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

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Features

  • Contains a large number of examples and case studies, including trials and studies on schizophrenia, aging, HIV/AIDS, and smoking cessation
  • Applies the specification of priors, Markov chain Monte Carlo algorithms, model fit assessment, and other Bayesian inference methods to real data
  • Describes commonly used missing data mechanisms, such as missing at random (MAR), missing not at random (MNAR), and ignorability, and shows how they are used in longitudinal data
  • Presents a Bayesian framework for drawing principled inferences from incomplete data, including methods for sensitivity analysis and the incorporation of informative prior information
  • Makes recommendations for the use of standard regression, mixture, selection, and varying coefficient models in different settings
  • Implements many of the analyses using WinBUGS, offering the code on a supplementary web page
  • Summary

    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.

    Table of Contents

    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

    Editorial Reviews

    The authors combine their expertise in longitudinal data and Bayesian inference to missing data problems to give an overview of methods that can be used in various longitudinal studies. … the examples … are very helpful to illustrate the potential of the theory.
    —Michael Bücker, Statistical Papers (2011) 52

    Daniels and Hogan’s is the first to explicitly focus on missing data in the context of longitudinal studies. … I found the book extremely clear and illuminating. It is well written, with comprehensive and up-to-date references. The use of example datasets from a number of epidemiological and clinical studies illustrates how the methods and strategies being advocated can be applied in real-life settings. … an extremely valuable resource both to applied statisticians who are faced with analyzing longitudinal data subject to missingness and methodological researchers in the area.
    —Jonathan Bartlett, Statistics in Medicine, 2011, 30

    … They [the authors] have gone further than anyone else in developing methods for the not missing at random (NMAR) case. … The focus on longitudinal studies will attract many readers. … this book is an excellent introduction and is also a first-rate treatment of cutting-edge topics. …
    —Paul D. Allison, University of Pennsylvania, Significance, September 2010

    This text is the only Bayesian textbook that provides a contemporary and comprehensive treatment of Bayesian approaches to a common and critically important topic. The authors provide a scholarly treatment of Bayesian inference and supplement their treatise with concrete practical examples. The writing is clear, precise and interesting. A particularly innovative and enormously useful contribution is the authors’ formalization of sensitivity analyses. They distinguish between local and global sensitivity analyses, providing the reader with examples of each. I have used the techniques proposed in the text with much success, teaching people the importance of separating what is observed from what is assumed. I strongly endorse this book.
    —Sharon-Lise Normand, Harvard School of Public Health, Boston, Massachusetts, USA

    …the book under review appears to be the first reference that solely focuses on Bayesian approaches to handle missing data in longitudinal studies. … Overall I think this is a well-written technical monograph. The preliminary sections on longitudinal data analysis, Bayesian statistics, and missing data … are well written and serve to make this book a self-contained reference. The models presented to analyze missing data in longitudinal studies cover many ideas from the current literature, and some of the methods are at the cutting edge of research. The book will probably have greatest appeal to statisticians with a research interest in missing data. Although I also think applied biostatisticians who like to use Bayesian approaches and in particular WinBUGS will find this book very useful.
    Journal of Biopharmaceutical Statistics, 2009

    …a timely and thorough review of this maturing research area. … The book is comprehensive in covering models for both continuous and discrete outcomes from both the pattern mixture and selection modeling perspectives. … The book’s composition offers much to admire. The writing is clear and direct, the notation is sensible and consistent, and tables and figures are simple and uncluttered. Typos are mercifully rare … Biostatisticians who seek a clear and thorough overview of the state of knowledge in this area would do well to make this excellent book their first stop.
    Biometrics, March 2009

    Downloads / Updates

    Resource OS Platform Updated Description Instructions
    Cross Platform October 06, 2009 It has datasets, software code, reviews and errata click on http://www.stat.ufl.edu/~mdaniels/book.html