The Statistical Analysis of Recurrent Events (eBook)

Preface 6
Glossary 9
Contents 12
1 Introduction 18
1.1 The Scope of Recurrent Events 18
1.2 Some Preliminary Examples 19
1.3 Notation and Frameworks 26
1.4 Selection of Individuals and Observation Schemes 33
1.5 Multitype Event Data 37
1.6 Some Other Aspects of Analysis and Design 40
1.7 Bibliographic Notes 41
2 Models and Frameworks for Analysis of Recurrent Events 43
2.1 Mathematical Background 43
2.2 Poisson Processes and Models for Event Counts 47
2.3 Renewal Processes and Models for Gap Times 55
2.4 General Intensity-Based Models 59
2.5 Discrete-Time Models and Time-Varying Covariates 61
2.6 Likelihood for Selection and Observation Schemes 63
2.7 Bibliographic Notes 67
2.8 Problems and Supplements 68
3 Methods Based on Counts and Rate Functions 75
3.1 Introduction 75
3.2 Parametric Maximum Likelihood for Poisson Models 77
3.3 Poisson Models with Piecewise-Constant Rates 81
3.4 Nonparametric and Semiparametric Poisson Models 84
3.5 Poisson Models with Random Effects 92
3.6 Robust Methods for Rate and Mean Functions 98
3.7 Some Useful Tests for Rate Functions 104
3.8 Applications and Illustrations 116
3.9 Bibliographic Notes 128
3.10 Problems and Supplements 130
4 Analysis of Gap Times 136
4.1 Renewal Processes and Related Methods of Analysis 136
4.2 Extensions of Renewal Models 141
4.3 Examples 148
4.4 Estimation of Marginal Gap Time Probabilities 152
4.5 Left Truncation of First Gap Times and Initial Conditions 161
4.6 Bibliographic Notes 167
4.7 Problems and Supplements 168
5 General Intensity-Based Models 175
5.1 Time Scales and Intensity Modeling 175
5.2 Parametric Analysis for Two Useful Models 177
5.3 Semiparametric Markov Analysis 185
5.4 Semiparametric Modulated Renewal Analysis 197
5.5 Some Additional Illustrations 203
5.6 Bibliographic Notes 214
5.7 Problems and Supplements 215
6 Multitype Recurrent Events 219
6.1 Multivariate Event Data 219
6.2 Intensity-Based Methods 220
6.3 Random Effect Models for Multitype Events 223
6.4 Robust Methods for Multitype Events 226
6.5 Alternating Two-State Processes 230
6.6 Recurrent Events with a Terminal Event 232
6.7 Applications and Illustrations 241
6.8 Bibliographic Notes 260
6.9 Problems and Supplements 261
7 Observation Schemes Giving Incomplete or Selective Data 265
7.1 Intermittent Observation During Followup 265
7.2 Dependent Censoring or Inspections 278
7.3 Event-Dependent Selection 287
7.4 Bibliographic Notes 298
7.5 Problems and Supplements 300
8 Other Topics 306
8.1 Event Processes with Marks 306
8.2 Models for Cumulative Costs 308
8.3 Prediction 315
8.4 Recurrent Events in Randomized Trials 324
8.5 Clustered Data 337
8.6 Missing Covariate Values 340
8.7 Covariate Measurement Error 342
8.8 Bayesian Methods 344
8.9 Bibliographic Notes 345
8.10 Problems and Supplements 346
A Estimation and Statistical Inference 350
A.1 Maximum Likelihood 350
A.2 Estimating Functions 355
B Computational Methods 357
B.1 Software for Recurrent Events 357
B.2 Optimization Methods 358
B.3 Simulation and Resampling Methods 358
C Code and Remarks for Selected Examples 361
C.1 Tumorgenicity Data Analysis of Chapter 3 361
C.2 Code for rhDNase Data Analyses of Chapter 4 367
C.3 Code for Chronic Bronchitis Trial of Chapter 6 370
D Datasets 374
D.1 Bladder Cancer Data 374
D.2 Bowel Motility Data 375
D.3 Pulmonary Exacerbations and rhDNase 376
D.4 Software Debugging Data 378
D.5 Artificial Field Repair Data 378
References 381
Author Index 401
Subject Index 407