Applied Categorical Data Analysis and Translational Research

by Chap T. Le

Overview

An updated treatment of categorical data analysis in the biomedical sciences that now explores applications to translational research

Thoroughly updated with the latest advances in the field, Applied Categorical Data Analysis and Translational Research, Second Edition maintains the accessible style of its predecessor while also exploring the importance of translational research as it relates to basic scientific findings within clinical practice. With its easy-to-follow style, updated coverage of major methodologies, and broadened scope of coverage, this new edition provides an accessible guide to statistical methods involving categorical data and the steps to their application in problem solving in the biomedical sciences.

Delving even further into the applied direction, this update offers many real-world examples from biomedicine, epidemiology, and public health along with detailed case studies taken straight from modern research in these fields. Additional features of the Second Edition include:

• A new chapter on the relationship between translational research and categorical data, focusing on design study, bioassay, and Phase I and Phase II clinical trials

• A new chapter on categorical data and diagnostic medicine, with coverage of the diagnostic process, prevalence surveys, the ROC function and ROC curve, and important statistical considerations

• A revised chapter on logistic regression models featuring an updated treatment of simple and multiple regression analysis

• An added section on quantal bioassays

Each chapter features updated and new exercise sets along with numerous graphs that demonstrate the highly visual nature of the topic. A related Web site features the book's examples as well as additional data sets that can be worked with using SAS® software.

The only book of its kind to provide balanced coverage of methods for both categorical data and translational research, Applied Categorical Data Analysis and Translational Research, Second Edition is an excellent book for courses on applied statistics and biostatistics at the upper-undergraduate and graduate levels. It is also a valuable reference for researchers and practitioners in the biomedical and public health fields.

Product Details

ISBN-13:	9780470371305
Publisher:	Wiley
Publication date:	12/14/2009
Edition description:	2nd ed.
Pages:	416
Product dimensions:	6.10(w) x 9.20(h) x 1.00(d)

About the Author

Chap T. Le, PhD, is Distinguished Professor and Director of Biostatistics at the University of Minnesota Cancer Center. In addition to providing statistical consulting for a variety of biomedical research projects, he has worked on collaborations that have focused on the analyses of survival and categorical data and, currently, in the areas of cancer and tobacco research. Dr. Le is the author of Health and Numbers: A Problems-Based Introduction to Biostatistics, Third Edition; Introductory Biostatistics; and Applied Survival Analysis, all published by Wiley.

