencies. The
log likelihood under the null hypothesis, log L0, is calculated based on these hap-
lotype frequencies with degrees of freedom df0 =
m (k
i=1
i − 1), where m is the
number of loci and ki is the number of alleles for the ith locus (Zhao, Curtis, and
Sham 2000). Under the alternative hypothesis, the log likelihood, log L1 is calcu-
lated from the EM estimates of the haplotype frequencies with degrees of freedom
df1 = number of haplotypes − 1. A likelihood ratio test is used to test this hypothesis
as follows:
2(log L1 − log L0) ∼ χ2ν
where ν = df1 − df0 is the difference between the number of degrees of freedom
under the null hypothesis and the alternative.
Testing for Trait Associations
When the TRAIT statement is included in PROC HAPLOTYPE, case-control tests
are performed to test for association between the dichotomous trait (often, an indica-
tor of individuals with or without a disease) and the marker loci using haplotypes. In
addition to an omnibus test that is performed over all haplotypes, when the TESTALL
option is speciﬁed in the TRAIT statement, a test for association between each indi-
vidual haplotype and the trait is performed. Note that the individual haplotype tests
should only be performed if the omnibus test statistic is signiﬁcant.
Chi-Square Tests
The test performed over all haplotypes is based on the log likelihoods: under the
null hypothesis, the log likelihood over all the individuals in the sample, regardless
of the value of their trait variable, is calculated as described in the section “The EM
Algorithm” on page 71; the log likelihood is also calculated separately for the two sets
of individuals within the sample as determined by the trait value under the alternative
hypothesis of marker-trait association. A likelihood ratio test (LRT) statistic can then
be formed as follows:
X2 = 2(log L1 + log L2 − log L0)
where log L0, log L1, and log L2 are the log likelihoods under the null hypothesis, for
individuals with the ﬁrst trait value, and for individuals with the second trait value,
respectively (Zhao, Curtis, and Sham 2000). Deﬁning degrees of freedom for each
log likelihood similarly, this statistic has an asymptotic chi-square distribution with
(df1 + df2 − df0) degrees of freedom.
An association between individual haplotypes and the trait can also be tested. To do
so, the following contingency table is formed:

Missing Values
75
Table 5.1.
Haplotype-Trait Counts
Hap 1
Hap 2
Total
Trait 1
c11
c12
t1
Trait 2
c21
c22
t2
Total
h1
h2
T
where T = 2n = t1 + t2 = h1 + h2, the total number of haplotypes in the sample,
“Hap 1” refers to the current haplotype being tested, “Hap 2” refers to all other hap-
lotypes, and cij is the count of individuals with trait i and haplotype j (note that these
counts are not necessarily integers since haplotypes are not observed; they are cal-
culated based on the estimated haplotype frequencies). The usual contingency table
chi-square test statistic
(cij − tihj/T )2
tihj/T
i=1,2 j=1,2
has a 1 df chi-square distribution.
Exact Tests
Since the assumption of a chi-square distribution in the preceding section may not
hold, exact p-values can also be calculated. New samples are formed by randomly
permuting the trait values, and either of the chi-square test statistics shown in the
previous section can be calculated for each of these samples. The number of new
samples created is determined by the number given in the PERMUTATION= option
of the TRAIT statement. The exact p-value is then calculated as m/p, where m is
the number of samples with a test statistic greater than or equal to the test statistic
in the actual sample and p is the total number of permutation samples. This method
is used to obtain empirical p-values for both the overall and the individual haplotype
tests (Zhao, Curtis, and Sham 2000; Fallin et al. 2001).
Missing Values
An individual’s m-locus genotype is considered to be partially missing if any, but not
all, of the alleles are missing. Genotypes with all missing alleles are dropped. Also,
if there are any markers with all missing values in a BY group (or the entire data set if
there is no BY statement), no calculations are performed for that BY group. Partially
missing genotypes are used in the EM algorithm and the jackknife procedure. In
calculating the allele frequencies, missing alleles are dropped and the frequency of
an allele u at a marker is obtained as the number of u alleles in the data divided by
the total number of non-missing alleles at the marker in the data. In the E-step of
the EM algorithm, the frequency of a partially missing genotype is updated for every
possible genotype. In the M-step, haplotypes resulting from a missing genotype may
bear some missing alleles. Such a haplotype is not considered as a new haplotype,
but rather all existing haplotypes that have alleles identical to the nonmissing alle-
les of this haplotype are updated. Dealing with missing genotypes involves looping
through all possible genotypes in the E-step and all possible haplotypes in the M-step.

76
Chapter 5. The HAPLOTYPE Procedure
Depending on the input data set, missing genotypes can increase the computation time
substantially.
When the TRAIT statement is speciﬁed, any observation with a missing trait value is
dropped from calculations used in the tests for marker-trait association and haplotype-
trait associations. However, observations with missing trait values are included in
calculating the frequencies shown in the “Haplotype Frequencies” table, which are
then used in the OUT= data set. The combined frequencies listed in the “Tests for
Haplotype-Trait Association” table may therefore be different than these frequencies
in this situation.
OUT= Data Set
The OUT= data set contains the following variables: the BY variables (if any),
ID that identiﬁes the individual, the 2m variables listed in the VAR statement,
HAPLOTYPE1 and HAPLOTYPE2 that contain the pair of haplotypes of which
each genotype can be comprised, and PROB containing the probability of each indi-
vidual’s genotype being resolved into that haplotype pair.
Displayed Output
This section describes the displayed output from PROC HAPLOTYPE. See the “ODS
Table Names” section on page 78 for details about how this output interfaces with the
Output Delivery System.
Analysis Information
The “Analysis Information” table lists information on the following settings used in
PROC HAPLOTYPE:
• Loci Used, the loci used to form haplotypes
• Number of Individuals
• Number of Starts, the value speciﬁed in the NSTART= option or the default (1)
• Convergence Criterion, the value speciﬁed in the CONV= option or the default
(0.00001)
• Iterations Checked for Conv., the value speciﬁed in the NLAG= option or the
default (1)
• Maximum Number of Iterations, the value speciﬁed in the MAXITER= option
or the default (100)
• Number of Iterations Used, as determined by the CONV= or MAXITER= op-
tion
• Log Likelihood, from the last iteration performed
• Initialization Method, the method speciﬁed in the INIT= option or “Linkage
Equilibrium” by default
• Random Number Seed, the value speciﬁed in the SEED= option or generated
by the system clock, or “Not Used” if INIT=LINKEQ or INIT=UNIFORM

Displayed Output
77
• Standard Error Method, the method speciﬁed in the SE= option or “Binomial”
by default
• Haplotype Frequency Cutoff, the value speciﬁed in the CUTOFF= option or
the default (0)
Iteration History
The “Iteration History” table displays the log likelihood and the ratio of change for
each iteration of the EM algorithm.
Haplotype Frequencies
The “Haplotype Frequencies” table lists all the possible m-locus haplotypes in the
sample (where 2m variables are speciﬁed in the VAR statement), with an estimate of
the haplotype frequency, the standard error of the frequency, and the lower and up-
per limits of the conﬁdence interval for the frequency based on the conﬁdence level
determined by the ALPHA= option of the PROC HAPLOTYPE statement (0.95 by
default). When the LD option is speciﬁed in the PROC HAPLOTYPE statement,
haplotype frequency estimates are calculated both under the null hypothesis of no al-
lelic association by taking the product of allele frequencies, and under the alternative,
which allows for associations, using the EM algorithm.
Test for Allelic Associations
The “Test for Allelic Associations” table displays the degrees of freedom and log
likelihood for the null hypothesis of no association and the alternative hypothesis of
associations between markers. The chi-square statistic and its p-value are also shown
for the test of these hypotheses.
Test for Marker-Trait Association
The “Test for Marker-Trait Association” table displays the number of observations,
degrees of freedom, and log likelihood for both trait values as well as the com-
bined sample. The chi-square test statistic and its corresponding p-value from per-
forming the case-control test, testing the hypothesis of no association between the
trait and the marker loci used in PROC HAPLOTYPE, are also given. When the
PERMUTATION= option is included in the TRAIT statement, exact p-values are
provided as well.
Tests for Haplotype-Trait Association
The “Tests for Haplotype-Trait Association” table displays statistics from case-
control tests performed on each individual haplotype when the TESTALL option is
included in the TRAIT statement. A signiﬁcant p-value indicates that there is an as-
sociation between the haplotype and the trait. When the PERMUTATION= option is
also given in the TRAIT statement, exact p-values are provided as well.

78
Chapter 5. The HAPLOTYPE Procedure
ODS Table Names
PROC HAPLOTYPE assigns a name to each table it creates, and you must use this
name to reference the table when using the Output Delivery System (ODS). These
names are listed in the following table.
Table 5.2.
ODS Tables Created by the HAPLOTYPE Procedure
ODS Table Name
Description
Statement or Option
AnalysisInfo
Analysis information
default
IterationHistory
Iteration history
ITPRINT
ConvergenceStatus
Convergence status
default
HaplotypeFreq
Haplotype frequencies
default
LDTest
Test for allelic associations
LD
CCTest
Test for marker-trait association
TRAIT statement
HapTraitTest
Tests for haplotype-trait association
TRAIT / TESTALL
Examples
Example 5.1. Estimating Three-Locus Haplotype Frequencies
Here is an example of 227 individuals genotyped at three markers, data which were
created based on genotype frequency tables from the Lab of Statistical Genetics at
Rockefeller University (2001). Note that when reading in the data, there are four
individuals’ genotypes per line, except for the last line of the DATA step, which
contains three individuals’ genotypes. The SAS data set that is created contains one
individual per row with six columns representing the two alleles at each of three
marker loci.
data ehdata;
input m1-m6 @@;
datalines;
1 1 1 1 1 3 1 1 1 1 1 3 1 1 1 1 1 3 1 1 1 1 1 3
1 1 1 1 1 3 1 1 1 1 1 3 1 1 1 1 1 3 1 1 1 1 1 3
1 1 1 1 1 3 1 1 1 1 1 3 1 1 1 1 1 3 1 1 1 1 1 3
1 1 1 1 2 3 1 1 1 1 2 3 1 1 1 1 2 3 1 1 1 1 3 3
1 1 1 1 3 3 1 1 1 1 3 3 1 1 1 1 3 3 1 1 1 1 3 3
1 1 1 1 3 3 1 1 1 1 3 3 1 1 1 1 3 3 1 1 1 1 3 3
1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 2 1 1 1 2 1 2
1 1 1 2 1 2 1 1 1 2 1 2 1 1 1 2 1 2 1 1 1 2 1 2
1 1 1 2 1 2 1 1 1 2 1 2 1 1 1 2 1 2 1 1 1 2 1 2
1 1 1 2 1 2 1 1 1 2 1 2 1 1 1 2 2 2 1 1 1 2 2 2
1 1 1 2 1 3 1 1 1 2 1 3 1 1 1 2 2 3 1 1 1 2 2 3
1 1 1 2 2 3 1 1 1 2 3 3 1 1 1 2 3 3 1 1 1 2 3 3
1 1 1 2 3 3 1 1 2 2 1 1 1 1 2 2 1 1 1 1 2 2 1 1
1 1 2 2 1 1 1 1 2 2 1 1 1 1 2 2 1 2 1 1 2 2 1 2
1 1 2 2 1 2 1 1 2 2 1 2 1 1 2 2 2 2 1 1 2 2 2 2

