Analysis of Longitudinal Data with Examples

"Development in methodology on longitudinal data is fast. Currently, there are a lack of intermediate /advanced level textbooks which introduce students and practicing statisticians to the updated methods on correlated data inference. This book will present a discussion of the modern approach to semiparametric inference, including the links between the theories of random effects models, likelihood functions and estimators, and various types of efficient statistical models. The theory will be supported with practical examples of R-codes and R-packages applied to interesting case-studies from a number of different areas."--Provided by publisher Currently, there are a lack of intermediate /advanced level textbooks which introduce students and practicing statisticians to the updated methods on correlated data inference. T Cover 1 Half Title 2 Title Page 4 Copyright Page 5 Dedication 6 Contents 8 List of Figures 14 List of Tables 16 Preface 18 Author Bios 22 Contributors 24 Acknowledgment 26 1. Introduction 28 1.1. Longitudinal Studies 28 1.2. Notation 29 2. Examples and Organization of The Book 32 2.1. Examples for Longitudinal Studies 32 2.1.1. HIV Study 32 2.1.2. Progabide Study 32 2.1.3. Hormone Study 34 2.1.4. Teratology Studies 35 2.1.5. Schizophrenia Study 38 2.1.6. Labor Pain Study 38 2.1.7. Labor Market Experience 38 2.1.8. Water Quality Data 40 2.2. Organization of the Book 41 3. Model Framework and Its Components 44 3.1. Distributional Theory 44 3.1.1. Linear Exponential Distribution Family 45 3.1.2. Quadratic Exponential Distribution Family 47 3.1.3. Tilted Exponential Family 47 3.2. Quasi-Likelihood 48 3.3. Gaussian Likelihood 49 3.4. GLM and Mean Functions 50 3.5. Marginal Models 54 3.6. Modeling the Variance 55 3.7. Modeling the Correlation 58 3.8. Random Effects Models 62 4. Parameter Estimation 64 4.1. Likelihood Approach 65 4.2. Quasi-likelihood Approach 66 4.3. Gaussian Approach 68 4.4. Generalized Estimating Equations (GEE) 71 4.4.1. Estimation of Mean Parameters ß 72 4.4.2. Estimation of Variance Parameters τ 75 4.4.2.1. Gaussian Estimation 75 4.4.2.2. Extended Quasi-likelihood 76 4.4.2.3. Nonlinear Regression 77 4.4.2.4. Estimation of Scale Parameter φ 77 4.4.3. Estimation of Correlation Parameters 78 4.4.3.1. Stationary Correlation Structures 78 4.4.3.2. Generalized Markov Correlation Structure 81 4.4.3.3. Second Moment Method 82 4.4.3.4. Gaussian Estimation 82 4.4.3.5. Quasi Least-squares 84 4.4.3.6. Conditional Residual Method 85 4.4.3.7. Cholesky Decomposition 86 4.4.4. Covariance Matrix of ß 90 4.4.5. Example: Epileptic Data 93 4.4.6. Infeasibility 95 4.5. Quadratic Inference Function 99 5. Model Selection 102 5.1. Introduction 102 5.2. Selecting Covariates 103 5.2.1. Quasi-likelihood Criterion 103 5.2.2. Gaussian Likelihood Criterion 105 5.3. Selecting Correlation Structure 106 5.3.1. CIC Criterion 106 5.3.2. C(R) Criterion 106 5.3.3. Empirical Likelihood Criteria 107 5.4. Examples 109 5.4.1. Examples for Variable Selection 109 5.4.2. Examples for Correlation Structure Selection 109 6. Robust Approaches 116 6.1. Introduction 116 6.2. Rank-based Method 116 6.2.1. An Independence Working Model 116 6.2.2. A Weighted Method 117 6.2.3. Combined Method 119 6.2.4. A Method Based on GEE 120 6.2.5. Pediatric Pain Tolerance Study 121 6.3. Quantile Regression 124 6.3.1. An Independence Working Model 125 6.3.2. A Weighted Method Based on GEE 126 6.3.3. Modeling Correlation Matrix via Gaussian Copulas 126 6.3.3.1. Constructing Estimating Functions 127 6.3.3.2. Parameter and Covariance Matrix Estimation 128 6.3.4. Working Correlation Structure Selection 130 6.3.5. Analysis of Dental Data 130 6.4. Other Robust Methods 132 6.4.1. Score Function and Weighted Function 133 6.4.2. Main Algorithm 134 6.4.3. Choice of Tuning Parameters 135 7. Clustered Data Analysis 138 7.1. Introduction 138 7.1.1. Clustered Data 138 7.1.2. Intracluster Correlation 139 7.2. Analysis of Clustered Data: