Missing data in longitudinal studies: strategies for Bayesian Modeling and Sensitivity Analysis
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2008
|
| Series: | Monographs on statistics and applied probability
109 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XX, 303 S. graph. Darst. |
| ISBN: | 9781584886099 1584886099 |
Staff View
MARC
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| 245 | 1 | 0 | |a Missing data in longitudinal studies |b strategies for Bayesian Modeling and Sensitivity Analysis |c Michael J. Daniels ; Joseph W. Hogan |
| 264 | 1 | |a Boca Raton [u.a.] |b Chapman & Hall/CRC |c 2008 | |
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| 650 | 7 | |a Longitudinaal onderzoek |2 gtt | |
| 650 | 7 | |a Methode van Bayes |2 gtt | |
| 650 | 7 | |a Nauwkeurigheid |2 gtt | |
| 650 | 7 | |a Ontbrekende gegevens |2 gtt | |
| 650 | 4 | |a Bayes Theorem | |
| 650 | 4 | |a Bayesian statistical decision theory | |
| 650 | 4 | |a Data Interpretation, Statistical | |
| 650 | 4 | |a Longitudinal Studies | |
| 650 | 4 | |a Longitudinal method | |
| 650 | 4 | |a Missing observations (Statistics) | |
| 650 | 4 | |a Models, Statistical | |
| 650 | 4 | |a Sensitivity and Specificity | |
| 650 | 4 | |a Sensitivity theory (Mathematics) | |
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Record in the Search Index
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| adam_text | Contents
Preface xvii
1 Description of Motivating Examples 1
1.1 Overview 1
1.2 Dose-finding trial of an experimental treatment for schizophre¬
nia 2
1.2.1 Study and data 2
1.2.2 Questions of interest 2
1.2.3 Missing data 2
1.2.4 Data analyses 2
1.3 Clinical trial of recombinant human growth hormone (rhGH)
for increasing muscle strength in the elderly 4
1.3.1 Study and data 4
1.3.2 Questions of interest 4
1.3.3 Missing data 4
1.3.4 Data analyses 5
1.4 Clinical trials of exercise as an aid to smoking cessation in
women: the Commit to Quit studies 6
1.4.1 Studies and data 6
1.4.2 Questions of interest 6
1.4.3 Missing data 7
1.4.4 Data analyses 8
1.5 Natural history of HIV infection in women: HIV Epidemiology
Research Study (HERS) cohort 9
1.5.1 Study and data 9
1.5.2 Questions of interest 9
1.5.3 Missing data 9
1.5.4 Data analyses 10
1.6 Clinical trial of smoking cessation among substance abusers:
OASIS study 11
1.6.1 Study and data 11
1.6.2 Questions of interest 11
1.6.3 Missing data 12
1.6.4 Data analyses 12
ix
x CONTENTS
1.7 Equivalence trial of competing doses of AZT in HIV-infected
children: Protocol 128 of the AIDS Clinical Trials Group 13
1.7.1 Study and data 13
1.7.2 Questions of interest 14
1.7.3 Missing data 14
1.7.4 Data analyses 14
2 Regression Models 15
2.1 Overview 15
2.2 Preliminaries 15
2.2.1 Longitudinal data 15
2.2.2 Regression models 17
2.2.3 Full vs. observed data 18
2.2.4 Additional notation 19
2.3 Generalized linear models 19
2.4 Conditionally specified models 20
2.4.1 Random effects models based on GLMs 21
2.4.2 Random effects models for continuous response 22
2.4.3 Random effects models for discrete responses 23
2.5 Directly specified (marginal) models 25
2.5.1 Multivariate normal and Gaussian process models 26
2.5.2 Directly specified models for discrete longitudinal
responses 28
2.6 Semiparametric regression 31
2.6.1 Generalized additive models based on regression splines 32
2.6.2 Varying coefficient models 34
2.7 Interpreting covariate effects 34
2.7.1 Assumptions regarding time-varying covariates 35
2.7.2 Longitudinal vs. cross-sectional effects 36
2.7.3 Marginal vs. conditional effects 37
2.8 Further reading 38
3 Methods of Bayesian Inference 39
3.1 Overview 39
3.2 Likelihood and posterior distribution 39
3.2.1 Likelihood 39
3.2.2 Score function and information matrix 41
