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

by Daniels; Michael J.

• ISBN13: 9781584886099
• ISBN10: 1584886099
• eBook ISBN(s): 9781040171233
• Edition: 1st
• Format: Hardcover
• Copyright: 2008-03-11
• Publisher: Chapman & Hall/
• More Book Details

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 Analysisdescribes 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 bookstudies 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.

Author Biography

Michael J. Daniels University of Florida Gainesville, U.S.A. Joseph W. Hogan Brown University Providence, Rhode Island, U.S.A.

Table of Contents

Preface	p. xvii
Description of Motivating Examples	p. 1
Overview	p. 1
Dose-finding trial of an experimental treatment for schizophrenia	p. 2
Study and data	p. 2
Questions of interest	p. 2
Missing data	p. 2
Data analyses	p. 2
Clinical trial of recombinant human growth hormone (rhGH) for increasing muscle strength in the elderly	p. 4
Study and data	p. 4
Questions of interest	p. 4
Missing data	p. 4
Data analyses	p. 5
Clinical trials of exercise as an aid to smoking cessation in women: the Commit to Quit studies	p. 6
Studies and data	p. 6
Questions of interest	p. 6
Missing data	p. 7
Data analyses	p. 8
Natural history of HIV infection in women: HIV Epidemiology Research Study (HERS) cohort	p. 9
Study and data	p. 9
Questions of interest	p. 9
Missing data	p. 9
Data analyses	p. 10
Clinical trial of smoking cessation among substance abusers: OASIS study	p. 11
Study and data	p. 11
Questions of interest	p. 11
Missing data	p. 12
Data analyses	p. 12
Equivalence trial of competing doses of AZT in HIV-infected children: Protocol 128 of the AIDS Clinical Trials Group	p. 13
Study and data	p. 13
Questions of interest	p. 14
Missing data	p. 14
Data analyses	p. 14
Regression Models	p. 15
Overview	p. 15
Preliminaries	p. 15
Longitudinal data	p. 15
Regression models	p. 17
Full vs. observed data	p. 18
Additional notation	p. 19
Generalized linear models	p. 19
Conditionally specified models	p. 20
Random effects models based on GLMs	p. 21
Random effects models for continuous response	p. 22
Random effects models for discrete responses	p. 23
Directly specified (marginal) models	p. 25
Multivariate normal and Gaussian process models	p. 26
Directly specified models for discrete longitudinal responses	p. 28
Semiparametric regression	p. 31
Generalized additive models based on regression splines	p. 32
Varying coefficient models	p. 34
Interpreting covariate effects	p. 34
Assumptions regarding time-varying covariates	p. 35
Longitudinal vs. cross-sectional effects	p. 36
Marginal vs. conditional effects	p. 37
Further reading	p. 38
Methods of Bayesian Inference	p. 39
Overview	p. 39
Likelihood and posterior distribution	p. 39
Likelihood	p. 39
Score function and information matrix	p. 41
The posterior distribution	p. 42
Prior Distributions	p. 43
Conjugate priors	p. 43
Noninformative priors	p. 46
Informative priors	p. 49
Identifiability and incomplete data	p. 50
Computation of the posterior distribution	p. 51
The Gibbs sampler	p. 52
The Metropolis-Hastings algorithm	p. 54
Data augmentation	p. 55
Inference using the posterior sample	p. 58
Model comparisons and assessing model fit	p. 62
Deviance Information Criterion (DIC)	p. 63
Posterior predictive loss	p. 65
Posterior predictive checks	p. 67
Nonparametric Bayes	p. 68
Further reading	p. 69
Worked Examples using Complete Data	p. 72
Overview	p. 72
Multivariate normal model: Growth Hormone study	p. 72
Models	p. 72
Priors	p. 73
MCMC details	p. 73
Model selection and fit	p. 73
Results	p. 74
Conclusions	p. 75
Normal random effects model: Schizophrenia trial	p. 75
Models	p. 76
Priors	p. 77
MCMC details	p. 77
Results	p. 77
Conclusions	p. 78
Models for longitudinal binary data: CTQ I Study	p. 79
Models	p. 80
Priors	p. 81
MCMC details	p. 81
Model selection	p. 81
Results	p. 82
Conclusions	p. 83
Summary	p. 84
Missing Data Mechanisms and Longitudinal Data	p. 85
Introduction	p. 85
Full vs. observed data	p. 86
Overview	p. 86
Data structures	p. 87
Dropout and other processes leading to missing responses	p. 87
Full-data models and missing data mechanisms	p. 89
Targets of inference	p. 89
Missing data mechanisms	p. 90
Assumptions about missing data mechanism	p. 91
Missing completely at random (MCAR)	p. 91
Missing at random (MAR)	p. 93
Missing not at random (MNAR)	p. 93
Auxiliary variables	p. 94
Missing at random applied to dropout processes	p. 96
Observed data posterior of full-data parameters	p. 98
The ignorability assumption	p. 99
Likelihood and posterior under ignorability	p. 99
Factored likelihood with monotone ignorable missingness	p. 101
The practical meaning of 'ignorability'	p. 102
Examples of full-data models under MAR	p. 103
Full-data models under MNAR	p. 106
Selection models	p. 107
Mixture models	p. 109
Shared parameter models	p. 112
Summary	p. 114
Further reading	p. 114