Continuous Responses 140 7.2.1. Inference for Intraclass Correlation from One-way Analysis of Variance 140 7.2.2. Inference for Intracluster Correlation from More General Settings 142 7.2.3. Maximum Likelihood Estimation of the Parameters 144 7.2.4. Asymptotic Variance 147 7.2.5. Inference for Intracluster Correlation Coefficient 148 7.2.6. Analysis of Clustered or Intralitter Data: Discrete Responses 149 7.2.7. The Models 149 7.2.8. Estimation 150 7.2.9. Inference 152 7.3. Some Examples 152 7.4. Regression Models for Multilevel Clustered Data 153 7.5. Two-Level Linear Models 153 7.6. An Example: Developmental Toxicity Study of Ethylene Glycol 154 7.7. Two-Level Generalized Linear Model 156 7.8. Rank Regression 158 7.8.1. National Cooperative Gallstone Study 159 7.8.2. Reproductive Study 160 8. Missing Data Analysis 162 8.1. Introduction 162 8.2. Missing Data Mechanism 162 8.3. Missing Data Patterns 164 8.4. Missing Data Methodologies 166 8.4.1. Missing Data Methodologies: The Methods of Imputation 167 8.4.1.1. Last Value Carried Forward Imputation 167 8.4.1.2. Imputation by Related Observation 167 8.4.1.3. Imputation by Unconditional Mean 167 8.4.1.4. Imputation by Conditional Mean 167 8.4.1.5. Hot Deck Imputation 167 8.4.1.6. Cold Deck Imputation 168 8.4.1.7. Imputation by Substitution 168 8.4.1.8. Regression Imputation 168 8.4.2. Missing Data Methodologies: Likelihood Methods 168 8.5. Analysis of Zero-inflated Count Data With Missing Values 174 8.5.1. Estimation of the Parameters with No Missing Data 175 8.5.2. Estimation of the Parameters with Missing Responses 176 8.5.2.1. Estimation under MCAR 176 8.5.2.2. Estimation under MAR 177 8.5.2.3. Estimation under MNAR 180 8.6. Analysis of Longitudinal DataWith Missing Values 182 8.6.1. Normally Distributed Data 182 8.6.2. Complete-data Estimation via the EM 184 8.6.3. Estimation with Nonignorable Missing Response Data (MAR and MNAR) 187 8.6.4. Generalized Estimating Equations 191 8.6.4.1. Introduction 191 8.6.4.2. Weighted GEE for MAR Data 191 8.6.5. Some Applications of the Weighted GEE 192 8.6.5.1. Weighted GEE for Binary Data 192 8.6.5.2. Two Modifications 193 9. Random Effects and Transitional Models 198 9.1. A General Discussion 198 9.2. Random Intercept Models 199 9.3. Linear Mixed Effects models 200 9.4. Generalized Linear Mixed Effects Models 203 9.4.1. The Logistic Random Effects Models 203 9.4.2. The Binomial Random Effects Models 204 9.4.3. The Poisson Random Effects Models 204 9.4.4. Examples: Estimation for European Red Mites Data and the Ames Salmonella Assay Data 207 9.5. Transition Models 208 9.6. Fitting Transition Models 211 9.7. Transition Model for Categorical Data 212 9.8. Further reading 215 10. Handing High Dimensional Longitudinal Data 216 10.1. Introduction 216 10.2. Penalized Methods 217 10.2.1. Penalized GEE 217 10.2.2. Penalized Robust GEE-type Methods 219 10.3. Smooth-threshold Method 220 10.4. Yeast Data Study 222 10.5. Further Reading 223 Bibliography 228 Author Index 244 Subject Index 250 Generalized,linear,models;,parameter,estimation;,clustered,data,analysis;,R,software;,Spatio-temporal,models Generalized linear models,parameter estimation,clustered data analysis,R software,Spatio-temporal models Development in methodology on longitudinal data is fast. Currently, there are a lack of intermediate /advanced level textbooks which introduce students and practicing statisticians to the updated methods on correlated data inference. This book will present a discussion of the modern approaches to inference, including the links between the theories of estimators and various types of efficient statistical models including likelihood-based approaches. The theory will be supported with practical examples of R-codes and R-packages applied to interesting case-studies from a number of different areas. Key Features: Includes the most up-to-date methods Use simple examples to demonstrate complex methods Uses real data from a number of areas Examples utilize R code