3.2.3 The posterior distribution 42
3.3 Prior Distributions 43
3.3.1 Conjugate priors 43
3.3.2 Noninformative priors 46
3.3.3 Informative priors 49
3.3.4 Identifiability and incomplete data 50
CONTENTS xi
3.4 Computation of the posterior distribution 51
3.4.1 The Gibbs sampler 52
3.4.2 The Metropolis-Hastings algorithm 54
3.4.3 Data augmentation 55
3.4.4 Inference using the posterior sample 58
3.5 Model comparisons and assessing model fit 62
3.5.1 Deviance Information Criterion (DIC) 63
3.5.2 Posterior predictive loss 65
3.5.3 Posterior predictive checks 67
3.6 Nonparametric Bayes 68
3.7 Further reading 69
4 Worked Examples using Complete Data 72
4.1 Overview 72
4.2 Multivariate normal model: Growth Hormone study 72
4.2.1 Models 72
4.2.2 Priors 73
4.2.3 MCMC details 73
4.2.4 Model selection and fit 73
4.2.5 Results 74
4.2.6 Conclusions 75
4.3 Normal random effects model: Schizophrenia trial 75
4.3.1 Models 76
4.3.2 Priors 77
4.3.3 MCMC details 77
4.3.4 Results 77
4.3.5 Conclusions 78
4.4 Models for longitudinal binary data: CTQ I Study 79
4.4.1 Models 80
4.4.2 Priors 81
4.4.3 MCMC details 81
4.4.4 Model selection 81
4.4.5 Results 82
4.4.6 Conclusions 83
4.5 Summary 84
5 Missing Data Mechanisms and Longitudinal Data 85
5.1 Introduction 85
5.2 Full vs. observed data 86
5.2.1 Overview 86
5.2.2 Data structures 87
5.2.3 Dropout and other processes leading to missing re¬
sponses 87
xii CONTENTS
5.3 Full-data models and missing data mechanisms 89
5.3.1 Targets of inference 89
5.3.2 Missing data mechanisms 90
5.4 Assumptions about missing data mechanism 91
5.4.1 Missing completely at random (MCAR) 91
5.4.2 Missing at random (MAR) 93
5.4.3 Missing not at random (MNAR) 93
5.4.4 Auxiliary variables 94
5.5 Missing at random applied to dropout processes 96
5.6 Observed data posterior of full-data parameters 98
5.7 The ignorability assumption 99
5.7.1 Likelihood and posterior under ignorability 99
5.7.2 Factored likelihood with monotone ignorable missing-
ness 101
5.7.3 The practical meaning of ignorability 102
5.8 Examples of full-data models under MAR 103
5.9 Full-data models under MNAR 106
5.9.1 Selection models 107
5.9.2 Mixture models 109
5.9.3 Shared parameter models 112
5.10 Summary 114
5.11 Further reading 114
6 Inference about Full-Data Parameters under Ignorability 115
6.1 Overview 115
6.2 General issues in model specification 116
6.2.1 Mis-specification of dependence 116
6.2.2 Orthogonal parameters 118
6.3 Posterior sampling using data augmentation 121
6.4 Covariance structures for univariate longitudinal processes 124
6.4.1 Serial correlation models 124
6.4.2 Covariance matrices induced by random effects 128
6.4.3 Covariance functions for misaligned data 129
6.5 Covariate-dependent covariance structures 130
6.5.1 Covariance/correlation matrices 130
6.5.2 Dependence in longitudinal binary models 134
6.6 Joint models for multivariate processes 134
6.6.1 Continuous response and continuous auxiliary covariate 135
6.6.2 Binary response and binary auxiliary covariate 137
6.6.3 Binary response and continuous auxiliary covariate 138
6.7 Model selection and model fit under ignorability 138
6.7.1 Deviance information criterion (DIC) 139
6.7.2 Posterior predictive checks 141
CONTENTS xiii
6.8 Further reading 143
7 Case Studies: Ignorable Missingness 145
7.1 Overview 145
7.2 Structured covariance matrices: Growth Hormone study 145
7.2.1 Models 145
7.2.2 Priors 146
7.2.3 MCMC details 146
7.2.4 Model selection and fit 147
7.2.5 Results and comparison with completers-only analysis 147
7.2.6 Conclusions 149
7.3 Normal random effects model: Schizophrenia trial 149
7.3.1 Models and priors 149
7.3.2 MCMC details 150
7.3.3 Model selection 150
