Modeling Binary Correlated Responses: Using SAS, SPSS, R and STATA

This book is an updated edition of Modeling Binary Correlated Responses Using SAS, SPSS and R , and now it includes the use of STATA. It uses these Statistical tools to analyze correlated binary data, accessible to practitioners in a single volume. Chapters cover recently developed statistical tools and statistical packages, as well as showcase both traditional and new methods for application to health-related research. Data analysis presented in each chapter will provide step-by-step instructions so these new methods can be readily applied to projects. Short tutorials are in the appendix, for readers interested in learning more about the languages. Data and computer programs will be publicly available in order for readers to replicate model development, but learning a new statistical language is not necessary with this book. The inclusion of code for R, SAS, SPSS and STATA, allows for easy implementation by readers. Researchers and graduate students in Statistics, Epidemiology, and Public Health will find this book particularly useful. Preface Part I: Introduction and Review of Modeling Uncorrelated Observations Part II: Analyzing Correlated Data Through Random Component Part III: Analyzing Correlated Data Through Systematic Components Part IV: Analyzing Correlated Data Through the Joint Modeling of Mean and Variance Part V: Case Studies: USA Election 2020 and Netherlands COVID Contents Part I: Introduction and Review of Modeling Uncorrelated Observations Chapter 1: Introduction to Binary Logistic Regression 1.1 Motivating Example 1.2 Definition and Notation 1.2.1 Notation 1.2.2 Definitions Categorical Variable in the Form of a Series of Binary Variables Relationship Between Response and Predictor Variables 1.3 Exploratory Analyses 1.4 Statistical Models 1.4.1 Chapter 3: Standard Binary Logistic Regression Model 1.4.2 Chapter 4: Overdispersed Logistic Regression Model 1.4.3 Chapter 5: Survey Data Logistic Regression Model 1.4.4 Chapter 6: Generalized Estimating Equations (GEE) Logistic Regression Model 1.4.5 Chapter 7: Generalized Method of Moments (GMM) Logistic Regression Model 1.4.6 Chapter 8: Exact Logistic Regression Model 1.4.7 Chapter 9: Two-Level Nested Logistic Regression Model 1.4.8 Chapter 10: Hierarchical Logistic Regression Model 1.4.9 Chapter 11: Fixed Effects Logistic Regression Model 1.4.10 Chapter 12: Heteroscedastic Logistic Regression Model 1.4.11 Chapter 13: Case Studies—Election Data and COVID Data 1.5 Analysis of Data 1.5.1 SAS Programming 1.5.2 SPSS Programming 1.5.3 R Programming 1.5.4 STATA Programming 1.5.5 Fitting Models 1.6 Conclusions 1.7 Related Examples 1.7.1 Medicare Data 1.7.2 Philippines Data 1.7.3 Household Satisfaction Survey 1.7.4 NHANES: Treatment for Osteoporosis 1.7.5 COVID Data 1.7.6 Election Data References Chapter 2: Short History of the Logistic Regression Model 2.1 Motivating Example 2.2 Definition and Notation 2.2.1 Notation 2.2.2 Definition 2.3 Exploratory Analyses 2.4 Statistical Model 2.5 Analysis of Data 2.6 Conclusions References Chapter 3: Standard Binary Logistic Regression Model 3.1 Motivating Example 3.1.1 Study Hypotheses 3.2 Definition and Notation 3.3 Exploratory Analyses 3.4 Statistical Models 3.4.1 Probability 3.4.2 Odds 3.4.3 Logits 3.4.4 Logistic Regression Versus Ordinary Least Squares 3.4.5 Generalized Linear Models (GLMs) 3.4.6 Response Probability Distributions 3.4.7 Log-Likelihood Functions 3.4.8 Maximum Likelihood Fitting 3.4.9 Goodness-of-Fit 3.4.10 Other Fit Statistics 3.4.11 Assumptions for Logistic Regression Model 3.4.12 Interpretation of Coefficients 3.4.13 Interpretation of Odds Ratio (OR) 3.4.14 Model Fit 3.4.15 Null Hypothesis 3.4.16 Predicted Probabilities 3.4.17 Computational Issues Encountered with Logistic Regression 3.5 Analysis of Data 3.5.1 Medicare Data 3.5.2 Analysis of Medicare Data with SAS Computing 3.5.3 Analysis of Medicare Data with SPSS Computing 3.5.4 Analysis of Medicare Data with R Computing 3.5.5 Analysis of Medicare Data with STATA Computing 3.6 Conclusion 3.7 Related Examples Appendix References Part II: Analyzing Correlated Data Through Random Component Chapter 4: Overdispersed Logistic Regression Model 4.1 Motivating Example 4.2 Definition and Notation 4.3 Exploratory Data Analyses 4.4 Statistical Model 4.4.1 Williams’ Method of Analysis 4.4.2 Overdispersion Factor 