The Statistical Analysis of Recurrent Events (Statistics for Biology and Health)

Contents......Page 13
Preface......Page 7
Glossary......Page 10
1.1 The Scope of Recurrent Events......Page 19
1.2.1 Mammary Tumors in a Carcinogenicity Study......Page 20
1.2.3 Pulmonary Exacerbations in Cystic Fibrosis......Page 23
1.2.4 Automobile Warranty Claims......Page 25
1.3 Notation and Frameworks......Page 27
1.3.1 Methods Based on Event Counts......Page 29
1.3.2 Methods Based on Waiting or Gap Times......Page 30
1.3.4 Covariates......Page 32
1.3.5 Factors Influencing Model Choice......Page 33
1.4.1 The Choice of Time Scale......Page 34
1.4.2 Defining Periods "At Risk"......Page 36
1.4.3 Initial Conditions and Selecting Individuals for Study......Page 37
1.5.2 Recurrent Events with Termination......Page 38
1.5.3 Recurrent Episodes......Page 39
1.6 Some Other Aspects of Analysis and Design......Page 41
1.7 Bibliographic Notes......Page 42
2.1 Mathematical Background......Page 44
2.2.1 Poisson Processes......Page 48
2.2.2 Covariates in Poisson Processes......Page 51
2.2.3 Random Effects in Poisson Processes......Page 52
2.2.4 Example: Mammary Tumors in Rats......Page 54
2.3.1 Models for Gap Times Between Events......Page 56
2.3.2 Example: Bowel Motility Cycles......Page 59
2.4 General Intensity-Based Models......Page 60
2.5 Discrete-Time Models and Time-Varying Covariates......Page 62
2.6 Likelihood for Selection and Observation Schemes......Page 64
2.7 Bibliographic Notes......Page 68
2.8 Problems and Supplements......Page 69
3.1 Introduction......Page 76
3.2.1 Score and Information Functions......Page 78
3.2.2 A General Parametric Rate Function......Page 79
3.2.3 Time Transform Models......Page 80
3.2.4 Using Survival Software......Page 81
3.3 Poisson Models with Piecewise-Constant Rates......Page 82
3.4.1 Nonparametric Inference......Page 85
3.4.2 Semiparametric Regression......Page 87
3.4.3 Stratification......Page 90
3.4.4 Additive Models......Page 92
3.5.1 Formulation......Page 93
3.5.2 Models for Zero-Inflated Data......Page 95
3.5.3 Negative Binomial Models......Page 96
3.6.1 Nonparametric Estimation......Page 99
3.6.2 Parametric Estimation......Page 100
3.6.3 Robust Semiparametric Methods......Page 101
3.6.5 Methods Based on Multivariate Failure Time Data......Page 103
3.7.1 Tests for Trend......Page 105
3.7.2 Tests for Multiplicative Covariate Effects......Page 107
3.7.3 Generalized Residuals, Martingales, and Assessment of Fit......Page 109
3.7.5 Two-Sample Test Statistics Based on Rates......Page 114
3.8.1 Rat Mammary Tumor Data......Page 117
3.8.2 A Trial of Treatment for Herpes Simplex Virus......Page 122
3.8.3 Fitting and Prediction from a Software Debugging Model......Page 124
3.8.4 Comparing Warranty Claim Histories......Page 127
3.9 Bibliographic Notes......Page 129
3.10 Problems and Supplements......Page 131
4.1 Renewal Processes and Related Methods of Analysis......Page 137
4.2.1 Conditional Analysis of Successive Gap Times......Page 142
4.2.2 Models with Random Effects......Page 144
4.2.3 Joint Gap Time Distributions......Page 145
4.2.4 Modulated Renewal Processes......Page 148
4.3.1 Bowel Motility Cycles......Page 149
4.3.2 Pulmonary Exacerbations and rhDNase Treatment......Page 150
4.4 Estimation of Marginal Gap Time Probabilities......Page 153
4.4.1 Nonparametric Estimation of Marginal Gap Time Distributions......Page 155
4.4.3 Pulmonary Exacerbations in Cystic Fibrosis......Page 159
4.5 Left Truncation of First Gap Times and Initial Conditions......Page 162
4.5.1 Initial Conditions and Renewal Processes......Page 163
4.5.2 Initial Conditions and General Gap Time Analysis......Page 166
4.6 Bibliographic Notes......Page 168
4.7 Problems and Supplements......Page 169
5.1 Time Scales and Intensity Modeling......Page 176
5.2.1 Log-Linear Intensity Models......Page 178
5.2.2 A Trend-Renewal Model......Page 180