7.3.4 Results and comparison with completers-only analysis 150
7.3.5 Conclusions 151
7.4 Marginalized transition model: CTQ I trial 151
7.4.1 Models 152
7.4.2 MCMC details 153
7.4.3 Model selection 153
7.4.4 Results 154
7.4.5 Conclusions 154
7.5 Joint modeling with auxiliary variables: CTQ II trial 155
7.5.1 Models 156
7.5.2 Priors 157
7.5.3 Posterior sampling 157
7.5.4 Model selection and fit 157
7.5.5 Results 158
7.5.6 Conclusions 159
7.6 Bayesian p-spline model: HERS CD4 data 159
7.6.1 Models 160
7.6.2 Priors 161
7.6.3 MCMC details 161
7.6.4 Model selection 161
7.6.5 Results 161
7.7 Summary 162
8 Models for Handling Nonignorable Missingness 165
8.1 Overview 165
8.2 Extrapolation factorization and sensitivity parameters 166
8.3 Selection models 167
8.3.1 Background and history 167
xiv CONTENTS
8.3.2 Absence of sensitivity parameters in the missing data
mechanism 168
8.3.3 Heckman selection model for a bivariate response 171
8.3.4 Specification of the missing data mechanism for longi¬
tudinal data 173
8.3.5 Parametric selection models for longitudinal data 174
8.3.6 Feasibility of sensitivity analysis for parametric selection
models 175
8.3.7 Semiparametric selection models 176
8.3.8 Posterior sampling strategies 180
8.3.9 Summary of pros and cons of selection models 181
8.4 Mixture models 181
8.4.1 Background, specification, and identification 181
8.4.2 Identification strategies for mixture models 183
8.4.3 Mixture models with discrete-time dropout 188
8.4.4 Mixture models with continuous-time dropout 198
8.4.5 Combinations of MAR and MNAR dropout 201
8.4.6 Mixture models or selection models? 202
8.4.7 Covariate effects in mixture models 203
8.5 Shared parameter models 206
8.5.1 General structure 206
8.5.2 Pros and cons of shared parameter models 207
8.6 Model selection and model fit in nonignorable models 209
8.6.1 Deviance information criterion (DIC) 209
8.6.2 Posterior predictive checks 213
8.7 Further reading 215
9 Informative Priors and Sensitivity Analysis 216
9.1 Overview 216
9.1.1 General approach 216
9.1.2 Global vs. local sensitivity analysis 217
9.2 Some principles 219
9.3 Parameterizing the full-data model 220
9.4 Specifying priors 222
9.5 Pattern mixture models 224
9.5.1 General parameterization 224
9.5.2 Using model constraints to reduce dimensionality of
sensitivity parameters 225
9.6 Selection models 226
9.7 Further reading 231
10 Case Studies: Nonignorable Missingness 233
10.1 Overview 233
CONTENTS xv
10.2 Growth Hormone study: Pattern mixture models and sensitiv¬
ity analysis 234
10.2.1 Overview 234
10.2.2 Multivariate normal model under ignorability 234
10.2.3 Pattern mixture model specification 235
10.2.4 MAR constraints for pattern mixture model 235
10.2.5 Parameterizing departures from MAR 236
10.2.6 Constructing priors 238
10.2.7 Analysis using point mass MAR prior 238
10.2.8 Analyses using MNAR priors 239
10.2.9 Summary of pattern mixture analysis 246
10.3 OASIS Study: Selection models, mixture models, and elicited
priors 248
10.3.1 Overview 248
10.3.2 Selection model specification 249
10.3.3 Selection model analyses under MAR and MNAR 251
10.3.4 Pattern mixture model specification 252
10.3.5 MAR and MNAR parameterizations 252
10.3.6 Pattern mixture analysis under MAR 255
10.3.7 Pattern mixture analysis under MNAR using elicited
priors 255
10.3.8 Summary: selection vs. pattern mixture approaches 259
10.4 Pediatric AIDS trial: Mixture of varying coefficient models for
continuous dropout 261
10.4.1 Overview 261
10.4.2 Model specification: CD4 counts 263
10.4.3 Model specification: dropout times 265
10.4.4 Summary of analyses under MAR and MNAR 265
10.4.5 Summary 266
Distributions 268
Bibliography 271
Author Index 292
Index 298
|
| adam_txt |
Contents
Preface xvii