4.4.3 Datasets 4.4.4 Housing Satisfaction Survey 4.5 Analysis of Data 4.5.1 Standard Logistic Regression Model 4.5.2 Overdispersed Logistic Regression Model 4.5.3 Overdispersed Logistic Regression Model Using SAS Program 4.5.4 Overdispersed Logistic Regression Model Using R Program 4.5.5 Exchangeability Logistic Regression Model 4.5.6 Exchangeability Logistic Regression Model Using SAS Program 4.5.7 Exchangeability Logistic Regression Model Using R Program 4.6 Conclusion 4.7 Related Example 4.7.1 Use of Word Einai References Chapter 5: Weighted Logistic Regression Model 5.1 Motivating Example 5.2 Definition and Notation 5.3 Exploratory Analyses 5.3.1 Treatment for Osteoporosis 5.4 Statistical Model 5.5 Analysis of Data 5.5.1 Weighted Logistic Regression Model with Survey Weights 5.5.2 Weighted Logistic Regression Model with Survey Weights Using SAS Program 5.5.3 Weighted Logistic Regression Model with Survey Weights Using SPSS Program 5.5.4 Weighted Logistic Regression Model with Survey Weights Using R Program 5.5.5 Weighted Logistic Regression Model with Strata and Clusters Identified 5.5.6 Comparison of Weighted Logistic Regression Models 5.6 Conclusion 5.7 Related Examples References Chapter 6: Generalized Estimating Equations Logistic Regression 6.1 Motivating Example 6.1.1 Description of the Rehospitalization Issues 6.2 Definition and Notation 6.3 Exploratory Analyses 6.4 Statistical Models: GEE Logistic Regression 6.4.1 Medicare Data 6.4.2 Generalized Linear Model 6.4.3 Generalized Estimating Equations 6.4.4 Marginal Model 6.4.5 Working Correlation Matrices 6.4.6 Model Fit 6.4.7 Properties of GEE Estimates 6.5 Data Analysis 6.5.1 GEE Logistic Regression Model 6.5.2 GEE Logistic Regression Model with SAS Programming 6.5.3 GEE Logistic Regression Model with SPSS Programming 6.5.4 GEE Logistic Regression Model with R Programming 6.5.5 GEE Logistic Regression Model with STATA Programming 6.6 Conclusion 6.7 Related Examples References Chapter 7: Generalized Method of Moments Logistic Regression Model 7.1 Motivating Example 7.1.1 Description of the Case Study 7.1.2 Study Hypotheses 7.2 Definition and Notation 7.3 Exploratory Analyses 7.4 Statistical Model 7.4.1 GEE Models for Time-Dependent Covariates 7.4.2 Lai and Small GMM Method 7.4.3 Types of Classification of Time-Dependent Covariates 7.4.4 Lalonde Wilson and Yin Method 7.5 Analysis of Data 7.5.1 Modeling Probability of Rehospitalization 7.5.2 Modeling Probability of Rehospitalization SAS: Results 7.6 Conclusions 7.7 Related Examples References Chapter 8: Exact Logistic Regression Model 8.1 Motivating Example 8.2 Definition and Notation 8.3 Exploratory Analysis 8.3.1 Artificial Data for Clustering 8.3.2 Standard Logistic Regression Sparse and Skewed Correlated Binary Data 8.3.3 Two-Stage Clustered Data 8.4 Statistical Models 8.4.1 Independent Observations 8.4.2 One-Stage Cluster Model 8.4.3 Two-Stage Cluster Exact Logistic Regression Model 8.5 Analysis of Data 8.5.1 Exact Logistic Regression for Independent Observations 8.5.2 Exact Logistic Regression for One-Stage Clustered Data 8.5.3 Exact Logistic Regression for Independent Observations with R Programming 8.5.4 Exact Logistic Regression for One-Stage Clustered Data with R Program 8.5.5 Exact Logistic Regression for One-Stage Clustered Data with C++ Program 8.5.6 Exact Logistic Regression for Two-Stage Clustered Data with C++ Program 8.6 Conclusions 8.7 Related Examples 8.7.1 Description of the Data 8.7.2 Clustering References Part III: Analyzing Correlated Data Through Systematic Components Chapter 9: Two-Level Nested Logistic Regression Model 9.1 Motivating Example 9.1.1 Description of the Case Study 9.1.2 Study Hypotheses 9.2 Definition and Notation 9.3 Exploratory Analyses 9.3.1 Medicare 9.4 Statistical Model 9.4.1 Marginal and Conditional Models 9.4.2 Two-Level Nested Logistic Regression with Random Intercept Model 9.4.3 Interpretation of Parameter Estimates 9.4.4 Two-Level Nested Logistic Regression Model with Random Intercept and Slope 9.5 Analysis of Data 9.5.1 Two-Level Nested Logistic Regression Model with Random Intercepts Using SAS (PROC NLMIXED Versus PROC GLIMMIX) Two-Level Nested Logistic Regression Model with Random Intercepts Using SAS (PROC GLIMMIX) Two-Level Nested Logistic Regression Model with Random Intercepts Using SAS (PROC NLMIXED) 9.5.2 Two-Level Nested Logistic Regression Model with Random Intercepts