Inference about Full-Data Parameters under Ignorability	p. 115
Overview	p. 115
General issues in model specification	p. 116
Mis-specification of dependence	p. 116
Orthogonal parameters	p. 118
Posterior sampling using data augmentation	p. 121
Covariance structures for univariate longitudinal processes	p. 124
Serial correlation models	p. 124
Covariance matrices induced by random effects	p. 128
Covariance functions for misaligned data	p. 129
Covariate-dependent covariance structures	p. 130
Covariance/correlation matrices	p. 130
Dependence in longitudinal binary models	p. 134
Joint models for multivariate processes	p. 134
Continuous response and continuous auxiliary covariate	p. 135
Binary response and binary auxiliary covariate	p. 137
Binary response and continuous auxiliary covariate	p. 138
Model selection and model fit under ignorability	p. 138
Deviance information criterion (DIC)	p. 139
Posterior predictive checks	p. 141
Further reading	p. 143
Case Studies: Ignorable Missingness	p. 145
Overview	p. 145
Structured covariance matrices: Growth Hormone study	p. 145
Models	p. 145
Priors	p. 146
MCMC details	p. 146
Model selection and fit	p. 147
Results and comparison with completers-only analysis	p. 147
Conclusions	p. 149
Normal random effects model: Schizophrenia trial	p. 149
Models and priors	p. 149
MCMC details	p. 150
Model selection	p. 150
Results and comparison with completers-only analysis	p. 150
Conclusions	p. 151
Marginalized transition model: CTQ I trial	p. 151
Models	p. 152
MCMC details	p. 153
Model selection	p. 153
Results	p. 154
Conclusions	p. 154
Joint modeling with auxiliary variables: CTQ II trial	p. 155
Models	p. 156
Priors	p. 157
Posterior sampling	p. 157
Model selection and fit	p. 157
Results	p. 158
Conclusions	p. 159
Bayesian p-spline model: HERS CD4 data	p. 159
Models	p. 160
Priors	p. 161
MCMC details	p. 161
Model selection	p. 161
Results	p. 161
Summary	p. 162
Models for Handling Nonignorable Missingness	p. 165
Overview	p. 165
Extrapolation factorization and sensitivity parameters	p. 166
Selection models	p. 167
Background and history	p. 167
Absence of sensitivity parameters in the missing data mechanism	p. 168
Heckman selection model for a bivariate response	p. 171
Specification of the missing data mechanism for longitudinal data	p. 173
Parametric selection models for longitudinal data	p. 174
Feasibility of sensitivity analysis for parametric selection models	p. 175
Semiparametric selection models	p. 176
Posterior sampling strategies	p. 180
Summary of pros and cons of selection models	p. 181
Mixture models	p. 181
Background, specification, and identification	p. 181
Identification strategies for mixture models	p. 183
Mixture models with discrete-time dropout	p. 188
Mixture models with continuous-time dropout	p. 198
Combinations of MAR and MNAR dropout	p. 201
Mixture models or selection models?	p. 202
Covariate effects in mixture models	p. 203
Shared parameter models	p. 206
General structure	p. 206
Pros and cons of shared parameter models	p. 207
Model selection and model fit in nonignorable models	p. 209
Deviance information criterion (DIC)	p. 209
Posterior predictive checks	p. 213
Further reading	p. 215
Informative Priors and Sensitivity Analysis	p. 216
Overview	p. 216
General approach	p. 216
Global vs. local sensitivity analysis	p. 217
Some principles	p. 219
Parameterizing the full-data model	p. 220
Specifying priors	p. 222
Pattern mixture models	p. 224
General parameterization	p. 224
Using model constraints to reduce dimensionality of sensitivity parameters	p. 225
Selection models	p. 226
Further reading	p. 231
Case Studies: Nonignorable Missingness	p. 233
Overview	p. 233
Growth Hormone study: Pattern mixture models and sensitivity analysis	p. 234
Overview	p. 234
Multivariate normal model under ignorability	p. 234
Pattern mixture model specification	p. 235
MAR constraints for pattern mixture model	p. 235
Parameterizing departures from MAR	p. 236
Constructing priors	p. 238
Analysis using point mass MAR prior	p. 238
Analyses using MNAR priors	p. 239
Summary of pattern mixture analysis	p. 246
OASIS Study: Selection models, mixture models, and elicited priors	p. 248
Overview	p. 248
Selection model specification	p. 249
Selection model analyses under MAR and MNAR	p. 251
Pattern mixture model specification	p. 252
MAR and MNAR parameterizations	p. 252
Pattern mixture analysis under MAR	p. 255
Pattern mixture analysis under MNAR using elicited priors	p. 255
Summary: selection vs. pattern mixture approaches	p. 259
Pediatric AIDS trial: Mixture of varying coefficient models for continuous dropout	p. 261
Overview	p. 261
Model specification: CD4 counts	p. 263
Model specification: dropout times	p. 265
Summary of analyses under MAR and MNAR	p. 265
Summary	p. 266
Distributions	p. 268
Bibliography	p. 271
Author Index	p. 292
Index	p. 298
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