Bayesian survival analysis / Joseph G. Ibrahim, Ming-Hui Chen, Debajyoti Sinha.

Format:

Book

Author/Creator:

Ibrahim, Joseph George.

Contributor:

Chen, Ming-Hui, 1961-

Sinha, Debajyoti

Hazel M. Hussong Fund.

Series:

Springer series in statistics

Language:

English

Subjects (All):

Failure time data analysis.

Bayesian statistical decision theory.

Physical Description:

xiv, 479 pages : illustrations ; 25 cm.

Place of Publication:

New York : Springer, [2001]

Contents:

1.3 Motivating Examples 3

1.4 Survival Analysis 13

1.4.1 Proportional Hazards Models 15

1.4.2 Censoring 15

1.4.3 Partial Likelihood 16

1.5 The Bayesian Paradigm 17

1.6 Sampling from the Posterior Distribution 18

1.7 Informative Prior Elicitation 22

1.8 Why Bayes? 26

2 Parametric Models 30

2.1 Exponential Model 30

2.2 Weibull Model 35

2.3 Extreme Value Model 37

2.4 Log-Normal Model 39

2.5 Gamma Model 40

3 Semiparametric Models 47

3.1 Piecewise Constant Hazard Model 47

3.2 Models Using a Gamma Process 50

3.2.1 Gamma Process on Cumulative Hazard 50

3.2.2 Gamma Process with Grouped-Data Likelihood 51

3.2.3 Relationship to Partial Likelihood 53

3.2.4 Gamma Process on Baseline Hazard 55

3.3 Prior Elicitation 56

3.3.1 Approximation of the Prior 57

3.3.2 Choices of Hyperparameters 59

3.3.3 Sampling from the Joint Posterior Distribution of ([beta], [delta], a[subscript 0]) 60

3.4 A Generalization of the Cox Model 63

3.5 Beta Process Models 66

3.5.1 Beta Process Priors 66

3.5.2 Interval Censored Data 71

3.6 Correlated Gamma Processes 72

3.7 Dirichlet Process Models 78

3.7.1 Dirichlet Process Prior 78

3.7.2 Dirichlet Process in Survival Analysis 81

3.7.3 Dirichlet Process with Doubly Censored Data 84

3.7.4 Mixtures of Dirichlet Process Models 87

3.7.5 Conjugate MDP Models 89

3.7.6 Nonconjugate MDP Models 90

3.7.7 MDP Priors with Censored Data 91

3.7.8 Inclusion of Covariates 94

4 Frailty Models 100

4.1 Proportional Hazards Model with Frailty 101

4.1.1 Weibull Model with Gamma Frailties 102

4.1.2 Gamma Process Prior for H[subscript 0](t) 104

4.1.3 Piecewise Exponential Model for h[subscript 0](t) 106

4.1.4 Positive Stable Frailties 112

4.1.5 A Bayesian Model for Institutional Effects 118

4.1.6 Posterior Likelihood Methods 126

4.1.7 Methods Based on Partial Likelihood 131

4.2 Multiple Event and Panel Count Data 134

4.3 Multilevel Multivariate Survival Data 136

4.4 Bivariate Measures of Dependence 147

5 Cure Rate Models 155

5.2 Parametric Cure Rate Model 156

5.2.1 Models 156

5.2.2 Prior and Posterior Distributions 160

5.2.3 Posterior Computation 163

5.3 Semiparametric Cure Rate Model 171

5.4 An Alternative Semiparametric Cure Rate Model 179

5.4.1 Prior Distributions 180

5.5 Multivariate Cure Rate Models 185

5.5.1 Models 185

5.5.2 The Likelihood Function 188

5.5.3 The Prior and Posterior Distributions 190

5.5.4 Computational Implementation 191

6 Model Comparison 208

6.1 Posterior Model Probabilities 209

6.1.1 Variable Selection in the Cox Model 210

6.1.2 Prior Distribution on the Model Space 211

6.1.3 Computing Prior and Posterior Model Probabilities 212

6.2 Criterion-Based Methods 219

6.2.1 The L Measure 220

6.2.2 The Calibration Distribution 223

6.3 Conditional Predictive Ordinate 227

6.4 Bayesian Model Averaging 234

6.4.1 BMA for Variable Selection in the Cox Model 236

6.4.2 Identifying the Models in A' 237

6.4.3 Assessment of Predictive Performance 239

6.5 Bayesian Information Criterion 246

6.5.1 Model Selection Using BIC 249

6.5.2 Exponential Survival Model 249

6.5.3 The Cox Proportional Hazards Model 250

7 Joint Models for Longitudinal and Survival Data 262

7.1.1 Joint Modeling in AIDS Studies 263

7.1.2 Joint Modeling in Cancer Vaccine Trials 263

7.1.3 Joint Modeling in Health-Related Quality of Life Studies 264

7.2 Methods for Joint Modeling of Longitudinal and Survival Data 265

7.2.1 Partial Likelihood Models 265

7.2.2 Joint Likelihood Models 267

7.2.3 Mixture Models 273

7.3 Bayesian Methods for Joint Modeling of Longitudinal and Survival Data 275

8 Missing Covariate Data 290

8.2 The Cure Rate Model with Missing Covariate Data 292

8.3 A General Class of Covariate Models 293

8.4 The Prior and Posterior Distributions 297

8.5 Model Checking 301

9 Design and Monitoring of Randomized Clinical Trials 320

9.1 Group Sequential Log-Rank Tests for Survival Data 320

9.2 Bayesian Approaches 322

9.2.1 Range of Equivalence 326

9.2.2 Prior Elicitation 328

9.2.3 Predictions 332

9.2.4 Checking Prior-Data Compatibility 334

9.3 Bayesian Sample Size Determination 336

9.4 Alternative Approaches to Sample Size Determination 340

10 Other Topics 352

10.1 Proportional Hazards Models Built from Monotone Functions 352

10.1.1 Likelihood Specification 354

10.1.2 Prior Specification 356

10.1.3 Time-Dependent Covariates 357

10.2 Accelerated Failure Time models 359

10.2.1 MDP Prior for [theta subscript i] 360

10.2.2 Polya Tree Prior for [theta subscript i] 364

10.3 Bayesian Survival Analysis Using MARS 373

10.3.1 The Bayesian Model 374

10.3.2 Survival Analysis with Frailties 379

10.4 Change Point Models 381

10.4.1 Basic Assumptions and Model 382

10.4.2 Extra Poisson Variation 385

10.4.3 Lag Functions 386

10.4.4 Recurrent Tumors 388

10.4.5 Bayesian Inference 389

10.5 The Poly-Weibull Model 395

10.5.1 Likelihood and Priors 396

10.5.2 Sampling the Posterior Distribution 397

10.6 Flexible Hierarchical Survival Models 398

10.6.1 Three Stages of the Hierarchical Model 400

10.6.2 Implementation 403

10.7 Bayesian Model Diagnostics 413

10.7.1 Bayesian Latent Residuals 413

10.7.2 Prequential Methods 417.

Notes:

Includes bibliographical references (pages [483]-466) and indexes.

Local Notes:

Acquired for the Penn Libraries with assistance from the Hazel M. Hussong Fund.

ISBN:

0387952772

OCLC:

46240278