The Statistical Analysis of Recurrent Events

Preface

Glossary

Contents

1 Introduction

1.1 The Scope of Recurrent Events

1.2 Some Preliminary Examples

1.3 Notation and Frameworks

1.4 Selection of Individuals and Observation Schemes

1.5 Multitype Event Data

1.6 Some Other Aspects of Analysis and Design

1.7 Bibliographic Notes

2 Models and Frameworks for Analysis of Recurrent Events

2.1 Mathematical Background

2.2 Poisson Processes and Models for Event Counts

2.3 Renewal Processes and Models for Gap Times

2.4 General Intensity-Based Models

2.5 Discrete-Time Models and Time-Varying Covariates

2.6 Likelihood for Selection and Observation Schemes

2.7 Bibliographic Notes

2.8 Problems and Supplements

3 Methods Based on Counts and Rate Functions

3.1 Introduction

3.2 Parametric Maximum Likelihood for Poisson Models

3.3 Poisson Models with Piecewise-Constant Rates

3.4 Nonparametric and Semiparametric Poisson Models

3.5 Poisson Models with Random Effects

3.6 Robust Methods for Rate and Mean Functions

3.7 Some Useful Tests for Rate Functions

3.8 Applications and Illustrations

3.9 Bibliographic Notes

3.10 Problems and Supplements

4 Analysis of Gap Times

4.1 Renewal Processes and Related Methods of Analysis

4.2 Extensions of Renewal Models

4.3 Examples

4.4 Estimation of Marginal Gap Time Probabilities

4.5 Left Truncation of First Gap Times and Initial Conditions

4.6 Bibliographic Notes

4.7 Problems and Supplements

5 General Intensity-Based Models

5.1 Time Scales and Intensity Modeling

5.2 Parametric Analysis for Two Useful Models

5.3 Semiparametric Markov Analysis

5.4 Semiparametric Modulated Renewal Analysis

5.5 Some Additional Illustrations

5.6 Bibliographic Notes

5.7 Problems and Supplements

6 Multitype Recurrent Events

6.1 Multivariate Event Data

6.2 Intensity-Based Methods

6.3 Random Effect Models for Multitype Events

6.4 Robust Methods for Multitype Events

6.5 Alternating Two-State Processes

6.6 Recurrent Events with a Terminal Event

6.7 Applications and Illustrations

6.8 Bibliographic Notes

6.9 Problems and Supplements

7 Observation Schemes Giving Incomplete or Selective Data

7.1 Intermittent Observation During Followup

7.2 Dependent Censoring or Inspections

7.3 Event-Dependent Selection

7.4 Bibliographic Notes

7.5 Problems and Supplements

8 Other Topics

8.1 Event Processes with Marks

8.2 Models for Cumulative Costs

8.3 Prediction

8.4 Recurrent Events in Randomized Trials

8.5 Clustered Data

8.6 Missing Covariate Values

8.7 Covariate Measurement Error

8.8 Bayesian Methods

8.9 Bibliographic Notes

8.10 Problems and Supplements

A Estimation and Statistical Inference

A.1 Maximum Likelihood

A.2 Estimating Functions

B Computational Methods

B.1 Software for Recurrent Events

B.2 Optimization Methods

B.3 Simulation and Resampling Methods

C Code and Remarks for Selected Examples

C.1 Tumorgenicity Data Analysis of Chapter 3

C.2 Code for rhDNase Data Analyses of Chapter 4

C.3 Code for Chronic Bronchitis Trial of Chapter 6

D Datasets

D.1 Bladder Cancer Data

D.2 Bowel Motility Data

D.3 Pulmonary Exacerbations and rhDNase

D.4 Software Debugging Data

D.5 Artificial Field Repair Data

References

Author Index

Subject Index