Example 5.1. Estimating Three-Locus Haplotype Frequencies
79
1 1 2 2 2 2 1 1 2 2 2 2 1 1 2 2 1 3 1 1 2 2 1 3
1 1 2 2 3 3 1 1 2 2 3 3 1 1 2 2 3 3 1 1 2 2 3 3
1 1 2 2 3 3 1 1 2 2 3 3 1 1 2 2 3 3 1 1 2 2 3 3
1 1 2 2 3 3 1 1 2 2 3 3 1 1 2 2 3 3 1 1 2 2 3 3
1 1 2 2 3 3 1 1 2 2 3 3 1 1 2 2 3 3 1 1 2 2 3 3
1 1 2 2 3 3 1 1 2 2 3 3 1 2 1 1 1 1 1 2 1 1 1 1
1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1
1 2 1 1 1 1 1 2 1 1 1 2 1 2 1 1 1 2 1 2 1 1 1 3
1 2 1 1 1 3 1 2 1 1 2 3 1 2 1 1 2 3 1 2 1 1 2 3
1 2 1 1 2 3 1 2 1 1 2 3 1 2 1 1 2 3 1 2 1 1 3 3
1 2 1 1 3 3 1 2 1 1 3 3 1 2 1 2 1 1 1 2 1 2 1 1
1 2 1 2 1 1 1 2 1 2 1 1 1 2 1 2 1 1 1 2 1 2 1 1
1 2 1 2 1 1 1 2 1 2 1 1 1 2 1 2 1 1 1 2 1 2 1 3
1 2 1 2 1 3 1 2 1 2 1 3 1 2 1 2 2 3 1 2 1 2 2 3
1 2 1 2 2 3 1 2 1 2 2 3 1 2 1 2 3 3 1 2 1 2 3 3
1 2 2 2 1 1 1 2 2 2 1 1 1 2 2 2 1 1 1 2 2 2 1 1
1 2 2 2 1 1 1 2 2 2 1 1 1 2 2 2 1 1 1 2 2 2 1 1
1 2 2 2 1 1 1 2 2 2 1 1 1 2 2 2 1 2 1 2 2 2 1 2
1 2 2 2 1 2 1 2 2 2 1 3 1 2 2 2 1 3 1 2 2 2 2 3
1 2 2 2 2 3 1 2 2 2 2 3 1 2 2 2 3 3 1 2 2 2 3 3
1 2 2 2 3 3 1 2 2 2 3 3 1 2 2 2 3 3 1 2 2 2 3 3
1 2 2 2 3 3 1 2 2 2 3 3 2 2 1 1 1 1 2 2 1 1 1 2
2 2 1 1 1 2 2 2 1 1 2 2 2 2 1 1 2 2 2 2 1 1 2 2
2 2 1 1 2 2 2 2 1 1 2 2 2 2 1 1 2 2 2 2 1 1 2 2
2 2 1 1 2 2 2 2 1 1 2 2 2 2 1 1 2 2 2 2 1 1 1 3
2 2 1 1 1 3 2 2 1 1 2 3 2 2 1 1 2 3 2 2 1 1 2 3
2 2 1 1 2 3 2 2 1 1 2 3 2 2 1 1 2 3 2 2 1 1 2 3
2 2 1 1 2 3 2 2 1 1 2 3 2 2 1 1 3 3 2 2 1 1 3 3
2 2 1 1 3 3 2 2 1 1 3 3 2 2 1 2 1 1 2 2 1 2 1 1
2 2 1 2 1 1 2 2 1 2 1 1 2 2 1 2 1 1 2 2 1 2 1 2
2 2 1 2 1 2 2 2 1 2 1 2 2 2 1 2 2 2 2 2 1 2 2 2
2 2 1 2 2 2 2 2 1 2 2 2 2 2 1 2 1 3 2 2 1 2 1 3
2 2 1 2 1 3 2 2 1 2 1 3 2 2 1 2 1 3 2 2 1 2 1 3
2 2 1 2 2 3 2 2 1 2 2 3 2 2 1 2 2 3 2 2 1 2 2 3
2 2 1 2 2 3 2 2 1 2 2 3 2 2 1 2 2 3 2 2 1 2 3 3
2 2 1 2 3 3 2 2 1 2 3 3 2 2 2 2 1 1 2 2 2 2 1 1
2 2 2 2 1 1 2 2 2 2 1 1 2 2 2 2 1 1 2 2 2 2 1 1
2 2 2 2 1 1 2 2 2 2 1 1 2 2 2 2 1 1 2 2 2 2 1 2
2 2 2 2 1 2 2 2 2 2 1 2 2 2 2 2 2 3 2 2 2 2 2 3
2 2 2 2 2 3 2 2 2 2 3 3 2 2 2 2 3 3 2 2 2 2 3 3
2 2 2 2 3 3 2 2 2 2 3 3 2 2 2 2 3 3 2 2 2 2 3 3
2 2 2 2 3 3 2 2 2 2 3 3 2 2 2 2 3 3
;
The haplotype frequencies can be estimated using the EM algorithm and their stan-
dard errors estimated using the jackknife method by implementing the following
code:
proc haplotype data=ehdata se=jackknife maxiter=20 itprint nlag=4;
var m1-m6;
run;
This produces the following ODS output:

80
Chapter 5. The HAPLOTYPE Procedure
Output 5.1.1.
Analysis Information for the HAPLOTYPE Procedure
The HAPLOTYPE Procedure
Analysis Information
Loci Used
M1 M2 M3
Number of Individuals
227
Number of Starts
1
Convergence Criterion
0.00001
Iterations Checked for Conv.
4
Maximum Number of Iterations
20
Number of Iterations Used
11
Log Likelihood
-934.97918
Initialization Method
Linkage Equilibrium
Standard Error Method
Jackknife
Haplotype Frequency Cutoff
0
Output 5.1.1 displays information on several of the settings used to perform the
HAPLOTYPE procedure on the ehdata data set. Note that though the MAXITER=
option was set to 20 iterations, convergence according to the criterion of 0.00001
was reached for four consecutive iterations prior to the 20th iteration, at which point
the estimation process stopped. To obtain more precise frequency estimates, a lower
convergence criterion can be used.
Output 5.1.2.
Iteration History for the HAPLOTYPE Procedure
Iteration History
Ratio
Iter
LogLike
Changed
0
-953.89697
1
-937.92181
0.01675
2
-935.91870
0.00214
3
-935.35775
0.00060
4
-935.13050
0.00024
5
-935.03710
0.00010
6
-935.00051
0.00004
7
-934.98679
0.00001
8
-934.98180
0.00001
9
-934.98002
0.00000
10
-934.97940
0.00000
11
-934.97918
0.00000
Output 5.1.3.
Convergence Status for the HAPLOTYPE Procedure
Algorithm converged.
Because the ITPRINT option was speciﬁed in the PROC HAPLOTYPE statement,
the iteration history of the EM algorithm is included in the ODS output. Output 5.1.2
contains the table displaying this information. By default, the “Convergence Status”
table is displayed (Output 5.1.3), which only consists of one line indicating whether

Example 5.2. Estimating Three-Locus Haplotype Frequencies
81
convergence was met.
Output 5.1.4.
Haplotype Frequencies from the HAPLOTYPE Procedure
Haplotype Frequencies
Standard
95% Confidence
Number
Haplotype
Freq
Error
Limits
1
1-1-1
0.09170
0.01505
0.06221
0.12119
2
1-1-2
0.02080
0.00952
0.00214
0.03946
3
1-1-3
0.11509
0.01766
0.08048
0.14971
4
1-2-1
0.07904
0.01696
0.04580
0.11228
5
1-2-2
0.06768
0.01546
0.03738
0.09799
6
1-2-3
0.12788
0.02094
0.08685
0.16891
7
2-1-1
0.05521
0.01227
0.03115
0.07926
8
2-1-2
0.11700
0.01782
0.08207
0.15193
9
2-1-3
0.07376
0.01495
0.04446
0.10307
10
2-2-1
0.11766
0.01831
0.08177
0.15355
11
2-2-2
0.03020
0.00899
0.01257
0.04782
12
2-2-3
0.10397
0.01833
0.06805
0.13989
Output 5.1.4 displays the 12 possible three-locus haplotypes in the data and their
estimated haplotype frequencies, standard errors, and bounds for the 95% conﬁdence
intervals for the estimates.
To see how the CUTOFF= option affects the “Haplotype Frequencies” table, suppose
you want to view only the haplotypes with an estimated frequency of at least 0.10.
The following code creates such a table:
proc haplotype data=ehdata se=jackknife cutoff=0.10 nlag=4;
var m1-m6;
run;
Now, the “Haplotype Frequencies” table is displayed as:
Output 5.1.5.
Haplotype Frequencies from the HAPLOTYPE Procedure Using
the CUTOFF= Option
The HAPLOTYPE Procedure
Haplotype Frequencies
Standard
95% Confidence
Number
Haplotype
Freq
Error
Limits
1
1-1-3
0.11509
0.01766
0.08048
0.14971
2
1-2-3
0.12788
0.02094
0.08685
0.16891
3
2-1-2
0.11700
0.01782
0.08207
0.15193
4
2-2-1
0.11766
0.01831
0.08177
0.15355
5
2-2-3
0.10397
0.01833
0.06805
0.13989
Output 5.1.5 displays only the four three-locus haplotypes with estimated frequen-
cies of at least 0.10. This option is especially useful for keeping the “Haplotype
Frequencies” table to a manageable size when many marker loci or loci with several

82
Chapter 5. The HAPLOTYPE Procedure
alleles are used, and many of the haplotypes have estimated frequencies very near
zero. Using CUTOFF=1 suppresses the “Haplotype Frequencies” table.
Example 5.2. Using Multiple Runs of the EM Algorithm
Continuing the example from the section “Getting Started” on page 64, suppose you
are concerned that the likelihood reached a local and not a global maximum. You can
request that PROC HAPLOTYPE use several different sets of initial haplotype fre-
quencies to ensure that you ﬁnd a global maximum of the likelihood. The following
code invokes the EM algorithm using ﬁve different sets of initial values, including
the set used in the Getting Started example:
proc haplotype data=markers prefix=SNP init=random seed=51220
nstart=5;
var m1-m8;
run;
The NSTART=5 option requests that the EM algorithm be run three times using ran-
domly generated initial frequencies, including once using the seed 51220 that was
previously used, once using uniform initial frequencies, and once using haplotype
frequencies given by the product of the allele frequencies. The following two tables
are from the run that produced the best log likelihood:

Example 5.3. Testing for Linkage Disequilibrium
83
Output 5.2.1.
Output from PROC HAPLOTYPE
The HAPLOTYPE Procedure
Analysis Information
Loci Used
SNP1 SNP2 SNP3 SNP4
Number of Individuals
25
Number of Starts
5
Convergence Criterion
0.00001
Iterations Checked for Conv.
1
Maximum Number of Iterations
100
Number of Iterations Used
15
Log Likelihood
-95.94738
Initialization Method
Random
Random Number Seed
23152
Standard Error Method
Binomial
Haplotype Frequency Cutoff
0
Haplotype Frequencies
Standard
95% Confidence
Number
Haplotype
Freq
Error
Limits
1
A-A-A-A
0.14302
0.05001
0.04500
0.24105
2
A-A-A-B
0.07527
0.03769
0.00140
0.14914
3
A-A-B-A
0.00000
0.00000
0.00000
0.00000
4
A-A-B-B
0.00000
0.00010
0.00000
0.00020
5
A-B-A-A
0.09307
0.04151
0.01173
0.17442
6
A-B-A-B
0.05335
0.03210
0.00000
0.11627
7
A-B-B-A
0.00002
0.00061
0.00000
0.00122
8
A-B-B-B
0.07526
0.03769
0.00140
0.14913
9
B-A-A-A
0.08638
0.04013
0.00772
0.16504
10
B-A-A-B
0.08792
0.04046
0.00863
0.16722
11
B-A-B-A
0.07921
0.03858
0.00359
0.15482
12
B-A-B-B
0.10819
0.04437
0.02122
0.19517
13
B-B-A-A
0.10098
0.04304
0.01662
0.18534
14
B-B-A-B
0.00000
0.00001
0.00000
0.00002
15
B-B-B-A
0.09732
0.04234
0.01433
0.18030
16
B-B-B-B
0.00000
0.00001
0.00000
0.00002
Example 5.3. Testing for Linkage Disequilibrium
Again looking at the data from the Lab of Statistical Genetics at Rockefeller
University (2001), if you request the test for linkage disequilibrium by specifying the
LD option in the PROC HAPLOTYPE statement, the “Test for Allelic Associations”
table containing the test statistics is included in the output.
proc haplotype data=ehdata ld;
var m1-m6;
run;
The “Haplotype Frequencies” table now contains an extra column of the haplotype
frequencies under the null hypothesis.

