Missing Data in Longitudinal Studies: Strategies for Bayesian Modeling and Sensitivity Analysis, 1st Edition (Hardback) book cover

Missing Data in Longitudinal Studies

Strategies for Bayesian Modeling and Sensitivity Analysis, 1st Edition

By Michael J. Daniels, Joseph W. Hogan

Chapman and Hall/CRC

328 pages | 21 B/W Illus.

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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.


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

Table of Contents


Description of Motivating Examples


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



Generalized Linear Models

Conditionally Specified Models

Directly Specified (Marginal) Models

Semiparametric Regression

Interpreting Covariate Effects

Further Reading

Methods of Bayesian Inference


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


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


Missing Data Mechanisms and Longitudinal Data


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


Further Reading

Inference about Full-Data Parameters under Ignorability


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


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


Models for handling Nonignorable Missingness


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


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


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



About the Series

Chapman & Hall/CRC Monographs on Statistics and Applied Probability

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Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Probability & Statistics / General