1 Description of Motivating Examples 1
1.1 Overview 1
1.2 Dose-finding trial of an experimental treatment for schizophre¬
nia 2
1.2.1 Study and data 2
1.2.2 Questions of interest 2
1.2.3 Missing data 2
1.2.4 Data analyses 2
1.3 Clinical trial of recombinant human growth hormone (rhGH)
for increasing muscle strength in the elderly 4
1.3.1 Study and data 4
1.3.2 Questions of interest 4
1.3.3 Missing data 4
1.3.4 Data analyses 5
1.4 Clinical trials of exercise as an aid to smoking cessation in
women: the Commit to Quit studies 6
1.4.1 Studies and data 6
1.4.2 Questions of interest 6
1.4.3 Missing data 7
1.4.4 Data analyses 8
1.5 Natural history of HIV infection in women: HIV Epidemiology
Research Study (HERS) cohort 9
1.5.1 Study and data 9
1.5.2 Questions of interest 9
1.5.3 Missing data 9
1.5.4 Data analyses 10
1.6 Clinical trial of smoking cessation among substance abusers:
OASIS study 11
1.6.1 Study and data 11
1.6.2 Questions of interest 11
1.6.3 Missing data 12
1.6.4 Data analyses 12
ix
x CONTENTS
1.7 Equivalence trial of competing doses of AZT in HIV-infected
children: Protocol 128 of the AIDS Clinical Trials Group 13
1.7.1 Study and data 13
1.7.2 Questions of interest 14
1.7.3 Missing data 14
1.7.4 Data analyses 14
2 Regression Models 15
2.1 Overview 15
2.2 Preliminaries 15
2.2.1 Longitudinal data 15
2.2.2 Regression models 17
2.2.3 Full vs. observed data 18
2.2.4 Additional notation 19
2.3 Generalized linear models 19
2.4 Conditionally specified models 20
2.4.1 Random effects models based on GLMs 21
2.4.2 Random effects models for continuous response 22
2.4.3 Random effects models for discrete responses 23
2.5 Directly specified (marginal) models 25
2.5.1 Multivariate normal and Gaussian process models 26
2.5.2 Directly specified models for discrete longitudinal
responses 28
2.6 Semiparametric regression 31
2.6.1 Generalized additive models based on regression splines 32
2.6.2 Varying coefficient models 34
2.7 Interpreting covariate effects 34
2.7.1 Assumptions regarding time-varying covariates 35
2.7.2 Longitudinal vs. cross-sectional effects 36
2.7.3 Marginal vs. conditional effects 37
2.8 Further reading 38
3 Methods of Bayesian Inference 39
3.1 Overview 39
3.2 Likelihood and posterior distribution 39
3.2.1 Likelihood 39
3.2.2 Score function and information matrix 41
3.2.3 The posterior distribution 42
3.3 Prior Distributions 43
3.3.1 Conjugate priors 43
3.3.2 Noninformative priors 46
3.3.3 Informative priors 49
3.3.4 Identifiability and incomplete data 50
CONTENTS xi
3.4 Computation of the posterior distribution 51
3.4.1 The Gibbs sampler 52
3.4.2 The Metropolis-Hastings algorithm 54
3.4.3 Data augmentation 55
3.4.4 Inference using the posterior sample 58
3.5 Model comparisons and assessing model fit 62
3.5.1 Deviance Information Criterion (DIC) 63
3.5.2 Posterior predictive loss 65
3.5.3 Posterior predictive checks 67
3.6 Nonparametric Bayes 68
3.7 Further reading 69
4 Worked Examples using Complete Data 72
4.1 Overview 72
4.2 Multivariate normal model: Growth Hormone study 72
4.2.1 Models 72
4.2.2 Priors 73
4.2.3 MCMC details 73
4.2.4 Model selection and fit 73
4.2.5 Results 74
4.2.6 Conclusions 75
4.3 Normal random effects model: Schizophrenia trial 75
4.3.1 Models 76
4.3.2 Priors 77
4.3.3 MCMC details 77
4.3.4 Results 77
4.3.5 Conclusions 78
4.4 Models for longitudinal binary data: CTQ I Study 79
4.4.1 Models 80
4.4.2 Priors 81
4.4.3 MCMC details 81
4.4.4 Model selection 81
4.4.5 Results 82
4.4.6 Conclusions 83
4.5 Summary 84
5 Missing Data Mechanisms and Longitudinal Data 85
5.1 Introduction 85
5.2 Full vs. observed data 86
5.2.1 Overview 86
5.2.2 Data structures 87
5.2.3 Dropout and other processes leading to missing re¬
sponses 87
xii CONTENTS
5.3 Full-data models and missing data mechanisms 89