84
Chapter 5. The HAPLOTYPE Procedure
Output 5.3.1.
Haplotype Frequencies Under the Null and Alternative Hypotheses
The HAPLOTYPE Procedure
Haplotype Frequencies
Standard
95% Confidence
Number
Haplotype
H0 Freq
H1 Freq
Error
Limits
1
1-1-1
0.08172
0.09124
0.01353
0.06472
0.11775
2
1-1-2
0.05605
0.02124
0.00677
0.00796
0.03452
3
1-1-3
0.10006
0.11501
0.01499
0.08563
0.14439
4
1-2-1
0.09084
0.07952
0.01271
0.05461
0.10443
5
1-2-2
0.06231
0.06726
0.01177
0.04419
0.09032
6
1-2-3
0.11122
0.12794
0.01569
0.09718
0.15870
7
2-1-1
0.08100
0.05540
0.01075
0.03433
0.07647
8
2-1-2
0.05556
0.11690
0.01510
0.08732
0.14649
9
2-1-3
0.09918
0.07378
0.01228
0.04971
0.09785
10
2-2-1
0.09005
0.11746
0.01513
0.08781
0.14711
11
2-2-2
0.06176
0.03028
0.00805
0.01450
0.04606
12
2-2-3
0.11025
0.10398
0.01434
0.07587
0.13209
Note that since the INIT= option was omitted from the PROC HAPLOTYPE state-
ment, the initial haplotype frequencies used in the EM algorithm are identical to the
frequencies that appear in the H0 FREQ column in Output 5.3.1. The frequencies
in the H1 FREQ column are those calculated from the ﬁnal iteration of the EM al-
gorithm, and these frequencies’ standard errors and conﬁdence limits are included in
the table as well.
Output 5.3.2.
Testing for Linkage Disequilibrium Using the LD Option
Test for Allelic Associations
Chi-
Pr >
Hypothesis
DF
LogLike
Square
ChiSq
H0: No Association
4
-953.89697
H1: Allelic Associations
11
-934.98180
37.8303
<.0001
Output 5.3.2 displays the log likelihood under the null hypothesis assuming indepen-
dence among all the loci and the alternative, which allows for associations between
markers. The empirical chi-square test statistic of the likelihood ratio test is calcu-
lated as X2 = 2[−934.98180 − (−953.89697)] = 37.8303 with degrees of freedom
ν = 11 − 4 = 7 that gives a p-value < 0.0001. The test indicates signiﬁcant linkage
disequilibrium among the three loci, as shown in the online documentation from the
Lab of Statistical Genetics at Rockefeller University (2001).

Example 5.4. Testing for Marker-Trait Associations
85
Example 5.4. Testing for Marker-Trait Associations
To demonstrate how the TRAIT statement can be utilized, a subset of data from
GAW12 (Wijsman et al. 2001) is read into a SAS data set as follows:
data gaw;
input status $ a1-a24;
datalines;
U 8 4 4 4 2 7 3 2 1 4 10 2
6 6 1 2 1 1 7
7
8 7 8
8
U 5 9 3 5 3 4 2 3 4 3 14 10 3 6 7 7 1 4 5
12 3 3 1
2
A 8 2 5 1 6 3 3 5 3 4 5
3
3 1 5 3 3 4 7
7
7 3 7
7
U 7 8 5 3 8 4 5 3 3 4 13 8
1 3 4 5 4 4 10 7
1 2 2
2
U 9 2 2 5 7 6 9 3 2 4 3
2
5 2 1 2 2 4 5
7
4 3 1
12
U 2 7 1 4 6 7 8 4 4 3 10 5
5 2 4 3 3 1 8
11 2 3 7
7
U 7 7 6 6 1 4 9 5 3 1 14 6
5 3 1 3 3 1 12 1
3 7 7
7
U 4 4 3 7 3 2 8 9 3 1 9
10 6 4 5 3 1 4 10 8
8 5 8
2
A 8 9 6 5 6 4 3 4 4 1 9
1
7 7 2 5 4 1 1
1
5 1 10 2
U 9 5 6 1 2 6 3 3 3 2 8
7
1 5 3 8 1 3 1
8
3 5 1
4
U 8 1 1 5 8 6 3 3 4 3 1
10 3 1 2 3 4 4 5
10 4 5 7
9
A 7 2 3 4 1 3 2 3 3 3 7
1
7 7 2 3 3 4 5
1
5 5 7
9
U 9 3 1 1 2 3 9 8 3 1 13 13 7 1 2 2 3 4 10 3
1 1 10 1
U 2 9 6 1 3 4 3 2 4 3 2
1
4 3 8 1 4 3 9
5
4 2 1
10
U 2 1 1 4 4 7 5 8 3 4 10 13 5 4 4 4 4 3 12 2
3 7 2
12
U 7 7 6 6 3 3 9 3 4 3 14 14 2 1 2 2 1 4 9
1
5 8 4
10
U 1 3 6 5 5 4 9 4 3 4 13 1
2 3 1 2 1 3 1
3
5 3 2
1
U 9 2 6 6 3 4 3 4 2 4 14 9
5 2 4 4 1 1 12 7
5 5 11 7
U 3 3 5 5 8 4 6 5 4 3 2
13 7 1 1 2 3 2 10 7
3 4 7
10
U 4 3 4 5 7 7 8 8 3 3 8
13 3 4 3 2 4 1 1
12 1 3 10 7
U 3 8 1 1 3 8 8 3 4 4 13 12 1 4 5 7 1 4 1
8
3 2 3
3
U 7 8 5 7 7 3 3 3 4 3 14 5
5 1 8 5 4 4 12 12 5 5 10 10
A 7 2 5 4 1 3 3 9 4 3 13 9
2 3 6 5 4 4 1
10 5 2 1
10
U 7 2 4 5 6 1 1 2 4 4 10 8
4 5 5 4 1 1 6
9
2 7 2
12
U 3 3 4 2 7 3 8 3 4 4 14 12 3 2 5 4 3 3 9
3
2 1 12 12
A 2 3 4 1 4 3 3 3 4 4 6
14 1 1 2 2 1 3 3
1
2 8 2
7
U 5 9 3 1 7 4 3 4 2 4 9
8
5 7 3 1 1 3 9
9
2 5 1
9
U 8 5 6 5 3 7 4 4 4 3 10 9
7 5 2 8 4 1 7
8
2 7 12 1
U 9 8 5 5 7 3 6 5 1 3 13 5
2 2 8 7 3 3 9
12 1 3 4
1
A 7 8 5 2 3 5 3 9 3 3 12 5
1 1 1 2 1 4 7
2
5 3 6
1
A 5 4 1 1 3 7 4 5 3 3 14 13 7 3 3 1 4 3 1
8
3 3 2
9
U 8 9 3 2 7 3 8 9 4 1 1
12 5 4 4 6 3 4 2
7
5 2 3
10
A 9 2 3 5 3 3 2 3 2 3 14 13 6 1 3 1 4 3 3
2
3 1 1
7
A 2 5 7 5 6 7 9 4 3 4 14 13 5 1 2 3 4 4 2
10 3 1 12 12
U 7 2 3 1 1 3 4 4 3 4 2
8
5 3 4 6 3 3 10 12 8 3 2
1
A 7 5 1 5 3 3 9 2 3 3 10 6
1 7 2 4 4 4 10 9
1 8 7
3
U 3 2 5 5 4 3 3 5 1 3 1
1
5 2 1 2 3 3 10 3
3 3 10 4
A 3 2 5 5 8 5 3 7 4 3 2
14 5 5 3 3 3 4 11 1
6 2 1
10
A 2 7 5 5 3 2 9 4 3 3 1
7
7 5 4 7 4 1 12 7
2 3 12 9
A 5 7 2 3 7 3 3 3 3 4 9
2
4 1 2 7 1 4 6
1
2 1 7
7
U 7 4 3 4 5 3 3 8 3 3 2
8
4 6 7 7 4 1 3
1
2 4 12 1
U 7 8 5 4 4 7 9 9 4 3 5
13 7 1 4 4 4 4 9
8
8 3 3
10
U 2 8 4 5 3 7 3 4 3 3 8
14 6 4 6 2 3 4 7
1
3 3 3
10
U 6 8 1 3 6 7 5 4 3 4 1
12 3 7 8 4 3 4 12 12 4 7 12 6
A 8 7 3 1 3 6 4 4 3 3 4
10 6 5 8 1 1 4 1
10 2 2 5
2

86
Chapter 5. The HAPLOTYPE Procedure
U 2 8 6 6 4 8 4 3 4 3 9
1
1 1 2 3 4 4 2
6
2 3 9
7
U 9 8 4 3 7 3 8 4 4 3 8
8
6 6 4 5 3 4 5
5
1 8 10 1
U 9 3 5 1 8 6 5 3 3 2 13 2
3 5 8 2 1 3 1
10 3 3 10 12
U 2 9 1 6 7 4 9 9 4 1 8
1
3 2 5 8 4 4 3
1
3 3 12 7
U 8 8 6 2 3 2 2 4 3 4 6
12 3 1 7 2 4 4 5
9
2 3 1
10
;
This data set contains twelve markers. Suppose you are interested in testing three of
the marker loci at a time for association with the trait (status in this case: “A” for
affected or “U” for unaffected with a particular disease) over all of their haplotypes.
That is, assuming the markers are numbered in the order they appear on the chromo-
some, haplotypes at marker loci 1 through 3 are analyzed, then haplotypes at marker
loci 4 through 6 are analyzed, and so on. These tests may be performed in addition to,
or in place of, single-marker case-control tests (see Chapter 3 for more information).
In order to reduce the amount of SAS code needed for this analysis, a SAS macro can
be used as follows:
%macro hap_trait;
%do firsta=1 %to 19 %by 6;
%let lasta=%eval(&firsta+5);
%let firstm=%eval((&firsta+1)/2);
%let lastm=%eval(&lasta/2);
title "Markers &firstm through &lastm";
proc haplotype data=gaw noprint;
var a&firsta-a&lasta;
trait status;
run;
%end;
%mend;
%hap_trait
Since the NOPRINT option is speciﬁed, this code produces only the “Test for Marker-
Trait Association” table each of the four times PROC HAPLOTYPE is invoked.