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Table of Contents

Preface xiii

Preface to First Edition xv

1 Introduction 1

1.1 A Prototype Example 2

1.2 A Review of Likelihood-Based Methods 5

1.3 Interval Estimation for a Proportion 11

1.4 About This Book 13

2 Contingency Tables 15

2.1 Some Sampling Models for Categorical Data 16

2.1.1 The Binomial and Multinomial Distributions 16

2.1.2 The Hypergeometric Distributions 19

2.2 Inferences for 2-by-2 Contingency Tables 22

2.2.1 Comparison of Two Proportions 22

2.2.2 Tests for Independence 28

2.2.3 Fisher's Exact Test 30

2.2.4 Relative Risk and Odds Ratio 32

2.2.5 Etiologic Fraction 41

2.2.6 Crossover Designs 43

2.3 The Mantel-Haenszel Method 45

2.4 Inferences for General Two-Way Tables 51

2.4.1 Comparison of Several Proportions 52

2.4.2 Testing for Independence in Two-Way Tables 53

2.4.3 Ordered 2-by-k Contingency Tables 55

2.5 Sample Size Determination 60

Exercises 62

3 Loglinear Models 72

3.1 Loglinear Models for Two-Way Tables 74

3.2 Loglinear Models for Three-Way Tables 76

3.2.1 The Models of Independence 78

3.2.2 Relationships Between Terms and Hierarchy of Models 79

3.2.3 Testing a Specific Model 80

3.2.4 Searching for the Best Model 88

3.2.5 Collapsing Tables 92

3.3 Loglinear Models for Higher-Dimensional Tables 92

3.3.1 Testing a Specific Model 93

3.3.2 Searching for the Best Model 95

3.3.3 Measures of Association with an Effect Modification 99

3.3.4 Searching for a Model with a Dependent Variable 104

Exercises 105

4 Logistic Regression Models 113

4.1 Modeling a Probability 116

4.1.1 The Logarithmic Transformation 118

4.1.2 The Probit Transformation 118

4.1.3 The Logistic Transformation 119

4.2 Simple Regression Analysis 119

4.2.1 The Logistic Regression Model 120

4.2.2 Measure of Association 121

4.2.3 Tests of Association 124

4.2.4 Use of the Logistic Model for Different Designs 124

4.2.5 Overdispersion 125

4.3 Multiple Regression Analysis 128

4.3.1 Logistic Regression Model with Several Covariates 128

4.3.2 Effect Modifications 130

4.3.3 Polynomial Regression 131

4.3.4 Testing Hypotheses in Multiple Logistic Regression 132

4.3.5 Measures of Goodness-of-Fit 140

4.4 Ordinal Logistic Model 142

4.5 Quantal Bioassays 145

4.5.1 Types of Bioassays 146

4.5.2 Quantal Response Bioassays 147

Exercises 150

5 Methods for Matched Data 158

5.1 Measuring Agreement 159

5.2 Pair-Matched Case-Control Studies 162

5.2.1 The Model 162

5.2.2 The Analysis 164

5.2.3 The Case of Small Samples 167

5.2.4 Risk Factors with Multiple Categories and Ordinal Risks 169

5.3 Multiple Matching 171

5.3.1 The Conditional Approach 171

5.3.2 Estimation of the Odds Ratio 172

5.3.3 Testing for Exposure Effect 173

5.3.4 Testing for Homogeneity 175

5.4 Conditional Logistic Regression 176

5.4.1 Simple Regression Analysis 177

5.4.2 Multiple Regression Analysis 182

Exercises 189

6 Methods for Count Data 198

6.1 The Poisson Distribution 198

6.2 Testing Goodness-of-Fit 202

6.3 The Poisson Regression Model 204

6.3.1 Simple Regression Analysis 206

6.3.2 Multiple Regression Analysis 208

6.3.3 Overdispersion 215

6.3.4 Stepwise Regression 217

Exercise 219

7 Categorical Data and Translational Research 227

7.1 Types of Clinical Studies 228

7.2 From Bioassays to Translational Research 230

7.2.1 Analysis of In Vitro Experiments 231

7.2.2 Design and Analysis of Experiments for Combination Therapy 234

7.3 Phase I Clinical Trials 238

7.3.1 Standard Design 238

7.3.2 Fast Tracts Design 243

7.3.3 Continual Reassessment Method 247

7.4 Phase II Clinical Trials 253

7.4.1 Sample Size Determination for Phase II Clinical Trials 255

7.4.2 Phase II Clinical Trial Designs for Selection 259

7.4.3 Two-Stage Phase II Design 264

7.4.4 Toxicity Monitoring in Phase II Trials 271

7.4.5 Multiple Decisions 279

Exercises 285

8 Categorical Data and Diagnostic Medicine 289

8.1 Some Examples 290

8.2 The Diagnosis Process 294

8.2.1 The Developmental Stage 294

8.2.2 The Applicational Stage 298

8.3 Some Statistical Issues 302

8.3.1 The Response Rate 302

8.3.2 The Issue of Population Random Testing 303

8.3.3 Screenable Disease Prevalence 304

8.3.4 An Index for Diagnostic Competence 306

8.4 Prevalence Surveys 308

8.4.1 Known Sensitivity and Specificity 309

8.4.2 Unknown Sensitivity and Specificity 312

8.4.3 Prevalence Survey with a New Test 315

8.5 The Receiver Operating Characteristic Curve 317

8.5.1 The ROC Function and ROC Curve 317

8.5.2 Some Parametric ROC Models 319

8.5.3 Estimation of the ROC Curve 320

8.5.4 Index for Diagnostic Accuracy 322

8.5.5 Estimation of Area Under ROC Curve 323

8.6 The Optimization Problem 325

8.6.1 Basic Criterion: Youden's Index 326

8.6.2 Possible Solutions 327

8.7 Statistical Considerations 331

8.7.1 Evaluation of Screening Tests 332

8.7.2 Comparison of Screening Tests 333

8.7.3 Consideration of Subjects' Characteristics 338

Exercises 340

9 Transition from Categorical to Survival Data 342

9.1 Survival Data 343

9.2 Introductory Survival Analysis 346

9.2.1 Kaplan-Meier Curve 346

9.2.2 Comparison of Survival Distributions 349

9.3 Simple Regression and Correlation 353

9.3.1 Model and Approach 354

9.3.2 Measures of Association 355

9.3.3 Tests of Association 357

9.4 Multiple Regression and Correlation 358

9.4.1 Proportional Hazards Models with Several Covariates 358

9.4.2 Testing Hypotheses in Multiple Regression 359

9.4.3 Time-Dependent Covariates and Applications 364

9.5 Competing Risks 367

9.5.1 Redistribution to the Right Method 368

9.5.2 Estimation of the Cumulative Incidence 370

9.5.3 Brief Discussion of Proportional Hazards Regression 374

Exercise 376

Bibliography 383

Index 393

Editorial Reviews

"The book works out, in painstaking detail, many analytical and numerical examples." (Journal of Biopharmaceutical Statistics, 2010)

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