Using SPSS SPSS Model 1: Logistic Regression Model with random Intercepts SPSS Pull Down Menu 9.5.3 Two-Level Nested Logistic Regression Model with Random Intercepts Using R 9.5.4 Two-Level Nested Logistic Regression Model with Random Intercepts Using STATA 9.5.5 Two-Level Nested Logistic Regression Model Random Intercept and Slope with SAS Two-Level Nested Logistic Regression Model Random Intercept and Slope with SAS GLIMMIX Two-Level Nested Logistic Regression Model Random Intercept and Slope with SAS NLMIXED 9.5.6 Two-Level Nested Logistic Regression Model Random Intercept and Slope with SPSS Model 2: Logistic Regression with Random Intercept/Random Slope for LOS 9.5.7 Two-Level Nested Logistic Regression Model Random Intercept and Slope with STATA 9.6 Conclusions 9.7 Related Examples 9.7.1 Multicenter Randomized Controlled Data (Beitler & Landis, 1985) References Chapter 10: Hierarchical Logistic Regression Models 10.1 Motivation 10.1.1 Description of Case Study 10.1.2 Study Hypotheses 10.2 Definitions and Notations 10.3 Exploratory Analyses 10.4 Statistical Model 10.4.1 Multilevel Modeling Approaches with Binary Outcomes 10.4.2 Potential Problems 10.4.3 Three-Level Logistic Regression Models with Multiple Random Intercepts 10.4.4 Three-Level Logistic Regression Models with Random Intercepts and Random Slopes 10.4.5 Nested Higher Level Logistic Regression Models 10.4.6 Cluster Sizes and Number of Clusters 10.4.7 Parameter Estimations 10.5 Analysis of Data 10.5.1 Modeling Random Intercepts for Levels 2 and 3 10.5.2 Modeling Random Intercepts for Levels 2 and 3 Modeling Random Intercepts for Levels 2 and 3 Using SAS An Alternative SAS Program Making Use of Option ABSFCONV 10.5.3 Modeling Random Intercepts for Levels 2 and 3 Using STATA 10.5.4 Three-Level Logistic Regression Model with Random Slopes Using SAS 10.5.5 Modeling Random Intercepts for Levels 2 and 3 Using R 10.5.6 Three-Level Logistic Regression Model with Random Slopes Using R 10.5.7 Three-Level Logistic Regression Model with Random Slopes at Doctor Level Using STATA 10.5.8 Interpretation 10.6 Conclusions 10.7 Related Examples References Chapter 11: Fixed Effects Logistic Regression Model 11.1 Motivating Example 11.2 Definition and Notation 11.3 Exploratory Analysis 11.3.1 Philippine’s Data 11.4 Statistical Models 11.4.1 Fixed Effects Regression Models with Two Observations Per Unit 11.4.2 Modeling More Than Two Observations Per Unit: Conditional Logistic Regression Model 11.5 Analysis of Data 11.5.1 Fixed Effects Logistic Regression Model with Two Observations Per Unit 11.5.2 Fixed Effects Logistic Regression Model with Two Observations Per Unit Using SAS 11.5.3 Fixed Effects Logistic Regression Model with Two Observations Per Unit Using SPSS 11.5.4 Fixed Effects Logistic Regression Model with Two Observations Per Unit Using R 11.5.5 Fixed Effects Logistic Regression Model with Two Observations Per Unit Using STATA 11.6 Fixed Effects Logistic Regression Model with More Than Two Observations 11.6.1 Fixed Effects Logistic Regression Model with More Than Two Observations Using SAS 11.6.2 Fixed Effects Logistic Regression Model with More Than Two Observations Using SPSS 11.6.3 Fixed Effects Logistic Regression Model with More Than Two Observations Using R 11.6.4 Fixed Effects Logistic Regression Model with More Than Two Observations Using STATA 11.7 Conclusions 11.8 Related Examples References Part IV: Analyzing Correlated Data Through the Joint Modeling of Mean and Variance Chapter 12: Heteroscedastic Logistic Regression Model 12.1 Motivating Example 12.2 Definitions and Notations 12.3 Exploratory Analyses 12.3.1 Dispersion Sub-model 12.4 Statistical Model 12.4.1 Joint Modeling 12.5 Analysis of Data 12.5.1 Heteroscedastic Logistic Regression Model 12.5.2 Standard Logistic Regression Model 12.5.3 Model Comparisons Mean Sub-model Versus Joint Modeling 12.6 Conclusions 12.7 Related Examples 12.7.1 Logistic Predicted References Part V: Case Studies- USA Election 2020 and Netherlands COVID Chapter 13: Case Studies: Election Data and COVID Data 13.1 Two Case Studies- Election and COVID 13.2 USA 2020 Election Data 13.2.1 Election Data Questions 13.2.2 Election Variables and Data Analysis 13.2.3 Election Data Interpretation 13.3 The Netherlands 2020–2021 COVID Data 13.3.1 COVID Data Questions 13.3.2 COVID Data Variables and Analysis 13.3.3 COVID Data Interpretation References Index