Example 5.4. Testing for Marker-Trait Associations
87
Output 5.4.1.
Testing for Marker-Trait Associations Using Haplotypes
Markers 1 through 3
The HAPLOTYPE Procedure
Test for Marker-Trait Association
Trait
Trait
Num
Chi-
Pr >
Number
Value
Obs
DF
LogLike
Square
ChiSq
1
U
36
156
-245.18487
2
A
14
68
-69.90500
Combined
50
181
-355.16139
40.0715
0.5990
Markers 4 through 6
The HAPLOTYPE Procedure
Test for Marker-Trait Association
Trait
Trait
Num
Chi-
Pr >
Number
Value
Obs
DF
LogLike
Square
ChiSq
1
U
36
140
-236.78471
2
A
14
62
-78.22280
Combined
50
162
-349.30084
34.2933
0.7243
Markers 7 through 9
The HAPLOTYPE Procedure
Test for Marker-Trait Association
Trait
Trait
Num
Chi-
Pr >
Number
Value
Obs
DF
LogLike
Square
ChiSq
1
U
36
119
-242.53993
2
A
14
56
-68.34854
Combined
50
139
-348.95917
38.0707
0.3753
Markers 10 through 12
The HAPLOTYPE Procedure
Test for Marker-Trait Association
Trait
Trait
Num
Chi-
Pr >
Number
Value
Obs
DF
LogLike
Square
ChiSq
1
U
36
180
-268.92245
2
A
14
75
-85.15400
Combined
50
233
-395.70275
41.6263
0.0069

88
Chapter 5. The HAPLOTYPE Procedure
Output 5.4.1 displays the four tables that are created by this macro. The ﬁrst cor-
responds to testing the three-locus haplotypes at the ﬁrst three marker loci with the
TRAIT variable, the second to the second set of three markers, and so on. From
the LRTs that are performed and summarized in the output, it can be concluded that
out of the four sets of marker loci tested, only haplotypes at markers 10, 11, and 12
show a signiﬁcant association with the trait variable status. The chi-square statis-
tic for testing the haplotypes at these markers for association with disease status is
calculated as 41.62630 = 2(−268.9224489 − 85.15400274 + 395.70275165) with
degrees of freedom 22 = 180 + 75 − 233, which has a p-value of 0.0069.
Suppose you would like to further explore the association between these three mark-
ers and the trait. You can also perform tests of association between each individual
haplotype at these marker loci and disease status using the following code:
ods output haplotype.haptraittest=outhap;
proc haplotype data=gaw noprint;
var a19-a24;
trait status / testall perm=100;
run;
proc print data=outhap(obs=20) noobs;
title ’The HAPLOTYPE Procedure’;
title2 ’ ’;
title3 ’Tests for Haplotype-Trait Association’;
run;
ods output close;
The TESTALL option indicates that a test for trait association should be performed
on each haplotype using a chi-square test statistic, which is performed by default. In
addition, since the PERM=100 option is included, an empirical p-value is calculated.
Due to the number of alleles at each marker in this example, this option increases the
computation time substantially, even with this small number of permutations.

Example 5.5. Creating a Data Set for Haplotype Trend Regression (HTR)
89
Output 5.4.2.
Using the TESTALL Option on Markers 10-12
The HAPLOTYPE Procedure
Tests for Haplotype-Trait Association
Combined
Prob
Prob
Number
Haplotype
Trait1Freq
Trait2Freq
Freq
ChiSq
ChiSq
Exact
1
1-1-2
0.00000
0.03571
0.00000
0
1.0000
1.0000
2
1-1-7
0.00000
0.00000
0.01000
1.0101
0.3149
0.3600
3
1-1-10
0.00000
0.00000
0.01950
1.9883
0.1585
0.1800
4
1-2-1
0.00000
0.01786
0.03000
2.3686
0.1238
0.1700
5
1-2-2
0.00000
0.05357
0.01000
6.0967
0.0135
0.0600
6
1-2-3
0.00000
0.00000
0.00000
0.001666
0.9674
0.6100
7
1-2-5
0.00000
0.00000
0.01000
1.0101
0.3149
0.2700
8
1-2-7
0.00000
0.05357
0.00000
0
1.0000
1.0000
9
1-2-10
0.00000
0.01786
0.00000
0
1.0000
1.0000
10
1-2-12
0.00000
0.00000
0.00000
0
1.0000
1.0000
11
1-3-1
0.00694
0.00000
0.00000
0
1.0000
1.0000
12
1-3-2
0.00000
0.01786
0.01000
0.9019
0.3423
0.4300
13
1-3-3
0.02777
0.00000
0.02000
0.7934
0.3731
0.7500
14
1-3-4
0.00000
0.00000
0.00000
0
1.0000
1.0000
15
1-3-7
0.04167
0.00000
0.02045
2.2035
0.1377
0.1700
16
1-3-9
0.00000
0.01786
0.00000
0
1.0000
1.0000
17
1-3-10
0.00000
0.00000
0.00000
7.8011E-8
0.9998
0.9300
18
1-3-12
0.01389
0.00000
0.01006
0.3905
0.5320
0.8200
19
1-4-1
0.01389
0.00000
0.00000
0
1.0000
1.0000
20
1-4-12
0.00000
0.00000
0.00000
0
1.0000
1.0000
Output 5.4.2 displays the table “Test for Haplotype-Trait Association” as a SAS data
set using the ODS system in order to show only the ﬁrst 20 rows. The table con-
tains haplotypes at markers 10, 11, and 12 and their estimated frequencies among
individuals with the ﬁrst trait value, individuals with the second trait value, and all
individuals. The chi-square statistic testing whether the frequencies between the two
trait groups are signiﬁcantly different is also shown, along with its 1 df p-value. Note
that none of the haplotypes shown here have a signiﬁcant association with disease
status.
Example 5.5. Creating a Data Set for Haplotype Trend
Regression (HTR)
Zaykin et al. (2002) discuss HTR, an approach to testing haplotypes for association
with a phenotype using a regression model, which can be more powerful than the
omnibus chi-square test performed in PROC HAPLOTYPE. The output data set pro-
duced by PROC HAPLOTYPE can easily be transformed into one that can be used
by one of the regression procedures offered by SAS/STAT to implement HTR.
Here is an example data set that can be analyzed using PROC HAPLOTYPE:

90
Chapter 5. The HAPLOTYPE Procedure
data alleles;
input (a1-a6) ($) disease;
datalines;
A
a
B
B
c
C
1
A
A
B
b
c
C
1
a
A
B
b
c
c
0
A
A
B
B
c
C
1
A
A
b
B
c
C
1
A
A
B
b
C
c
0
A
a
b
B
C
c
1
A
A
b
B
C
c
1
A
a
B
B
c
c
1
a
a
B
b
c
c
0
A
A
B
B
C
C
1
A
A
B
B
c
c
1
a
A
b
b
c
c
0
A
A
B
B
c
c
1
A
A
b
b
c
c
0
A
A
b
B
c
C
0
A
A
B
b
c
C
1
A
a
b
B
c
c
1
A
a
B
B
c
C
1
A
A
b
b
C
C
0
A
A
B
B
C
C
1
A
A
b
B
C
c
1
A
A
b
B
c
C
1
a
A
B
b
C
c
0
A
a
B
B
C
C
0
A
A
B
B
C
c
1
A
A
B
b
C
c
0
A
A
B
B
c
C
1
a
A
B
b
C
C
1
A
a
B
b
C
c
1
A
A
B
b
c
C
1
A
a
B
B
c
c
1
A
A
B
b
C
c
1
a
A
B
b
C
c
1
A
A
B
b
C
C
1
A
a
B
B
C
C
1
a
A
B
b
C
c
0
a
A
b
B
C
C
0
A
A
B
b
c
C
1
a
A
B
b
c
c
0
A
A
B
B
C
C
0
A
A
B
B
c
c
1
A
a
B
B
C
c
1
;
An output data set containing individuals’ probabilities of having particular haplotype
pairs can be created in the usual manner, while also performing an omnibus test for
association between the three markers and disease status.

Example 5.5. Creating a Data Set for Haplotype Trend Regression (HTR)
91
proc haplotype data=alleles out=out;
var a1-a6;
trait disease;
run;
This code executes the omnibus marker-trait association test whose p-value is given
by the chi-square distribution.
Output 5.5.1.
Testing for an Overall Marker-Trait Association
The HAPLOTYPE Procedure
Test for Marker-Trait Association
Trait
Trait
Num
Chi-
Pr >
Number
Value
Obs
DF
LogLike
Square
ChiSq
1
1
29
7
-68.11558
2
0
14
7
-37.28544
Combined
43
7
-115.48338
10.0824
0.1840
Output 5.5.1 shows that there is no signiﬁcant association between the markers and
the trait, disease status. However, the more powerful HTR can be used to perform the
same test.

92
Chapter 5. The HAPLOTYPE Procedure
data out1;
set out;
haplotype=tranwrd(haplotype1,’-’,’_’);
data out2;
set out;
haplotype=tranwrd(haplotype2,’-’,’_’);
data outnew;
set out1 out2;
proc sort data=outnew;
by haplotype;
run;
data outnew2;
set outnew;
lagh=lag(haplotype);
if haplotype ne lagh then num+1;
hapname=compress("H"||num,’ ’);
proc sort data=outnew2;
by id hapname;
run;
data outt;
set outnew2;
by id haplotype;
if first.haplotype then totprob=prob/2;
else totprob+prob/2;
if last.haplotype;
proc transpose data=outt out=outreg(drop=_NAME_) ;
id hapname;
idlabel haplotype;
var totprob;
by id;
run;
data outmissto0(drop=i);
set outreg;
array h{8};
do i=1 to 8;
if h{i}=. then h{i}=0;
end;
data htr(keep=id disease h1-h8);
merge outmissto0 alleles;
run;
proc print data=htr noobs round label;
run;

Example 5.5. Creating a Data Set for Haplotype Trend Regression (HTR)
93
proc logistic data=all descending;
model disease = h1-h8 / selection=stepwise;
run;
This SAS code produces a data set htr from the output data set of PROC
HAPLOTYPE that contains the variables needed to be able to perform HTR. There
is now one column for each possible haplotype in the sample, with each column con-
taining the haplotype’s frequency, or probability, within an individual.
Output 5.5.2.
HTR Data Set
ID
A_B_C
A_B_c
a_B_C
a_B_c
A_b_C
A_b_c
a_b_c
a_b_C
disease
1
0.29
0.21
0.21
0.29
0.00
0.00
0.00
0.00
1
2
0.27
0.23
0.00
0.00
0.23
0.27
0.00
0.00
1
3
0.00
0.27
0.00
0.23
0.00
0.23
0.27
0.00
0
4
0.50
0.50
0.00
0.00
0.00
0.00
0.00
0.00
1
5
0.27
0.23
0.00
0.00
0.23
0.27
0.00
0.00
1
6
0.27
0.23
0.00
0.00
0.23
0.27
0.00
0.00
0
7
0.22
0.00
0.13
0.15
0.15
0.13
0.22
0.00
1
8
0.27
0.23
0.00
0.00
0.23
0.27
0.00
0.00
1
9
0.00
0.50
0.00
0.50
0.00
0.00
0.00
0.00
1
10
0.00
0.00
0.00
0.50
0.00
0.00
0.50
0.00
0
11
1.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
1
12
0.00
1.00
0.00
0.00
0.00
0.00
0.00
0.00
1
13
0.00
0.00
0.00
0.00
0.00
0.50
0.50
0.00
0
14
0.00
1.00
0.00
0.00
0.00
0.00
0.00
0.00
1
15
0.00
0.00
0.00
0.00
0.00
1.00
0.00
0.00
0
16
0.27
0.23
0.00
0.00
0.23
0.27
0.00
0.00
0
17
0.27
0.23
0.00
0.00
0.23
0.27
0.00
0.00
1
18
0.00
0.27
0.00
0.23
0.00
0.23
0.27
0.00
1
19
0.29
0.21
0.21
0.29
0.00
0.00
0.00
0.00
1
20
0.00
0.00
0.00
0.00
1.00
0.00
0.00
0.00
0
21
1.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
1
22
0.27
0.23
0.00
0.00
0.23
0.27
0.00
0.00
1
23
0.27
0.23
0.00
0.00
0.23
0.27
0.00
0.00
1
24
0.22
0.00
0.13
0.15
0.15
0.13
0.22
0.00
0
25
0.50
0.00
0.50
0.00
0.00
0.00
0.00
0.00
0
26
0.50
0.50
0.00
0.00
0.00
0.00
0.00
0.00
1
27
0.27
0.23
0.00
0.00
0.23
0.27
0.00
0.00
0
28
0.50
0.50
0.00
0.00
0.00
0.00
0.00
0.00
1
29
0.01
0.00
0.49
0.00
0.49
0.00
0.00
0.01
1
30
0.22
0.00
0.13
0.15
0.15
0.13
0.22
0.00
1
31
0.27
0.23
0.00
0.00
0.23
0.27
0.00
0.00
1
32
0.00
0.50
0.00
0.50
0.00
0.00
0.00
0.00
1
33
0.27
0.23
0.00
0.00
0.23
0.27
0.00
0.00
1
34
0.22
0.00
0.13
0.15
0.15
0.13
0.22
0.00
1
35
0.50
0.00
0.00
0.00
0.50
0.00
0.00
0.00
1
36
0.50
0.00
0.50
0.00
0.00
0.00
0.00
0.00
1
37
0.22
0.00
0.13
0.15
0.15
0.13
0.22
0.00
0
38
0.01
0.00
0.49
0.00
0.49
0.00
0.00
0.01
0
39
0.27
0.23
0.00
0.00
0.23
0.27
0.00
0.00
1
40
0.00
0.27
0.00
0.23
0.00
0.23
0.27
0.00
0
41
1.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0
42
0.00
1.00
0.00
0.00
0.00
0.00
0.00
0.00
1
43
0.29
0.21
0.21
0.29
0.00
0.00
0.00
0.00
1

