Applied Categorical Data Analysis and Translational Research

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.

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

• Preface. Preface to the First Edition.1 Introduction.1.1 A Prototype Example.1.2 A Review of Likelihood-Based Methods.1.3 Interval Estimation for a Proportion.1.4 About This Book.2 Contingency Tables.2.1 Some Sampling Models for Categorical Data.2.1.1 The Binomial and Multinomial Distributions.2.1.2 The Hypergeometric Distributions.2.2 Inferences for 2-by-2 Contingency Tables.2.2.1 Comparison of Two Proportions.2.2.2 Tests for Independence.2.2.3 Fisher’s Exact Test.2.2.4 Relative Risk and Odds Ratio.2.2.5 Etiologic Fraction.2.2.6 Crossover Designs.2.3 The Mantel–Haenszel Method.2.4 Inferences for General Two-Way Tables.2.4.1 Comparison of Several Proportions.2.4.2 Testing for Independence in Two-Way Tables.2.4.3 Ordered 2-by-k Contingency Tables.2.5 Sample Size Determination.Exercises.3 Loglinear Models.3.1 Loglinear Models for Two-Way Tables.3.2 Loglinear Models for Three-Way Tables.3.2.1 The Models of Independence.3.2.2 Relationships Between Terms and Hierarchy of Models.3.2.3 Testing a Specific Model.3.2.4 Searching for the Best Model.3.2.5 Collapsing Tables.3.3 Loglinear Models for Higher-Dimensional Tables.3.3.1 Testing a Specific Model.3.3.2 Searching for the Best Model.3.3.3 Measures of Association with an Effect Modification.3.3.4 Searching for a Model with a Dependent Variable.Exercises.4 Logistic Regression Models.4.1 Modeling a Probability.4.1.1 The Logarithmic Transformation.4.1.2 The Probit Transformation.4.1.3 The Logistic Transformation.4.2 Simple Regression Analysis.4.2.1 The Logistic Regression Model.4.2.2 Measure of Association.4.2.3 Tests of Association.4.2.4 Use of the Logistic Model for Different Designs.4.2.5 Overdispersion.4.3 Multiple Regression Analysis.4.3.1 Logistic Regression Model with Several Covariates.4.3.2 Effect Modifications.4.3.3 Polynomial Regression.4.3.4 Testing Hypotheses in Multiple Logistic Regression.4.3.5 Measures of Goodness-of-Fit.4.4 Ordinal Logistic Model.4.5 Quantal Bioassays.4.5.1 Types of Bioassays.4.5.2 Quantal Response Bioassays.Exercises.5 Methods for Matched Data.5.1 Measuring Agreement.5.2 Pair-Matched Case-Control Studies.5.2.1 The Model.5.2.2 The Analysis.5.2.3 The Case of Small Samples.5.2.4 Risk Factors with Multiple Categories and Ordinal Risks.5.3 Multiple Matching.5.3.1 The Conditional Approach.5.3.2 Estimation of the Odds Ratio.5.3.3 Testing for Exposure Effect.5.3.4 Testing for Homogeneity.5.4 Conditional Logistic Regression.5.4.1 Simple Regression Analysis.5.4.2 Multiple Regression Analysis.Exercises.6 Methods for Count Data.6.1 The Poisson Distribution.6.2 Testing Goodness-of-Fit.6.3 The Poisson Regression Model.6.3.1 Simple Regression Analysis.6.3.2 Multiple Regression Analysis.6.3.3 Overdispersion.6.3.4 Stepwise Regression.Exercise.7 Categorical Data and Translational Research.7.1 Types of Clinical Studies.7.2 From Bioassays to Translational Research.7.2.1 Analysis of In Vitro Experiments.7.2.2 Design and Analysis of Experiments for Combination Therapy.7.3 Phase I Clinical Trials.7.3.1 Standard Design.7.3.2 Fast Track Design.7.3.3 Continual Reassessment Method.7.4 Phase II Clinical Trials.7.4.1 Sample Size Determination for Phase II Clinical Trials.7.4.2 Phase II Clinical Trial Designs for Selection.7.4.3 Two-Stage Phase II Design.7.4.4 Toxicity Monitoring in Phase II Trials.7.4.5 Multiple Decisions.Exercises.8 Categorical Data and Diagnostic Medicine.8.1 Some Examples.8.2 The Diagnosis Process.8.2.1 The Developmental Stage.8.2.2 The Applicational Stage.8.3 Some Statistical Issues.8.3.1 The Response Rate.8.3.2 The Issue of Population Random Testing.8.3.3 Screenable Disease Prevalence.8.3.4 An Index for Diagnostic Competence.8.4 Prevalence Surveys.8.4.1 Known Sensitivity and Specificity.8.4.2 Unknown Sensitivity and Specificity.8.4.3 Prevalence Survey with a New Test.8.5 The Receiver Operating Characteristic Curve.8.5.1 The ROC Function and ROC Curve.8.5.2 Some Parametric ROC Models.8.5.3 Estimation of the ROC Curve.8.5.4 Index for Diagnostic Accuracy.8.5.5 Estimation of Area Under ROC Curve.8.6 The Optimization Problem.8.6.1 Basic Criterion: Youden’s Index.8.6.2 Possible Solutions.8.7 Statistical Considerations.8.7.1 Evaluation of Screening Tests.8.7.2 Comparison of Screening Tests.8.7.3 Consideration of Subjects’ Characteristics.Exercises.9 Transition from Categorical to Survival Data.9.1 Survival Data.9.2 Introductory Survival Analysis.9.2.1 Kaplan–Meier Curve.9.2.2 Comparison of Survival Distributions.9.3 Simple Regression and Correlation.9.3.1 Model and Approach.9.3.2 Measures of Association.9.3.3 Tests of Association.9.4 Multiple Regression and Correlation.9.4.1 Proportional Hazards Models with Several Covariates.9.4.2 Testing Hypotheses in Multiple Regression.9.4.3 Time-Dependent Covariates and Applications.9.5 Competing Risks.9.5.1 Redistribution to the Right Method.9.5.2 Estimation of the Cumulative Incidence.9.5.3 Brief Discussion of Proportional Hazards Regression.Exercise.Bibliography.Index.