5.3.1 Targets of inference 89
5.3.2 Missing data mechanisms 90
5.4 Assumptions about missing data mechanism 91
5.4.1 Missing completely at random (MCAR) 91
5.4.2 Missing at random (MAR) 93
5.4.3 Missing not at random (MNAR) 93
5.4.4 Auxiliary variables 94
5.5 Missing at random applied to dropout processes 96
5.6 Observed data posterior of full-data parameters 98
5.7 The ignorability assumption 99
5.7.1 Likelihood and posterior under ignorability 99
5.7.2 Factored likelihood with monotone ignorable missing-
ness 101
5.7.3 The practical meaning of 'ignorability' 102
5.8 Examples of full-data models under MAR 103
5.9 Full-data models under MNAR 106
5.9.1 Selection models 107
5.9.2 Mixture models 109
5.9.3 Shared parameter models 112
5.10 Summary 114
5.11 Further reading 114
6 Inference about Full-Data Parameters under Ignorability 115
6.1 Overview 115
6.2 General issues in model specification 116
6.2.1 Mis-specification of dependence 116
6.2.2 Orthogonal parameters 118
6.3 Posterior sampling using data augmentation 121
6.4 Covariance structures for univariate longitudinal processes 124
6.4.1 Serial correlation models 124
6.4.2 Covariance matrices induced by random effects 128
6.4.3 Covariance functions for misaligned data 129
6.5 Covariate-dependent covariance structures 130
6.5.1 Covariance/correlation matrices 130
6.5.2 Dependence in longitudinal binary models 134
6.6 Joint models for multivariate processes 134
6.6.1 Continuous response and continuous auxiliary covariate 135
6.6.2 Binary response and binary auxiliary covariate 137
6.6.3 Binary response and continuous auxiliary covariate 138
6.7 Model selection and model fit under ignorability 138
6.7.1 Deviance information criterion (DIC) 139
6.7.2 Posterior predictive checks 141
CONTENTS xiii
6.8 Further reading 143
7 Case Studies: Ignorable Missingness 145
7.1 Overview 145
7.2 Structured covariance matrices: Growth Hormone study 145
7.2.1 Models 145
7.2.2 Priors 146
7.2.3 MCMC details 146
7.2.4 Model selection and fit 147
7.2.5 Results and comparison with completers-only analysis 147
7.2.6 Conclusions 149
7.3 Normal random effects model: Schizophrenia trial 149
7.3.1 Models and priors 149
7.3.2 MCMC details 150
7.3.3 Model selection 150
7.3.4 Results and comparison with completers-only analysis 150
7.3.5 Conclusions 151
7.4 Marginalized transition model: CTQ I trial 151
7.4.1 Models 152
7.4.2 MCMC details 153
7.4.3 Model selection 153
7.4.4 Results 154
7.4.5 Conclusions 154
7.5 Joint modeling with auxiliary variables: CTQ II trial 155
7.5.1 Models 156
7.5.2 Priors 157
7.5.3 Posterior sampling 157
7.5.4 Model selection and fit 157
7.5.5 Results 158
7.5.6 Conclusions 159
7.6 Bayesian p-spline model: HERS CD4 data 159
7.6.1 Models 160
7.6.2 Priors 161
7.6.3 MCMC details 161
7.6.4 Model selection 161
7.6.5 Results 161
7.7 Summary 162
8 Models for Handling Nonignorable Missingness 165
8.1 Overview 165
8.2 Extrapolation factorization and sensitivity parameters 166
8.3 Selection models 167
8.3.1 Background and history 167
xiv CONTENTS
8.3.2 Absence of sensitivity parameters in the missing data
mechanism 168
8.3.3 Heckman selection model for a bivariate response 171
8.3.4 Specification of the missing data mechanism for longi¬
tudinal data 173
8.3.5 Parametric selection models for longitudinal data 174
8.3.6 Feasibility of sensitivity analysis for parametric selection
models 175
8.3.7 Semiparametric selection models 176
8.3.8 Posterior sampling strategies 180
8.3.9 Summary of pros and cons of selection models 181
8.4 Mixture models 181
8.4.1 Background, specification, and identification 181
8.4.2 Identification strategies for mixture models 183
8.4.3 Mixture models with discrete-time dropout 188