94
Chapter 5. The HAPLOTYPE Procedure
The data set shown in Output 5.5.2 can now be used in one of the regression proce-
dures offered by SAS/STAT. In this example, since the trait is binary, the LOGISTIC
procedure can be used to perform HTR on the variable disease. Since HTR can be
more powerful than the chi-square test based on a contingency table, it might ﬁnd a
signiﬁcant association between the markers in the data set and disease status that the
chi-square LRT did not detect.
Output 5.5.3.
PROC LOGISTIC Output
The LOGISTIC Procedure
Testing Global Null Hypothesis: BETA=0
Test
Chi-Square
DF
Pr > ChiSq
Likelihood Ratio
6.1962
1
0.0128
Score
6.3995
1
0.0114
Wald
4.9675
1
0.0258
Analysis of Maximum Likelihood Estimates
Standard
Wald
Parameter
DF
Estimate
Error
Chi-Square
Pr > ChiSq
Intercept
1
1.1986
0.4058
8.7224
0.0031
H8
1
-6.3249
2.8378
4.9675
0.0258
Output 5.5.3 shows two of the tables produced by PROC LOGISTIC. The ﬁrst one
displays the test of the global null hypothesis, β = 0. You can see that this test
indicates a signiﬁcant association between the haplotypes at the three markers and
disease status. In particular, the second table shows that as a result of the stepwise
selection, the haplotype H8 (a-b-c) has a statistically signiﬁcant effect on disease
status. This is an example of a case where HTR detects a signiﬁcant association that
the LRT used in PROC HAPLOTYPE does not.

References
95
References
Excofﬁer, L. and Slatkin, M. (1995), “Maximum-Likelihood Estimation of
Molecular Haplotype Frequencies in a Diploid Population,” Molecular Biology
and Evolution, 12, 921–927.
Fallin, D., Cohen, A., Essioux, L., Chumakov, I., Blumenfeld, M., Cohen, D., and
Schork, N.J. (2001), “Genetic Analysis of Case/Control Data Using Estimated
Haplotype Frequencies: Application to APOE Locus Variation and Alzheimer’s
Disease,” Genome Research, 11, 143–151.
Fallin, D. and Schork, N.J. (2000), “Accuracy of Haplotype Frequency Estimation
for Biallelic Loci, via the Expectation-Maximization Algorithm for Unphased
Diploid Genotype Data,” American Journal of Human Genetics, 67, 947–959.
Hawley, M.E. and Kidd, K.K. (1995), “HAPLO: A Program Using the EM Algorithm
to Estimate the Frequencies of Multi-site Haplotypes,” Journal of Heredity, 86,
409–411.
Lab of Statistical Genetics at Rockefeller University (2001), “User’s Guide to the EH
Program,” [http://linkage.rockefeller.edu/ott/eh.htm].
Long, J.C., Williams, R.C., and Urbanek, M. (1995), “An E-M Algorithm and Testing
Strategy for Multiple-Locus Haplotypes,” American Journal of Human Genetics,
56, 799–810.
Wijsman, E.M., Almasy, L., Amos, C.I., Borecki, I., Falk, C.T., King, T.M.,
Martinez, M.M., Meyers, D., Neuman, R., Olson, J.M., Rich, S., Spence, M.A.,
Thomas, D.C., Vieland, V.J., Witte, J.S., and MacCluer, J.W. (2001), “Analysis of
Complex Genetic Traits: Applications to Asthma and Simulated Data,” Genetic
Epidemiology, 21, S1–S853.
Zaykin, D.V., Westfall, P.H., Young, S.S., Karnoub, M.A., Wagner, M.J., and Ehm,
M.G. (2002), “Testing Association of Statistically Inferred Haplotypes with
Discrete and Continuous Traits in Samples of Unrelated Individuals,” to appear
in Human Heredity.
Zhao, J.H., Curtis, D., and Sham, P.C. (2000), “Model-Free Analysis and Permutation
Tests for Allelic Associations,” Human Heredity, 50, 133–139.

96
Chapter 5. The HAPLOTYPE Procedure

Chapter 6
The PSMOOTH Procedure
Chapter Contents
OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
GETTING STARTED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
SYNTAX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
PROC PSMOOTH Statement . . . . . . . . . . . . . . . . . . . . . . . . . 101
BY Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
ID Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
VAR Statement
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
DETAILS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
Statistical Computations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
Missing Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
OUT= Data Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
EXAMPLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
Example 6.1. Displaying Plot of PROC PSMOOTH Output Data Set . . . . 106
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

98
Chapter 6. The PSMOOTH Procedure

Chapter 6
The PSMOOTH Procedure
Overview
In the search for complex disease genes, linkage and/or association tests are often per-
formed on markers from a genome-wide scan or SNPs from a ﬁnely scaled map. This
means hundreds or even thousands of hypotheses are being simultaneously tested.
Plotting the negative log p-values of all the marker tests will reveal many peaks that
indicate signiﬁcant test results, some of which are false positives. In order to reduce
the number of false positives or improve power, smoothing methods can be applied
that take into account p-values from neighboring, and possibly correlated, markers.
That is, the peak length can be used to indicate signiﬁcance in addition to the peak
height. The PSMOOTH procedure offers smoothing methods that implement either
Simes’ (1986) or Fisher’s (1932) method for multiple hypothesis testing. These meth-
ods modify the p-value from each marker test using a function of its original p-value
and the p-values of the tests on the nearest markers. Since the number of hypothesis
tests being performed is not reduced, adjustments to correct the smoothed p-values
for multiple testing are available as well.
PROC PSMOOTH can take any data set containing any number of columns of p-
values as an input data set, including the output data sets from the CASECONTROL
and FAMILY procedures (see Chapter 3 and Chapter 4 for more information).
Getting Started
Example
Suppose you have tested 48 markers for association with a disease using the geno-
type case-control and trend tests in PROC CASECONTROL. Now you are concerned
about the multiple hypothesis testing issue, and so you run PROC PSMOOTH on the
output data set from PROC CASECONTROL in order to eliminate the number of
false positives found using the individual p-values from the marker-trait association
tests.
proc casecontrol data=in outstat=cc_tests genotype trend;
trait affected;
var a1-a96;
run;
proc psmooth data=cc_tests simes fisher bw=2 sidak out=adj_p;
var ProbGenotype ProbTrend;
id Locus;
run;
proc print data=adj_p;
run;

100
Chapter 6. The PSMOOTH Procedure
This code modiﬁes the p-values contained in the output data set from PROC
CASECONTROL, ﬁrst by smoothing the p-values using both Simes’ and Fisher’s
methods with a bandwidth of 2, then by applying Sidak’s multiple testing adjustment
to the smoothed p-values.
Prob
Prob
Prob
Genotype_
Genotype_
Prob
Prob
Prob
Obs
Locus
Genotype
S2
F2
Trend
Trend_S2
Trend_F2
1
M01
0.20059
1.00000
1.00000
0.12947
1.00000
1.00000
2
M02
0.24984
1.00000
1.00000
0.27988
1.00000
1.00000
3
M03
0.61303
0.99989
0.99559
0.64512
0.99990
0.99176
4
M04
0.35724
0.99989
0.99992
0.38009
0.99990
0.99999
5
M05
0.03454
0.99989
1.00000
0.03486
0.99990
1.00000
6
M06
0.51121
0.99989
1.00000
0.57352
0.99990
1.00000
7
M07
0.48462
0.99989
0.99996
0.59738
0.99990
1.00000
8
M08
0.56565
1.00000
1.00000
0.66992
1.00000
1.00000
9
M09
0.22166
1.00000
1.00000
0.19083
1.00000
1.00000
10
M10
0.56964
1.00000
1.00000
0.68374
1.00000
1.00000
11
M11
0.42669
1.00000
1.00000
0.48177
1.00000
1.00000
12
M12
0.34151
1.00000
1.00000
0.39099
1.00000
1.00000
13
M13
0.35094
1.00000
1.00000
0.33305
1.00000
1.00000
14
M14
0.41437
1.00000
1.00000
0.44417
1.00000
1.00000
15
M15
0.36395
1.00000
1.00000
0.40781
1.00000
1.00000
16
M16
0.45854
1.00000
1.00000
0.50985
1.00000
1.00000
17
M17
0.61439
1.00000
1.00000
0.65185
1.00000
1.00000
18
M18
0.35993
1.00000
1.00000
0.41276
1.00000
1.00000
19
M19
0.26623
1.00000
1.00000
0.27373
1.00000
1.00000
20
M20
0.39734
0.93037
0.85928
0.47567
0.99978
0.97505
21
M21
0.18037
0.93037
0.79634
0.11657
0.99978
0.91010
22
M22
0.01080
0.93037
0.92348
0.03222
0.99978
0.98274
23
M23
0.26079
0.93037
0.43744
0.20915
0.98714
0.52502
24
M24
0.56114
0.93037
0.57991
0.63033
0.98714
0.79232
25
M25
0.04130
0.99998
0.99312
0.03468
0.99989
0.97502
26
M26
0.32966
0.99998
0.99112
0.35792
0.99989
0.98829
27
M27
0.16512
0.99998
0.95182
0.12327
0.99989
0.94535
28
M28
0.23915
1.00000
0.99999
0.28337
1.00000
1.00000
29
M29
0.27391
1.00000
0.99996
0.31744
1.00000
0.99999
30
M30
0.39576
1.00000
1.00000
0.40239
1.00000
1.00000
31
M31
0.25123
1.00000
0.99970
0.30787
0.98124
0.98142
32
M32
0.32687
1.00000
1.00000
0.36567
0.98124
0.99795
33
M33
0.08401
1.00000
1.00000
0.01590
0.98124
0.99975
34
M34
0.56936
0.99999
0.99962
0.65595
0.98124
0.96888
35
M35
0.60157
0.99999
0.99774
0.66286
0.98124
0.89811
36
M36
0.07535
1.00000
0.99999
0.07229
1.00000
1.00000
37
M37
0.21207
1.00000
0.99937
0.18823
1.00000
0.99950
38
M38
0.24277
0.83623
0.35131
0.29450
0.90310
0.39211
39
M39
0.27190
0.80769
0.11928
0.25095
0.90310
0.22619
40
M40
0.00740
0.80769
0.02802
0.00949
0.86357
0.04171
41
M41
0.01351
0.80769
0.01060
0.02809
0.83848
0.00730
42
M42
0.02846
0.80769
0.01860
0.01626
0.83848
0.01510
43
M43
0.06777
0.96512
0.34054
0.02982
0.91341
0.25411
44
M44
0.56635
0.99937
0.97025
0.64220
0.97572
0.83276
45
M45
0.50034
1.00000
1.00000
0.51227
0.99957
0.99989
46
M46
0.34136
1.00000
1.00000
0.40320
1.00000
1.00000
47
M47
0.25543
1.00000
0.99996
0.23193
1.00000
0.99998
48
M48
0.08614
1.00000
0.99900
0.08509
1.00000
0.99926
Figure 6.1.
PROC PSMOOTH Output Data Set
Figure 6.1 displays the original and modiﬁed p-values.

