Applied Categorical and Count Data Analysis

Description

Developed from the authors’ graduate-level biostatistics course, Applied Categorical and Count Data Analysis, Second Edition explains how to perform the statistical analysis of discrete data, including categorical and count outcomes. The authors have been teaching categorical data analysis courses at the University of Rochester and Tulane University for more than a decade. This book embodies their decade-long experience and insight in teaching and applying statistical models for categorical and count data. The authors describe the basic ideas underlying each concept, model, and approach to give readers a good grasp of the fundamentals of the methodology without relying on rigorous mathematical arguments. The second edition covers classic concepts and popular topics, such as contingency tables, logistic regression models, and Poisson regression models, along with modern areas that include models for zero-modified count outcomes, parametric and semiparametric longitudinal data analysis, reliability analysis, and methods for dealing with missing values. As in the first edition, R, SAS, SPSS, and Stata programming codes are provided for all the examples, enabling readers to immediately experiment with the data in the examples and even adapt or extend the codes to fit data from their own studies. Designed for a one-semester course for graduate and senior undergraduate students in biostatistics, this self-contained text is also suitable as a self-learning guide for biomedical and psychosocial researchers. It will help readers analyze data with discrete variables in a wide range of biomedical and psychosocial research fields. Features: Describes the basic ideas underlying each concept and modelIncludes R, SAS, SPSS and Stata programming codes for all the examplesFeatures significantly expanded Chapters 4, 5, and 8 (Chapters 4-6, and 9 in the second editionExpands discussion for subtle issues in longitudinal and clustered data analysis such as time varying covariates and comparison of generalized linear mixed-effect models with GEE Cover Half Title Series Page Title Page Copyright Page Contents Preface to the Second Edition Preface to the First Edition Author biographies 1. Introduction 1.1. Discrete Outcomes 1.2. Data Source 1.3. Outline of the Book 1.3.1. Distribution of random variables 1.3.2. Association between two random variables 1.3.3. Regression analysis 1.3.4. Log-linear methods for contingency tables 1.3.5. Discrete survival data analysis 1.3.6. Longitudinal data analysis 1.3.7. Validity and reliability data analysis 1.3.8. Incomplete data analysis 1.4. Review of Key Statistical Results 1.4.1. Central limit theorem and law of large numbers 1.4.2. Delta method and Slutsky's theorem 1.4.3. Maximum likelihood estimate 1.4.4. Estimating equations 1.4.5. U-statistics 1.5. Software Exercises 2. Contingency Tables 2.1. Inference for One-Way Frequency Table 2.1.1. Binary case 2.1.2. Inference for multinomial variable 2.1.3. Inference for Count variable 2.2. Inference for 2 × 2 Table 2.2.1. Testing association 2.2.2. Measures of association 2.2.3. Test for marginal homogeneity 2.2.4. Agreement 2.3. Inference for 2 × r Tables 2.3.1. Cochran–Armitage trend test 2.3.2. Mann–Whitney–Wilcoxon test 2.4. Inference for s × r Table 2.4.1. Tests of association 2.4.2. Marginal homogeneity and symmetry 2.4.3. Agreement 2.5. Measures of Association 2.5.1. Measures of association for ordinal outcome 2.5.2. Measures of association for nominal outcome Exercises 3. Sets of Contingency Tables 3.1. Confounding Effects 3.2. Sets of 2 × 2 Tables 3.2.1. Cochran–Mantel–Haenszel test for independence 3.2.2. Estimates and tests of common odds ratios 3.3. Sets of s × r Tables 3.3.1. Tests of general association 3.3.2. Mean score statistic 3.3.3. Correlation statistic 3.3.4. Kappa coefficients for stratified tables Exercises 4. Regression Models for Binary Response 4.1. Logistic Regression for Binary Response 4.1.1. Motivation of logistic regression 4.1.2. Denfition of logistic models 4.1.3. Parameter interpretation 4.1.4. Invariance to study designs 4.1.5. Simpson's paradox revisited 4.1.6. Breslow–Day test and moderation analysis 4.2. Inference About Model Parameters 4.2.1. Maximum likelihood estimate 4.2.2. General linear hypotheses 4.2.3. Exact inference for logistic regression 4.2.4. Bias-reduced logistic regression 4.3. Generalized Linear Models for Binary Responses 4.3.1. Generalized linear models 4.3.2. Probit model 4.3.3. Complementary log-log model 4.3.4. Linear probability model 4.3.5. Comparison of the link functions 4.4. Model Evaluation and Diagnosis 