Categorical Data Analysis Using the SAS System

Along with providing a useful discussion of categorical data analysis techniques, this book shows how to apply these methods with the SAS System. The authors include practical examples from a broad range of applications to illustrate the use of the FREQ, LOGISTIC, GENMOD, and CATMOD procedures in a variety of analyses. They also discuss other procedures such as PHREG and NPAR1WAY.

Maura E. Stokes is Senior Manager of Statistical Applications Research and Development at SAS Institute. She received her PhD in Biostatistics from the University of North Carolina at Chapel Hill and has taught and written about categorical data analysis for over fifteen years.<br> <br> Charles S. Davis is Professor of Biostatistics at the University of Iowa. He received his PhD in Biostatistics from the University of Michigan. His research and teaching interests include categorical data analysis and methods for the analysis of repeated measures.<br> <br> och is Professor of Biostatistics and Director of the biometrics Consulting Laboratory at the University of North Carolina at Chapel Hill. He has had a prominent roll in the field of categorical data analysis for the last thirty years. He teaches classes and seminars in categorical data analysis, consults in areas of statistical practice, conducts research, and trains many Biostatistics students.

Preface to the Second Edition

v

Acknowledgments

vii

Introduction

1

(16)

Overview

3

(1)

Scale of Measurement

3

(3)

Sampling Frameworks

6

(1)

Overview of Analysis Strategies

7

(3)

Working with Tables in the SAS System

10

(5)

Using This Book

15

(2)

The 2 x 2 Table

17

(26)

Introduction

19

(1)

Chi-Square Statistics

20

(3)

Exact Tests

23

(6)

Difference in Proportions

29

(3)

Odds Ratio and Relative Risk

32

(7)

Sensitivity and Specificity

39

(1)

McNemar's Test

40

(3)

Sets of 2 x 2 Tables

43

(22)

Introduction

45

(1)

Mantel-Haenszel Test

45

(12)

Measures of Association

57

(8)

Sets of 2 x r and s x 2 Tables

65

(24)

Introduction

67

(1)

Sets of 2 x r Tables

67

(11)

Sets of s x 2 Tables

78

(8)

Relationships Between Sets of Tables

86

(3)

The s x r Table

89

(32)

Introduction

91

(1)

Association

91

(9)

Exact Tests for Association

100

(5)

Measures of Association

105

(6)

Observer Agreement

111

(5)

Test for Ordered Differences

116

(5)

Sets of s x r Tables

121

(38)

Introduction

123

(1)

General Mantel-Haenszel Methodology

124

(3)

Mantel-Haenszel Applications

127

(10)

Advanced Topic: Application to Repeated Measures

137

(22)

Nonparametric Methods

159

(22)

Introduction

161

(1)

Wilcoxon-Mann-Whitney Test

161

(4)

Kruskal-Wallis Test

165

(3)

Friedman's Chi-Square Test

168

(2)

Aligned Ranks Test for Randomized Complete Blocks

170

(1)

Durbin's Test for Balanced Incomplete Blocks

171

(3)

Rank Analysis of Covariance

174

(7)

Logistic Regression I: Dichotomous Response

181

(60)

Introduction

183

(1)

Dichotomous Explanatory Variables

184

(11)

Using the CLASS Statement

195

(8)

Qualitative Explanatory Variables

203

(8)

Continuous and Ordinal Explanatory Variables

211

(6)

A Note on Diagnostics

217

(5)

Maximum Likelihood Estimation Problems and Alternatives

222

(3)

Exact Methods in Logistic Regression

225

(7)

Using the CATMOD and GENMOD Procedures for Logistic Regression

232

(9)

Appendix A: Statistical Methodology for Dichotomous Logistic Regression

239

(2)

Logistic Regression II: Polytomous Response

241

(30)

Introduction

243

(1)

Ordinal Response: Proportional Odds Model

243

(14)

Nominal Response: Generalized Logits Model

257

(14)

Conditional Logistic Regression

271

(52)

Introduction

273

(1)

Paired Observations from a Highly Stratified Cohort Study

273

(3)

Clinical Trials Study Analysis

276

(7)

Crossover Design Studies

283

(12)

General Conditional Logistic Regression

295

(5)

Paired Observations in a Retrospective Matched Study

300

(9)

1:m Conditional Logistic Regression

309

(5)

Exact Conditional Logistic Regression in the Stratified Setting

314

(9)

Appendix A: Theory for the Case-Control Retrospective Setting

318

(2)

Appendix B: Theory for Exact Conditional Inference

320

(1)

Appendix C: ODS Macro

321

(2)

Quantal Bioassay Analysis

323

(24)

Introduction

325

(1)

Estimating Tolerance Distributions

325

(5)

Comparing Two Drugs

330

(9)

Analysis of Pain Study

339

(8)

Poisson Regression

347

(16)

Introduction

349

(1)

Methodology for Poisson Regression

349

(2)

Simple Poisson Counts Example

351

(2)

Poisson Regression for Incidence Densities

353

(3)

Overdispersion in Lower Respiratory Infection Example

356

(7)

Weighted Least Squares

363

(64)

Introduction

365

(1)

Weighted Least Squares Methodology

365

(6)

Using PROC CATMOD for Weighted Least Squares Analysis

371

(6)

Analysis of Means: Performing Contrast Tests

377

(9)

Analysis of Proportions: Occupational Data

386

(9)

Obstetrical Pain Data: Advanced Modeling of Means

395

(14)

Analysis of Survey Sample Data

409

(9)

Modeling Rank Measures of Association Statistics

418

(9)

Appendix A: Statistical Methodology for Weighted Least Squares

422

(5)

Modeling Repeated Measurements Data with WLS

427

(42)

Introduction

429

(1)

Weighted Least Squares

430

(23)

Advanced Topic: Further Weighted Least Squares Applications

453

(16)

Generalized Estimating Equations

469

(82)

Introduction

471

(1)

Methodology

471

(7)

Summary of the GEE Methodology

478

(2)

Passive Smoking Example

480

(7)

Crossover Example

487

(7)

Respiratory Data

494

(9)

Using a Modified Wald Statistic to Assess Model Effects

503

(2)

Diagnostic Data

505

(5)

Using GEE for Count Data

510

(4)

Fitting the Proportional Odds Model

514

(4)

GEE Analyses for Data with Missing Values

518

(9)

Alternating Logistic Regression

527

(6)

Using GEE to Fit a Partial Proportional Odds Model: Univariate Outcome

533

(8)

Using GEE to Account for Overdispersion: Univariate Outcome

541

(10)

Appendix A: Steps to Find the GEE Solution

547

(1)

Appendix B: Macro for Adjusted Wald Statistic

548

(3)

Loglinear Models

551

(40)

Introduction

553

(1)

Two-Way Contingency Tables

554

(10)

Three-Way Contingency Tables

564

(10)

Higher-Order Contingency Tables

574

(11)

Correspondence Between Logistic Models and Loglinear Models

585

(6)

Appendix A: Equivalence of the Loglinear and Poisson Regression Models

588

(3)

Categorized Time-to-Event Data

591

(16)

Introduction

593

(1)

Life Table Estimation of Survival Rates

593

(3)

Mantel-Cox Test

596

(3)

Piecewise Exponential Models

599

(8)

References

607

(12)

Index

619

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Categorical Data Analysis Using the SAS System

Summary

Author Biography

Table of Contents

Supplemental Materials