PROC PSMOOTH Statement
101
Syntax
The following statements are available in PROC PSMOOTH.
PROC PSMOOTH < options > ;
BY variables ;
ID variables ;
VAR variables ;
Items within angle brackets (< >) are optional, and statements following the PROC
PSMOOTH statement can appear in any order. The VAR statement is required. The
syntax of each statement is described in the following section in alphabetical order
after the description of the PROC PSMOOTH statement.
PROC PSMOOTH Statement
PROC PSMOOTH < options > ;
You can specify the following options in the PROC PSMOOTH statement.
BANDWIDTH=number list
BW=number list
gives the values for the bandwidths to use in combining p-values. A bandwidth of w
indicates that w p-values on each side of the original p-value are included in the com-
bining method to create a sliding window of size 2w + 1. The number list can contain
any combination of the following forms, with each form separated by a comma:
w1, w2, ..., wn a list of several values
w1 to w2
a sequence where w1 is the starting value, w2 is the ending value,
and the increment is 1.
w1 to w2 by i
a sequence where w1 is the starting value, w2 is the ending value,
and the increment is i.
All numbers in the number list must be integers, and any negative numbers are ig-
nored. An example of a valid number list is
bandwidth = 1,2, 5 to 15 by 5, 18
which would perform the combining of p-values using bandwidths 1, 2, 5, 10, 15,
and 18, which create sliding windows of size 3, 5, 11, 21, 31, and 37, respectively.
BONFERRONI
BON
requests that the Bonferroni adjustment for multiple testing based on the number of
observations in the BY group be applied to the p-values in the output data set. This
adjustment is applied after the smoothing has occurred. This option is ignored if the
SIDAK option is speciﬁed.

102
Chapter 6. The PSMOOTH Procedure
DATA=SAS-data-set
names the input SAS data set to be used by PROC PSMOOTH. If this option is omit-
ted, the SAS system option –LAST– is used, which by default is the most recently
created data set.
FISHER
requests that Fisher’s method for combining p-values from multiple hypotheses be
applied to the original p-values.
NEGLOG
requests that all p-values, original and combined, be transformed to their negative log
(base e) in the output data set; that is, for each p-value, − ln(p-value) is reported in
the OUT= data set. This option is useful for graphing purposes.
NEGLOG10
requests that all p-values, original and combined, be transformed to their negative log
(base 10) in the output data set; that is, for each p-value, − log10(p-value) is reported
in the OUT= data set. This option is useful for graphing purposes.
OUT=SAS-data-set
names the output SAS data set containing the original p-values and the new combined
p-values. When this option is omitted, an output data set is created by default and
named according to the DATAn convention.
SIDAK
requests that the Sidak adjustment for multiple testing based on the number of ob-
servations in the BY group be applied to the p-values in the output data set. This
adjustment is applied after the smoothing has occurred.
SIMES
requests that Simes’ method for combining p-values from multiple hypotheses be
applied to the original p-values.
BY Statement
BY variables ;
You can specify a BY statement with PROC PSMOOTH to obtain separate analy-
ses on observations in groups deﬁned by the BY variables. When a BY statement
appears, the procedure expects the input data set to be sorted in order of the BY
variables. The variables are one or more variables in the input data set.

Statistical Computations
103
If your input data set is not sorted in ascending order, use one of the following alter-
natives:
• Sort the data using the SORT procedure with a similar BY statement.
• Specify the BY statement option NOTSORTED or DESCENDING in the BY
statement for the PSMOOTH procedure. The NOTSORTED option does not
mean that the data are unsorted but rather that the data are arranged in groups
(according to values of the BY variables) and that these groups are not neces-
sarily in alphabetical or increasing numeric order.
• Create an index on the BY variables using the DATASETS procedure (in Base
SAS software).
For more information on the BY statement, refer to the discussion in SAS Language
Reference: Concepts. For more information on the DATASETS procedure, refer to
the discussion in the SAS Procedures Guide.
ID Statement
ID variables ;
The ID statement identiﬁes the variables from the DATA= data set that should be
included in the OUT= data set.
VAR Statement
VAR variables ;
The VAR statement identiﬁes the variables containing the original p-values on which
the combining methods should be performed.
Details
Statistical Computations

104
Chapter 6. The PSMOOTH Procedure
Methods for Smoothing p-Values
PROC PSMOOTH offers two methods for combining p-values over speciﬁed sizes
of sliding windows. For each value w listed in the BANDWIDTH= option of the
PROC PSMOOTH statement, a sliding window of size 2w + 1 is used; that is, the
p-values for each set of 2w + 1 consecutive markers are considered in turn, for each
value w. The approach described by Zaykin et al. (2002) is implemented, where
the original p-value at the center of the sliding window is replaced by a function
of the original p-value and the p-values from the w nearest markers on each side
to create a new sequence of p-values. Note that for markers less than w from the
beginning or end of the data set (or BY group if any variables are speciﬁed in the
BY statement), the number of hypotheses tested, L, is adjusted accordingly. The two
methods for combining p-values from multiple hypotheses are Simes’ method and
Fisher’s method, described in the following two sections. Plotting the new p-values
versus the original p-values reveals the smoothing effect this technique has.
Simes’ Method
Simes’ method for combining p-values is performed as follows when the SIMES
option is speciﬁed in the PROC PSMOOTH statement: let pj be the original p-value
at the center of the current sliding window, which contains pj−w, ..., pj+w. From
these L = 2w + 1 p-values, the ordered p-values, p(1), ..., p(L) are formed. Then the
new value for pj is min1≤i≤L(Lp(i)/i).
This method controls the type I error rate even when hypotheses are positively corre-
lated (Sarkar and Chang 1997), which is expected for nearby markers. Thus if depen-
dencies are suspected among tests that are performed, this method is recommended
due to its conservativeness.
Fisher’s Method
When the FISHER option is issued in the PROC PSMOOTH statement, Fisher’s
method for combining p-values is applied by replacing the p-value at the center of
the current sliding window pj by the p-value of the statistic t, where
j+w
t = −2
ln(pi)
i=j−w
which has a χ2 distribution under the null hypothesis of all L = 2w + 1 hypotheses
2L
being true.

OUT= Data Set
105
CAUTION: t has a χ2 distribution only under the assumption that the tests performed
are mutually independent. When this assumption is violated, the probability of type
I error may exceed the signiﬁcance level α.
Multiple Testing Adjustments for p-Values
While the smoothing methods take into account the p-values from neighboring
markers, the number of hypothesis tests performed does not change. Therefore,
the Bonferroni and Sidak methods are offered by PROC PSMOOTH to adjust the
smoothed p-values for multiple testing. The number of tests performed, R, is the
number of observations in the current BY group if any variables are speciﬁed in the
BY statement, or the number of observations in the entire data set if there are no
variables speciﬁed in the BY statement. If both the BONFERRONI and SIDAK op-
tions are speciﬁed in the PROC PSMOOTH statement, only the Sidak method is used.
Note that these adjustments will not be applied to the original column(s) of p-values;
if you would like to adjust the original p-values for multiple testing, you must include
a bandwidth of 0 in the BANDWIDTH= option of the PROC PSMOOTH statement.
For R tests, the p-value p is adjusted as follows according to these two methods:
Bonferroni adjustment: min(Rp, 1.0)
Sidak adjustment (Sidak 1967): 1 − (1 − p)R
Both methods are conservative, with Sidak’s slightly less conservative than
Bonferroni’s method.
Missing Values
Missing values in a sliding window, even at the center of the window, are simply
ignored, and the number of hypotheses L is reduced accordingly. Thus the smoothing
methods can be applied to any window that contains at least one nonmissing value.
Any p-values in the input data set that fall outside the interval [0,1] are treated as
missing.
OUT= Data Set
The output data set speciﬁed in the OUT= option of the PROC PSMOOTH state-
ment contains any BY variables and ID variables. Then for each variable in the VAR
statement, the original column is included along with a column for each method and
bandwidth speciﬁed in the PROC PSMOOTH statement. These variable names are
formed by adding the sufﬁxes “–Sw” and “–Fw” for Simes’ and Fisher’s methods re-
spectively and a bandwidth of size w. For example, if the options BANDWIDTH=1,4
and SIMES and FISHER are all speciﬁed in the PROC PSMOOTH statement, and
RawP is the variable speciﬁed in the VAR statement, the OUT= data set includes
RawP, RawP–S1, RawP–F1, RawP–S4, and RawP–F4. If the NEGLOG
or NEGLOG10 option is speciﬁed in the PROC PSMOOTH statement, then these
columns all contain the negative logs (base e or base 10, respectively) of the p-values.

106
Chapter 6. The PSMOOTH Procedure
Example
Example 6.1. Displaying Plot of PROC PSMOOTH Output Data
Set
Data other than the output data sets from the CASECONTROL and FAMILY proce-
dures can be used in PROC PSMOOTH; here is an example of how to use p-values
from another source.

Example 6.1. Displaying Plot of PROC PSMOOTH Output Data Set
107
data tests;
input Marker Pvalue @@;
datalines;
1
0.72841
2
0.40271
3
0.32147
4
0.91616
5
0.27377
6
0.48943
7
0.40131
8
0.25555
9
0.57585
10
0.20925
11
0.01531
12
0.23306
13
0.69397
14
0.33040
15
0.97265
16
0.53639
17
0.88397
18
0.03188
19
0.13570
20
0.79138
21
0.99467
22
0.37831
23
0.86459
24
0.97092
25
0.19372
26
0.85339
27
0.32078
28
0.31806
29
0.00655
30
0.82401
31
0.65339
32
0.36115
33
0.92704
34
0.49558
35
0.64842
36
0.43606
37
0.67060
38
0.87520
39
0.78006
40
0.27252
41
0.28561
42
0.80495
43
0.98159
44
0.97030
45
0.53831
46
0.78712
47
0.88493
48
0.36260
49
0.53310
50
0.65709
51
0.26527
52
0.46860
53
0.55465
54
0.54956
55
0.44477
56
0.04933
57
0.12016
58
0.76181
59
0.80158
60
0.18244
61
0.01382
62
0.15100
63
0.04713
64
0.52655
65
0.59368
66
0.94420
67
0.60104
68
0.32848
69
0.90195
70
0.21374
71
0.95471
72
0.14145
73
0.95215
74
0.70330
75
0.19921
76
0.99086
77
0.75736
78
0.23761
79
0.87260
80
0.91472
81
0.33650
82
0.26160
83
0.41948
84
0.62817
85
0.48721
86
0.67093
87
0.53089
88
0.13623
89
0.44344
90
0.41172
;
The following code will apply Simes’ method for multiple hypothesis testing in order
to adjust the p-values.

108
Chapter 6. The PSMOOTH Procedure
proc psmooth data=tests out=pnew simes bandwidth=3 to 9 by 2 neglog;
var Pvalue;
id Marker;
run;
symbol1 v=none i=join;
symbol2 v=none i=join line=5;
symbol3 v=none i=join line=4;
symbol4 v=none i=join line=3;
symbol5 v=none i=join line=2;
legend1 label=none;
proc gplot data=pnew;
plot (Pvalue Pvalue_S3 Pvalue_S5 Pvalue_S7 Pvalue_S9)*Marker
/overlay vref=3.0 legend=legend1;
run;
The NEGLOG option is used in the PROC PSMOOTH statement to facilitate plotting
the p-values using the GPLOT procedure of SAS/GRAPH. The plot demonstrates the
effect of the different window sizes that are implemented.
Output 6.1.1.
Line Plot of Negative Log p-Values

References
109
Note how the plots become progressively smoother as the window size increases.
Points above the horizontal reference line in Output 6.1.1 represent signiﬁcant p-
values at the 0.05 level. While six of the markers have signiﬁcant p-values before
adjustment, only the method using a bandwidth of 3 ﬁnds any signiﬁcant markers,
all in the 26–32 region. This may be an indication that the other ﬁve markers are
signiﬁcant only by chance; that is, they may be false positives.
References
Fisher, R.A. (1932), Statistical Methods for Research Workers, London: Oliver and
Boyd.
Sarkar, S.K. and Chang, C-K. (1997), “The Simes Method for Multiple Hypothesis
Testing with Positively Dependent Test Statistics,” Journal of the American
Statistical Association, 92, 1601–1608.
Sidak, Z. (1967), “Rectangular Conﬁdence Regions for the Means of Multivariate
Normal Distributions,” Journal of the American Statistical Association, 62,
626–633.
Simes, R.J. (1986), “An Improved Bonferroni Procedure for Multiple Tests of
Signiﬁcance,” Biometrika, 73, 751–754.
Zaykin, D.V., Zhivotovsky, L.A., Westfall, P.H., and Weir, B.S. (2002), “Truncated
Product Method for Combining P -values,” Genetic Epidemiology, 22, 170–185.