4.4.1. Goodness of fit 4.4.2. Model diagnosis 4.4.3. Predictability and calibration 4.5. Models for Aggregated Binary Response 4.5.1. Binomial regression 4.5.2. Overdispersion issues 4.5.3. Beta binomial regression models Exercises 5. Regression Models for Polytomous Responses 5.1. Modeling Polytomous Responses 5.1.1. Scales of polytomous responses 5.1.2. GLM for polytomous responses 5.1.3. Inference for models for polytomous response 5.2. Models for Nominal Responses 5.2.1. Generalized logit models 5.2.2. Inference for Generalized Logit Models 5.2.3. Multinomial probit models 5.2.4. Independence of irrelevant alternatives 5.3. Models for Ordinal Responses 5.3.1. Cumulative models 5.3.2. Continuation ratio models 5.3.3. Adjacent categories models 5.3.4. Comparison of different models 5.4. Goodness of fit 5.4.1. The Pearson chi-Square statistic 5.4.2. The deviance test 5.4.3. The Hosmer–Lemeshow test Exercises 6. Regression Models for Count Response 6.1. Poisson Regression Model for Count Response 6.1.1. Parameter interpretation 6.1.2. Inference about model parameters 6.1.3. Incidence rates and offsets in log-linear models 6.2. Goodness of Fit 6.2.1. Pearson chi-Square statistic 6.2.2. Scaled deviance statistic 6.3. Overdispersion 6.3.1. Detection of overdispersion 6.3.2. Correction for overdispersion 6.4. Models for Overdispersed Count Responses 6.4.1. Distributions for overdispersed count variables 6.4.2. Regression models 6.5. Zero-Modification Models 6.5.1. Structural zeros and zero-inflated models 6.5.2. Data without zeros 6.5.3. Hurdle models 6.6. Model Comparisons Exercises 7. Log-Linear Models for Contingency Tables 7.1. Analysis of Log-Linear Models 7.1.1. Motivation 7.1.2. Log-linear models for contingency tables 7.1.3. Parameter interpretation 7.1.4. Inference 7.2. Two-Way Contingency Tables 7.2.1. Independence 7.2.2. Uniform associations 7.2.3. Symmetry and marginal homogeneity 7.3. Three-Way Contingency Tables 7.3.1. Independence 7.3.2. Association homogeneity 7.4. Irregular Tables 7.4.1. Structural zeros in contingency tables 7.4.2. Models for irregular tables 7.4.3. Bradley–Terry model 7.5. Model Selection 7.5.1. Model evaluation 7.5.2. Stepwise selection 7.5.3. Graphical models Exercises 8. Analyses of Discrete Survival Time 8.1. Special Features of Survival Data 8.1.1. Censoring 8.1.2. Truncation 8.1.3. Discrete survival time 8.1.4. Survival and hazard functions 8.2. Life Table Methods 8.2.1. Life tables 8.2.2. The Mantel–Cox test 8.3. Regression Models 8.3.1. Complementary log-log regression 8.3.2. Discrete proportional odds model Exercises 9. Longitudinal and Clustered Data Analysis 9.1. Data Preparation and Exploration 9.1.1. Longitudinal data formats 9.1.2. Exploratory analysis 9.2. Linear Mixed Effect Models 9.2.1. Multivariate linear regression models 9.2.2. Linear mixed-effects models 9.2.3. Inference of LMM 9.2.4. Clustered studies 9.2.5. Power for longitudinal and clustered studies 9.3. Generalized Linear Mixed-Effects Models 9.3.1. Binary response 9.3.2. Maximum likelihood inference 9.3.3. Polytomous responses 9.3.4. Count responses 9.4. Marginal Models for Longitudinal Data 9.4.1. Generalized estimation equations 9.4.2. Binary responses 9.4.3. Polytomous responses 9.4.4. Count responses 9.4.5. Comparison of GLMM with marginal models 9.5. Model Diagnosis 9.5.1. Marginal models 9.5.2. Generalized linear mixed-effect models Exercises 10. Evaluation of Instruments 10.1. Diagnostic-Ability 10.1.1. Receiver operating characteristic curves 10.1.2. Inference 10.1.3. Areas under ROC curves 10.2. Added Predictability 10.2.1. Difference in AUCs 10.2.2. Net reclassification improvement 10.2.3. Integrated discrimination improvement 10.3. Criterion Validity 10.3.1. Concordance correlation coefficient 10.4. Internal Reliability 10.4.1. Spearman–Brown Spearman-Brown Rho 10.4.2. Cronbach coefficient alpha 10.4.3. Intraclass correlation coefficient 10.5. Test-Retest Reliability Exercises 11. Analysis of Incomplete Data 11.1. Incomplete Data and Associated Impact 11.1.1. Observational missing 11.1.2. Missing by design 11.1.3. Counterfactual missing 11.1.4. Impact of missing values 11.2. Missing Data Mechanism 11.2.1. Missing completely at random 11.2.2. Missing at random 11.2.3. Missing not at random 11.3. Methods for Incomplete Data 11.3.1. Maximum likelihood method 11.3.2. Imputation methods 11.3.3. Inverse probability weighting 11.3.4. Doubly robust estimate 11.3.5. Sensitivity analysis 11.4. Applications 11.4.1. Verification bias of diagnostic studies 11.4.2. Causal inference of treatment effects 11.4.3. Longitudinal data with missing values 11.4.4. Survey studies Exercises References Index