The Statistical Analysis of Recurrent Events

The Statistical Analysis of Recurrent Events

von: Richard J. Cook, Jerald Lawless

Springer-Verlag, 2007

ISBN: 9780387698106 , 404 Seiten

Format: PDF, OL

Kopierschutz: Wasserzeichen

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Preis: 142,79 EUR

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Mehr zum Inhalt

The Statistical Analysis of Recurrent Events


 

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