8.4.4 Mixture models with continuous-time dropout 198
8.4.5 Combinations of MAR and MNAR dropout 201
8.4.6 Mixture models or selection models? 202
8.4.7 Covariate effects in mixture models 203
8.5 Shared parameter models 206
8.5.1 General structure 206
8.5.2 Pros and cons of shared parameter models 207
8.6 Model selection and model fit in nonignorable models 209
8.6.1 Deviance information criterion (DIC) 209
8.6.2 Posterior predictive checks 213
8.7 Further reading 215
9 Informative Priors and Sensitivity Analysis 216
9.1 Overview 216
9.1.1 General approach 216
9.1.2 Global vs. local sensitivity analysis 217
9.2 Some principles 219
9.3 Parameterizing the full-data model 220
9.4 Specifying priors 222
9.5 Pattern mixture models 224
9.5.1 General parameterization 224
9.5.2 Using model constraints to reduce dimensionality of
sensitivity parameters 225
9.6 Selection models 226
9.7 Further reading 231
10 Case Studies: Nonignorable Missingness 233
10.1 Overview 233
CONTENTS xv
10.2 Growth Hormone study: Pattern mixture models and sensitiv¬
ity analysis 234
10.2.1 Overview 234
10.2.2 Multivariate normal model under ignorability 234
10.2.3 Pattern mixture model specification 235
10.2.4 MAR constraints for pattern mixture model 235
10.2.5 Parameterizing departures from MAR 236
10.2.6 Constructing priors 238
10.2.7 Analysis using point mass MAR prior 238
10.2.8 Analyses using MNAR priors 239
10.2.9 Summary of pattern mixture analysis 246
10.3 OASIS Study: Selection models, mixture models, and elicited
priors 248
10.3.1 Overview 248
10.3.2 Selection model specification 249
10.3.3 Selection model analyses under MAR and MNAR 251
10.3.4 Pattern mixture model specification 252
10.3.5 MAR and MNAR parameterizations 252
10.3.6 Pattern mixture analysis under MAR 255
10.3.7 Pattern mixture analysis under MNAR using elicited
priors 255
10.3.8 Summary: selection vs. pattern mixture approaches 259
10.4 Pediatric AIDS trial: Mixture of varying coefficient models for
continuous dropout 261
10.4.1 Overview 261
10.4.2 Model specification: CD4 counts 263
10.4.3 Model specification: dropout times 265
10.4.4 Summary of analyses under MAR and MNAR 265
10.4.5 Summary 266
Distributions 268
Bibliography 271
Author Index 292
Index 298 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Daniels, Michael J. Hogan, Joseph W. |
| author_facet | Daniels, Michael J. Hogan, Joseph W. |
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| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV021794746 |
| illustrated | Illustrated |
| index_date | 2024-07-02T15:45:46Z |
| indexdate | 2024-07-09T20:44:47Z |
| institution | BVB |
| isbn | 9781584886099 1584886099 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015007340 |
| oclc_num | 173683726 |
| open_access_boolean | |
| owner | DE-M49 DE-BY-TUM DE-19 DE-BY-UBM DE-473 DE-BY-UBG DE-578 |
| owner_facet | DE-M49 DE-BY-TUM DE-19 DE-BY-UBM DE-473 DE-BY-UBG DE-578 |
| physical | XX, 303 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Chapman & Hall/CRC |
| record_format | marc |
| series | Monographs on statistics and applied probability |
| series2 | Monographs on statistics and applied probability |
| spelling | Daniels, Michael J. Verfasser aut Missing data in longitudinal studies strategies for Bayesian Modeling and Sensitivity Analysis Michael J. Daniels ; Joseph W. Hogan Boca Raton [u.a.] Chapman & Hall/CRC 2008 XX, 303 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Monographs on statistics and applied probability 109 Longitudinaal onderzoek gtt Methode van Bayes gtt Nauwkeurigheid gtt Ontbrekende gegevens gtt Bayes Theorem Bayesian statistical decision theory Data Interpretation, Statistical Longitudinal Studies Longitudinal method Missing observations (Statistics) Models, Statistical Sensitivity and Specificity Sensitivity theory (Mathematics) Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd rswk-swf Längsschnittuntersuchung (DE-588)4034036-3 gnd rswk-swf Fehlende Daten (DE-588)4264715-0 gnd rswk-swf Längsschnittuntersuchung (DE-588)4034036-3 s Bayes-Entscheidungstheorie (DE-588)4144220-9 s Fehlende Daten (DE-588)4264715-0 s b DE-604 Hogan, Joseph W. Verfasser aut Monographs on statistics and applied probability 109 (DE-604)BV002494005 109 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015007340&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Daniels, Michael J. Hogan, Joseph W. Missing data in longitudinal studies strategies for Bayesian Modeling and Sensitivity Analysis Monographs on statistics and applied probability Longitudinaal onderzoek gtt Methode van Bayes gtt Nauwkeurigheid gtt Ontbrekende gegevens gtt Bayes Theorem Bayesian statistical decision theory Data Interpretation, Statistical Longitudinal Studies Longitudinal method Missing observations (Statistics) Models, Statistical Sensitivity and Specificity Sensitivity theory (Mathematics) Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd Längsschnittuntersuchung (DE-588)4034036-3 gnd Fehlende Daten (DE-588)4264715-0 gnd |
| subject_GND | (DE-588)4144220-9 (DE-588)4034036-3 (DE-588)4264715-0 |
| title | Missing data in longitudinal studies strategies for Bayesian Modeling and Sensitivity Analysis |
| title_auth | Missing data in longitudinal studies strategies for Bayesian Modeling and Sensitivity Analysis |
| title_exact_search | Missing data in longitudinal studies strategies for Bayesian Modeling and Sensitivity Analysis |
| title_exact_search_txtP | Missing data in longitudinal studies strategies for Bayesian Modeling and Sensitivity Analysis |
| title_full | Missing data in longitudinal studies strategies for Bayesian Modeling and Sensitivity Analysis Michael J. Daniels ; Joseph W. Hogan |
| title_fullStr | Missing data in longitudinal studies strategies for Bayesian Modeling and Sensitivity Analysis Michael J. Daniels ; Joseph W. Hogan |
| title_full_unstemmed | Missing data in longitudinal studies strategies for Bayesian Modeling and Sensitivity Analysis Michael J. Daniels ; Joseph W. Hogan |
| title_short | Missing data in longitudinal studies |
| title_sort | missing data in longitudinal studies strategies for bayesian modeling and sensitivity analysis |
| title_sub | strategies for Bayesian Modeling and Sensitivity Analysis |
| topic | Longitudinaal onderzoek gtt Methode van Bayes gtt Nauwkeurigheid gtt Ontbrekende gegevens gtt Bayes Theorem Bayesian statistical decision theory Data Interpretation, Statistical Longitudinal Studies Longitudinal method Missing observations (Statistics) Models, Statistical Sensitivity and Specificity Sensitivity theory (Mathematics) Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd Längsschnittuntersuchung (DE-588)4034036-3 gnd Fehlende Daten (DE-588)4264715-0 gnd |
| topic_facet | Longitudinaal onderzoek Methode van Bayes Nauwkeurigheid Ontbrekende gegevens Bayes Theorem Bayesian statistical decision theory Data Interpretation, Statistical Longitudinal Studies Longitudinal method Missing observations (Statistics) Models, Statistical Sensitivity and Specificity Sensitivity theory (Mathematics) Bayes-Entscheidungstheorie Längsschnittuntersuchung Fehlende Daten |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015007340&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002494005 |
| work_keys_str_mv | AT danielsmichaelj missingdatainlongitudinalstudiesstrategiesforbayesianmodelingandsensitivityanalysis AT hoganjosephw missingdatainlongitudinalstudiesstrategiesforbayesianmodelingandsensitivityanalysis |