110
Chapter 6. The PSMOOTH Procedure

Chapter 7
The TPLOT Macro
Chapter Contents
OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
SYNTAX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
RESULTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
Plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
Menu Bar
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
Toolbar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
EXAMPLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

112
Chapter 7. The TPLOT Macro

Chapter 7
The TPLOT Macro
Overview
The %TPLOT macro creates a triangular plot that graphically displays genetic marker
test results. The plot has colors and shapes representing p-value ranges for tests of
the following quantities: linkage disequilibrium between pairs of markers, Hardy-
Weinberg equilibrium (HWE) for individual markers, and associations between
markers and a dichotomous trait (such as disease status). This is a convenient way of
combining information contained in output data sets from two separate SAS/Genetics
procedures and summarizing it in an easily interpretable plot. Thus, insights can be
gleaned by simply studying a plot rather than by having to search through many rows
of data or writing code to attempt to summarize the results.
The %TPLOT macro is a part of the SAS Autocall library, and is automati-
cally available for use in your SAS program provided that the SAS system option
MAUTOSOURCE is in effect. For more information about autocall libraries, refer to
SAS Macro Language: Reference, Version 8, 2000.
Syntax
The %TPLOT macro has the following form:
%TPLOT (SAS-data-set , SAS-data-set , variable [ , option ] )
The ﬁrst argument, SAS-data-set, speciﬁes the name of the SAS data set that is the
output data set from the ALLELE procedure (see Chapter 2), containing the linkage
disequilibrium test and HWE test p-values. A user-created data set may be used
instead, but is required to contain the variables Locus1 and Locus2 and a variable
ProbChi containing the p-values from the disequilibrium tests. The order in which
the Locus1 and Locus2 variables are sorted is the order in which the values are
displayed on the vertical and horizontal axes, respectively.
The second argument, SAS-data-set, speciﬁes the name of the SAS data set that con-
tains the p-values for the marker-trait association tests. This data set can be the out-
put data set from the CASECONTROL procedure, the FAMILY procedure, or the
PSMOOTH procedure, or it can be created by the user. A user-created data set must
contain a Locus variable for the values on the axes and a variable containing p-
values that is speciﬁed in the third argument, discussed in the following paragraph.
The Locus variable must be in the same sorted order as the Locus1 variable in the
data set named in the ﬁrst argument.
The third argument, variable, names the variable that contains the marker-trait asso-
ciation p-values in the SAS data set that is speciﬁed in the second argument.

114
Chapter 7. The TPLOT Macro
The ﬁrst three arguments are required. The following option can be used with the
%TPLOT macro. The option must follow the three required arguments.
ALPHA= number
speciﬁes the signiﬁcance level for the marker-trait association test. This level is used
as a cut-off for the p-value range corresponding to the symbol shape on the plot. This
number must be between 0 and 1. The default is ALPHA=0.05.
Results
Plot
Running the %TPLOT macro creates a window displaying a graphical representation
of the marker test results.
Here is an example of the TPLOT results window:
Figure 7.1.
Results Window for TPLOT Macro

Plot
115
This plot contains a grid of points with symbols that represent the p-values for various
marker tests. Colors and shapes of the data points are used to symbolize p-value
ranges. The Show Info About Points button in the toolbar enables the p-values to be
displayed. While holding down the left-hand mouse button on any point in the plot,
the pop-up menu will display for off-diagonal points, the two markers being tested
for linkage disequilibrium and the p-value of the test; it displays the marker and its
p-values for the HWE test and marker-trait association test for points on the diagonal,
as shown in Figure 7.1.
Disequilibrium Tests
The p-values from the linkage disequilibrium tests between all pairs of markers (or
all markers within a certain range of each other) are represented by the color of the
squares on the off-diagonal of the plot. For the points on the diagonal, the results
from the Hardy-Weinberg equilibrium test are displayed instead of the linkage dise-
quilibrium tests since the same marker locus is on the horizontal and vertical axes.
The three ranges of p-values that correspond to different colored symbols in the plot
are
Red
[0, 0.01]
Orange
(0.01, 0.05]
Yellow
(0.05, 1]
The disequilibrium test p-values that are plotted can be provided by the output data
set from PROC ALLELE, or by a user-created data set meeting the requirements
described in the “Syntax” section on page 113.
Marker-Trait Association Tests
Points on the diagonal also display p-values from marker-trait association tests, using
the shape of the symbol to correspond to two categories of p-values, signiﬁcant and
not signiﬁcant. The signiﬁcance level is set to 0.05 by default, but can be modiﬁed
using the ALPHA= option in the %TPLOT macro. Thus, for a signiﬁcance level of
α, the following shapes represent the following ranges:
Plus
[0, α]
Triangle
(α, 1]
Note that the square shape
of the off-diagonal points does not represent a marker-
trait association p-value since there are two different marker loci represented on the
horizontal and vertical axes. These p-values can be provided by the output data set
of PROC CASECONTROL, PROC FAMILY, or PROC PSMOOTH. Alternatively,
a user-created data set that meets the conditions described in the “Syntax” section
(page 113) can be used.

116
Chapter 7. The TPLOT Macro
Menu Bar
The results window contains the following pull-down menus:
File
Close
closes the results window.
Print Setup
opens the printer setup utility.
Print
prints the plot as it is currently shown.
Exit
exits the current SAS session.
Edit
Copy
copies the plot to the clipboard.

Example
117
Format
Rescale Axes when selected, changes the scale of the axes to ﬁt the entire plot
in the window.
These menus are also available by clicking the right-hand mouse button anywhere in
the TPLOT results window.
Toolbar
A toolbar is displayed at the top of the TPLOT results window. Use the toolbar to
display information about points on the plot or to modify the plot’s appearance. Tool
tips are displayed when you place your mouse pointer over an icon in the toolbar.
Figure 7.2.
Toolbar for the %TPLOT Results Window
Tool icons from left to right are as follows:
1. Print - prints the plot.
2. Copy - copies the plot to the clipboard.
3. Select a Node or Point - activates a point on the plot.
4. Show Info About Points - displays a text box with information about the se-
lected point.
5. Scroll Data - scrolls across data points within the plot. Use this tool when the
plot is not able to display all of the points in a single frame.
6. Move Graph - moves the plot within the window.
7. Zoom In/Out - reduces or increases the size of the plot.
8. Reset - returns the plot to its default settings.
9. What’s This? - displays the help for the results window.
Example

118
Chapter 7. The TPLOT Macro
Here is an example of the code that can be used to create the triangular plot of p-values
for the data set pop22. This data set is in the proper form for a PROC ALLELE input
data set, containing columns of alleles for 150 markers.
proc allele data=pop22 outstat=ldstats noprint maxdist=150;
var a1-a300;
run;
proc casecontrol data=pop22 outstat=assocstats genotype;
trait affected;
var a1-a300;
run;
proc psmooth data=assocstats out=sm_assocstats bw=5 simes;
id Locus;
var ProbGenotype;
run;
%tplot(ldstats, sm_assocstats, ProbGenotype_S5);
Note that the output data set from PROC CASECONTROL can be used in place of
the output data set from PROC PSMOOTH if you wish to use unadjusted p-values.
This code creates the following plot in the TPLOT window:
Figure 7.3.
Results Window for TPLOT Macro

Example
119
Figure 7.3 displays the bottom left-hand corner of the plot. The pop-up window is
displayed by selecting Show Info About Points from the toolbar then holding the
left-hand mouse button over the point shown. The orange color of this point indicates
that the p-value for testing that there is no linkage disequilibrium between M9 and
M14 is between 0.01 and 0.05. The pop-up window provides the exact value of this
p-value.
Other parts of the plot can be viewed by selecting Scroll Data from the toolbar.
Alternatively, the entire plot can be viewed in the window by selecting Format
→Rescale Axes from the menu bar. This creates the following view of the plot:
Figure 7.4.
Results Window for TPLOT Macro
The view shown in Figure 7.4 displays all the data points at once.

120
Chapter 7. The TPLOT Macro

Subject Index
A
PSMOOTH procedure, 104
allele case-control test
displayed output
CASECONTROL procedure, 39
HAPLOTYPE procedure, 76
allele frequencies
ALLELE procedure, 20, 26
E
ALLELE procedure
EM algorithm
allele frequencies, 20, 26
HAPLOTYPE procedure, 71
allelic diversity, 21
exact tests
bootstrap conﬁdence intervals, 20
HAPLOTYPE procedure, 75
displayed output, 26
genotype frequencies, 20, 26
F
haplotypes, 22, 29
FAMILY procedure
Hardy-Weinberg equilibrium, 21
DATA= Data Set, 56
heterozygosity, 21
missing values, 55
linkage disequilibrium, 22, 27, 29
output data set, 56
marker informativeness, 21
RC-TDT, 55
missing values, 25
SDT, 54
ODS table names, 27
S-TDT, 53
OUTSTAT= Data Set, 25
TDT, 52
PIC, 21
Fisher’s method
allelic diversity
PSMOOTH procedure, 104
ALLELE procedure, 21
G
B
genomic control
Base SAS software, 7
CASECONTROL procedure, 40
Bonferroni adjustment
genotype case-control test
PSMOOTH procedure, 105
CASECONTROL procedure, 40
bootstrap conﬁdence intervals
genotype frequencies
ALLELE procedure, 20
ALLELE procedure, 20, 26
C
H
case-control tests
haplotype frequencies
HAPLOTYPE procedure, 71, 74, 85
HAPLOTYPE procedure, 71
CASECONTROL procedure
HAPLOTYPE procedure
allele case-control test, 39
case-control tests, 71, 74, 85
genomic control, 40
displayed output, 76
genotype case-control test, 40
EM algorithm, 71
missing values, 41
exact tests, 75
output data set, 41
haplotype frequencies, 71
trend test, 39
haplotype trend regression (HTR), 89
correlated tests,
jackknife method, 73
See dependent tests
linkage disequilibrium, 74, 83
missing values, 75
D
ODS table names, 78
DATA step, 7
OUT= Data Set, 76
DATA= Data Set
standard error estimation, 70, 73
FAMILY procedure, 56
haplotype trend regression (HTR)
dependent tests
HAPLOTYPE procedure, 89

