Missing Data in Longitudinal Studies ─ Strategies for Bayesian Modeling and Sensitivity Analysis

Drawing from the authors’ own work and from the most recent developments in the field, Missing Data in Longitudinal Studies: Strategies for Bayesian Modeling and Sensitivity Analysis describes a comprehensive Bayesian approach for drawing inference from incomplete data in longitudinal studies. To illustrate these methods, the authors employ several data sets throughout that cover a range of study designs, variable types, and missing data issues. The book first reviews modern approaches to formulate and interpret regression models for longitudinal data. It then discusses key ideas in Bayesian inference, including specifying prior distributions, computing posterior distribution, and assessing model fit. The book carefully describes the assumptions needed to make inferences about a full-data distribution from incompletely observed data. For settings with ignorable dropout, it emphasizes the importance of covariance models for inference about the mean while for nonignorable dropout, the book studies a variety of models in detail. It concludes with three case studies that highlight important features of the Bayesian approach for handling nonignorable missingness. With suggestions for further reading at the end of most chapters as well as many applications to the health sciences, this resource offers a unified Bayesian approach to handle missing data in longitudinal studies.

PREFACE Description of Motivating Examples Overview Dose-Finding Trial of an Experimental Treatment for Schizophrenia Clinical Trial of Recombinant Human Growth Hormone (rhGH) for Increasing Muscle Strength in the Elderly Clinical Trials of Exercise as an Aid to Smoking Cessation in Women: The Commit to Quit Studies Natural History of HIV Infection in Women: HIV Epidemiology Research Study (HERS) Cohort Clinical Trial of Smoking Cessation among Substance Abusers: OASIS Study Equivalence Trial of Competing Doses of AZT in HIV-Infected Children: Protocol 128 of the AIDS Clinical Trials Group Regression Models Overview Preliminaries Generalized Linear Models Conditionally Specified Models Directly Specified (Marginal) Models Semiparametric Regression Interpreting Covariate Effects Further Reading Methods of Bayesian Inference Overview Likelihood and Posterior Distribution Prior Distributions Computation of the Posterior Distribution Model Comparisons and Assessing Model Fit Nonparametric Bayes Further Reading Bayesian Analysis using Data on Completers Overview Model Selection and Inference with a Multivariate Normal Model: Analysis of the Growth Hormone Clinical Study Inference with a Normal Random Effects Model: Analysis of the Schizophrenia Clinical Trial Model Selection and Inference for Binary Longitudinal Data: Analysis of CTQ I Summary Missing Data Mechanisms and Longitudinal Data Introduction Full vs. Observed Data Full-Data Models and Missing Data Mechanisms Assumptions about Missing Data Mechanism Missing at Random Applied to Dropout Processes Observed-Data Posterior of Full-Data Parameters The Ignorability Assumption Examples of Full-Data Models under MAR Full-Data Models under MNAR Summary Further Reading Inference about Full-Data Parameters under Ignorability Overview General Issues in Model Specification Posterior Sampling Using Data Augmentation Covariance Structures for Univariate Longitudinal Processes Covariate-Dependent Covariance Structures Multivariate Processes Model Comparisons and Assessing Model Fit with Incomplete Data under Ignorability Further Reading Case Studies: Ignorable Missingness Overview Analysis of the Growth Hormone Study under MAR Analysis of the Schizophrenia Clinical Trial under MAR Using Random Effects Models Analysis of CTQ I Using Marginalized Transition Models under MAR Analysis of Weekly Smoking Outcomes in CTQ II Using Auxiliary Variable MAR Analysis of HERS CD4 Data under Ignorability Using Bayesian p-Spline Models Summary Models for handling Nonignorable Missingness Overview Extrapolation Factorization Selection Models Mixture Models Shared Parameter Models Model Comparisons and Assessing Model Fit in Nonignorable Models Further Reading Informative Priors and Sensitivity Analysis Overview Some Principles Parameterizing the Full-Data Model Pattern-Mixture Models Selection Models Elicitation of Expert Opinion, Construction of Informative Priors, and Formulation of Sensitivity Analyses A Note on Sensitivity Analysis in Fully Parametric Models Literature on Local Sensitivity Further Reading Case Studies: Model Specification and Data Analysis under Missing Not at Random Overview Analysis of Growth Hormone Study Using Pattern-Mixture Models Analysis of OASIS Study Using Selection and Pattern-Mixture Models Analysis of Pediatric AIDS Trial Using Mixture of Varying Coefficient Models Appendix: distributions Bibliography Index