122
Subject Index
haplotypes
S
ALLELE procedure, 22, 29
SAS data set
Hardy-Weinberg equilibrium
DATA step, 7
ALLELE procedure, 21
SAS/GRAPH software, 8
help system, 7
SAS/IML software, 8
heterozygosity
SAS/INSIGHT software, 8
ALLELE procedure, 21
SAS/STAT software, 9
SDT
J
FAMILY procedure, 54
jackknife method
Sidak adjustment
HAPLOTYPE procedure, 73
PSMOOTH procedure, 105
Simes’ method
L
PSMOOTH procedure, 104
linkage disequilibrium
standard error estimation
ALLELE procedure, 22, 27, 29
HAPLOTYPE procedure, 70, 73
HAPLOTYPE procedure, 74, 83
S-TDT
FAMILY procedure, 53
M
marker informativeness
T
ALLELE procedure, 21
TDT
missing values
FAMILY procedure, 52
ALLELE procedure, 25
TPLOT Results Window, 114
CASECONTROL procedure, 41
trend test
FAMILY procedure, 55
CASECONTROL procedure, 39
HAPLOTYPE procedure, 75
PSMOOTH procedure, 105
multiple testing adjustments
PSMOOTH procedure, 105
O
ODS table names
HAPLOTYPE procedure, 78
OUT= Data Set
HAPLOTYPE procedure, 76
output data set
CASECONTROL procedure, 41
FAMILY procedure, 56
PSMOOTH procedure, 105
OUTSTAT= Data Set
ALLELE procedure, 25
P
PIC
ALLELE procedure, 21
PSMOOTH procedure
Bonferroni adjustment, 105
dependent tests, 104
Fisher’s method, 104
missing values, 105
multiple testing adjustments, 105
output data set, 105
Sidak adjustment, 105
Simes’ method, 104
R
RC-TDT
FAMILY procedure, 55

Syntax Index
A
CASECONTROL
procedure,
PROC
ALLELE option
CASECONTROL statement, 37
PROC CASECONTROL statement, 37, 39
ALLELE option, 37, 39
ALLELE procedure, 17
DATA= option, 37
syntax, 17
GENOTYPE option, 37
ALLELE procedure, BY statement, 19
NDATA= option, 37
ALLELE procedure, PROC ALLELE statement, 17
OUTSTAT= option, 38
ALPHA= option, 17
PREFIX= option, 38
BOOTSTRAP= option, 17
TREND option, 38, 39
CORRCOEFF option, 17
VIF option, 38, 40
DATA= option, 17
CASECONTROL procedure, TRAIT statement, 39
DELTA option, 17
CASECONTROL procedure, VAR statement, 39
DPRIME option, 17
COMBINE option
EXACT= option, 18
PROC FAMILY statement, 49
HAPLO= option, 18, 22
CONTCORR option
MAXDIST= option, 18
PROC FAMILY statement, 50
NDATA= option, 18, 27
CONV= option
NOFREQ option, 18
PROC HAPLOTYPE statement, 68
NOPRINT option, 19
CORRCOEFF option
OUTSTAT= option, 19
PROC ALLELE statement, 17
PREFIX= option, 19
CUTOFF= option
PROPDIFF option, 19
PROC HAPLOTYPE statement, 68, 81
SEED= option, 19
YULESQ option, 19
D
ALLELE procedure, VAR statement, 20
DATA= option
ALPHA= option
PROC ALLELE statement, 17
PROC ALLELE statement, 17
PROC CASECONTROL statement, 37
PROC HAPLOTYPE statement, 68
PROC FAMILY statement, 50
TPLOT macro, 114
PROC HAPLOTYPE statement, 68
PROC PSMOOTH statement, 102
B
DELTA option
BANDWIDTH= option
PROC ALLELE statement, 17
PROC PSMOOTH statement, 101
DPRIME option
BONFERRONI option
PROC ALLELE statement, 17
PROC PSMOOTH statement, 101, 105
BOOTSTRAP= option
E
PROC ALLELE statement, 17
EXACT= option
BY statement
PROC ALLELE statement, 18
ALLELE procedure, 19
CASECONTROL procedure, 38
F
FAMILY procedure, 51
FAMILY procedure, 49
HAPLOTYPE procedure, 70
syntax, 49
PSMOOTH procedure, 102
FAMILY procedure, BY statement, 51
FAMILY procedure, ID statement, 51
C
FAMILY procedure, PROC FAMILY statement, 49
CASECONTROL procedure, 37
COMBINE option, 49
syntax, 37
CONTCORR option, 50
CASECONTROL procedure, BY statement, 38
DATA= option, 50

124
Syntax Index
MULT= option, 50
M
NDATA= option, 50
MAXDIST= option
OUTSTAT= option, 50
PROC ALLELE statement, 18
PREFIX= option, 50
MAXITER= option
RCTDT option, 50, 55
PROC HAPLOTYPE statement, 69
SDT option, 50, 54
MULT= option
STDT option, 51, 53
PROC FAMILY statement, 50
TDT option, 51, 52
FAMILY procedure, TRAIT statement, 52
N
FAMILY procedure, VAR statement, 52
NDATA= option
FISHER option
PROC ALLELE statement, 18, 27
PROC PSMOOTH statement, 102, 104
PROC CASECONTROL statement, 37
PROC FAMILY statement, 50
G
PROC HAPLOTYPE statement, 69
GENOTYPE option
NEGLOG option
PROC CASECONTROL statement, 37
PROC PSMOOTH statement, 102
H
NEGLOG10 option
PROC PSMOOTH statement, 102
HAPLO= option
NLAG= option
PROC ALLELE statement, 18, 22
PROC HAPLOTYPE statement, 69
PROC HAPLOTYPE statement, 70
NOFREQ option
HAPLOTYPE procedure, 68
PROC ALLELE statement, 18
syntax, 68
NOPRINT option
HAPLOTYPE procedure, BY statement, 70
PROC ALLELE statement, 19
HAPLOTYPE procedure, PROC HAPLOTYPE state-
PROC HAPLOTYPE statement, 69
ment, 68
NSTART= option
ALPHA= option, 68
PROC HAPLOTYPE statement, 69, 82
CONV= option, 68
CUTOFF= option, 68, 81
O
DATA= option, 68
OUT= option
INIT= option, 68
PROC HAPLOTYPE statement, 67, 70
ITPRINT option, 69, 80
PROC PSMOOTH statement, 102
LD option, 69, 74, 83
OUTCUT= option
MAXITER= option, 69
PROC HAPLOTYPE statement, 70
NDATA= option, 69
OUTSTAT= option
NLAG= option, 69
PROC ALLELE statement, 19
NOPRINT option, 69
PROC CASECONTROL statement, 38
NSTART= option, 69, 82
PROC FAMILY statement, 50
OUT= option, 67, 70
OUTCUT= option, 70
P
PREFIX= option, 70
PERMUTATION= option
SE= option, 70
TRAIT statement (HAPLOTYPE), 71
SEED= option, 70
PREFIX= option
HAPLOTYPE procedure, TRAIT statement, 71, 85
PROC ALLELE statement, 19
PERMUTATION= option, 71
PROC CASECONTROL statement, 38
TESTALL option, 71
PROC FAMILY statement, 50
HAPLOTYPE procedure, VAR statement, 71
PROC HAPLOTYPE statement, 70
I
PROC ALLELE statement,
ID statement
See ALLELE procedure
FAMILY procedure, 51
PROC CASECONTROL statement,
PSMOOTH procedure, 103
See CASECONTROL procedure
INIT= option
PROC FAMILY statement,
PROC HAPLOTYPE statement, 68
See FAMILY procedure
ITPRINT option
PROC HAPLOTYPE statement,
PROC HAPLOTYPE statement, 69, 80
See HAPLOTYPE procedure
PROC PSMOOTH statement,
L
See PSMOOTH procedure
LD option
PROPDIFF option
PROC HAPLOTYPE statement, 69, 74, 83
PROC ALLELE statement, 19

Syntax Index
125
PSMOOTH procedure, 101
Y
syntax, 101
YULESQ option
PSMOOTH procedure, BY statement, 102
PROC ALLELE statement, 19
PSMOOTH procedure, ID statement, 103
PSMOOTH procedure, PROC PSMOOTH statement,
101
BANDWIDTH= option, 101
BONFERRONI option, 101, 105
DATA= option, 102
FISHER option, 102, 104
NEGLOG option, 102
NEGLOG10 option, 102
OUT= option, 102
SIDAK option, 102, 105
SIMES option, 102, 104
PSMOOTH procedure, VAR statement, 103
R
RCTDT option
PROC FAMILY statement, 50
PROC FAMILY statement (FAMILY), 55
S
SDT option
PROC FAMILY statement, 50
PROC FAMILY statement (FAMILY), 54
SEED= option
PROC ALLELE statement, 19
PROC HAPLOTYPE statement, 70
SIDAK option
PROC PSMOOTH statement, 102, 105
SIMES option
PROC PSMOOTH statement, 102, 104
STDT option
PROC FAMILY statement, 51, 53
T
TDT option
PROC FAMILY statement, 51, 52
TESTALL option
TRAIT statement (HAPLOTYPE), 71
TPLOT macro, 113
ALPHA= option, 114
syntax, 113
TRAIT statement
CASECONTROL procedure, 39
FAMILY procedure, 52
HAPLOTYPE procedure, 71, 85
TREND option
PROC CASECONTROL statement, 38, 39
V
VAR statement
ALLELE procedure, 20
CASECONTROL procedure, 39
FAMILY procedure, 52
HAPLOTYPE procedure, 71
PSMOOTH procedure, 103
VIF option
PROC CASECONTROL statement, 38, 40

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Document Outline

Chapter 1. Introduction
- Overview of SAS/Genetics Software
- About This Book
  - Chapter Organization
  - Typographical Conventions
  - Options Used in Examples
- Where to Turn for More Information
  - Online Help System
  - SAS Institute Technical Support Services
- Related SAS Software
  - Base SAS Software
  - SAS/GRAPH Software
  - SAS/IML Software
  - SAS/INSIGHT Software
  - SAS/STAT Software
Chapter 2. The ALLELE Procedure
- Overview
- Getting Started
  - Example
- Syntax
  - PROC ALLELE Statement
  - BY Statement
  - VAR Statement
- Details
  - Statistical Computations
  - Missing Values
  - OUTSTAT= Data Set
  - Displayed Output
  - ODS Table Names
- Examples
  - Example 2.1. Using the NDATA= Option with Microsatellites
  - Example 2.2. Computing Linkage Disequilibrium Measures for SNP Data
- References
Chapter 3. The CASECONTROL Procedure
- Overview
- Getting Started
  - Example
- Syntax
  - PROC CASECONTROL Statement
  - BY Statement
  - TRAIT Statement
  - VAR Statement
- Details
  - Statistical Computations
  - Missing Values
  - OUTSTAT= Data Set
- Example
  - Example 3.1. Performing Case-Control Tests on Multiallelic Markers
- References
Chapter 4. The FAMILY Procedure
- Overview
- Getting Started
  - Example
- Syntax
  - PROC FAMILY Statement
  - BY Statement
  - ID Statement
  - TRAIT Statement
  - VAR Statement
- Details
  - Statistical Computations
  - Missing Values
  - DATA= Data Set
  - OUTSTAT= Data Set
- Example
  - Example 4.1. Performing Tests with Missing Parental Data
- References
Chapter 5. The HAPLOTYPE Procedure
- Overview
- Getting Started
  - Example
- Syntax
  - PROC HAPLOTYPE Statement
  - BY Statement
  - TRAIT Statement
  - VAR Statement
- Details
  - Statistical Computations
  - Missing Values
  - OUT= Data Set
  - Displayed Output
  - ODS Table Names
- Examples
  - Example 5.1. Estimating Three-Locus Haplotype Frequencies
  - Example 5.2. Using Multiple Runs of the EM Algorithm
  - Example 5.3. Testing for Linkage Disequilibrium
  - Example 5.4. Testing for Marker-Trait Associations
  - Example 5.5. Creating a Data Set for Haplotype Trend Regression (HTR)
- References
Chapter 6. The PSMOOTH Procedure
- Overview
- Getting Started
  - Example
- Syntax
  - PROC PSMOOTH Statement
  - BY Statement
  - ID Statement
  - VAR Statement
- Details
  - Statistical Computations
  - Missing Values
  - OUT= Data Set
- Example
  - Example 6.1. Displaying Plot of PROC PSMOOTH Output Data Set
- References
Chapter 7. The TPLOT Macro
- Overview
- Syntax
- Results
  - Plot
  - Menu Bar
  - Toolbar
- Example
Subject Index
Syntax Index