5.2.4 An Illustration: Air-Conditioning System Failures......Page 182
5.3.1 Models with Dependence on Prior Counts......Page 186
5.3.2 Markov Nonparametric Estimation......Page 188
5.3.3 Models with Covariates......Page 190
5.3.4 Analysis of Outbreaks Due to Herpes Simplex Virus......Page 192
5.4.1 Analysis Based on the Cox Model......Page 198
5.4.2 Illustration: Cerebrospinal Fluid Shunts......Page 200
5.5 Some Additional Illustrations......Page 204
5.5.1 Pulmonary Exacerbations in the Study of rhDNase......Page 205
5.5.2 Analysis of Asthma Exacerbations......Page 208
5.6 Bibliographic Notes......Page 215
5.7 Problems and Supplements......Page 216
6.1 Multivariate Event Data......Page 220
6.2.1 Notation and Intensity Functions......Page 221
6.2.2 Remarks on Intensity-Based Models......Page 222
6.3 Random Effect Models for Multitype Events......Page 224
6.4.1 Methods Based on Working Independence Assumptions......Page 227
6.4.2 Robust Methods with Covariance Functions......Page 229
6.5 Alternating Two-State Processes......Page 231
6.6 Recurrent Events with a Terminal Event......Page 233
6.6.1 Intensity-Based Approaches......Page 234
6.6.2 Random Effects Models......Page 235
6.6.3 Robust Methods for Marginal Features......Page 237
6.6.4 Partially Conditional Methods......Page 239
6.7.1 Cerebrospinal Fluid Shunt Failures......Page 242
6.7.2 Exacerbations in Patients with Chronic Bronchitis......Page 247
6.7.3 Skeletal Complications in Metastatic Cancer......Page 251
6.7.4 Relationships Between Skeletal Complications......Page 256
6.8 Bibliographic Notes......Page 261
6.9 Problems and Supplements......Page 262
7.1 Intermittent Observation During Followup......Page 266
7.1.1 Methods Based on Poisson Processes......Page 267
7.1.2 Robust Estimation of Rate and Mean Functions......Page 269
7.1.3 Illustration: Superficial Tumors of the Bladder......Page 271
7.1.4 Interval-Count Data for Multiple Events......Page 275
7.1.5 Illustration: Joint Damage in Psoriatic Arthritis......Page 278
7.2.1 Dependent Censoring and Weighted Estimating Functions......Page 279
7.2.2 Rate or Mean Function Estimation with Event-Dependent Censoring......Page 283
7.2.3 Intermittent Observation......Page 285
7.3.1 Some Examples......Page 288
7.3.2 Supplementary Information on Selection......Page 296
7.4 Bibliographic Notes......Page 299
7.5 Problems and Supplements......Page 301
8.1 Event Processes with Marks......Page 307
8.2.1 Introduction......Page 309
8.2.2 Estimation for Cost Processes......Page 311
8.2.3 Examples......Page 313
8.3.1 Introduction......Page 316
8.3.2 Predictive Probabilities and Calibration......Page 318
8.3.3 Some Examples of Prediction......Page 320
8.4.1 Specification and Testing of Treatment Effects......Page 325
8.4.2 Trial Design for Mixed Poisson Processes......Page 329
8.4.3 Use of Baseline Count Data......Page 330
8.4.4 Interim Monitoring with Recurrent Events......Page 334
8.5 Clustered Data......Page 338
8.6 Missing Covariate Values......Page 341
8.7 Covariate Measurement Error......Page 343
8.8 Bayesian Methods......Page 345
8.9 Bibliographic Notes......Page 346
8.10 Problems and Supplements......Page 347
A.1.1 Introduction......Page 351
A.1.2 Asymptotic Pivotals......Page 352
A.1.3 Confidence Regions or Intervals......Page 354
A.1.4 Tests of Hypotheses......Page 355
A.2 Estimating Functions......Page 356
B.1 Software for Recurrent Events......Page 358
B.3 Simulation and Resampling Methods......Page 359
C.1.1 Poisson Analysis with Weibull Baseline Rate......Page 362
C.1.2 Poisson Analysis with Piecewise-Constant Rates......Page 364
C.1.4 Semiparametric Mixed Poisson Analysis......Page 366
C.1.5 Robust Semiparametric Analysis......Page 367
C.2 Code for rhDNase Data Analyses of Chapter 4......Page 368
C.3 Code for Chronic Bronchitis Trial of Chapter 6......Page 371
D.1 Bladder Cancer Data......Page 375
D.2 Bowel Motility Data......Page 376
D.3 Pulmonary Exacerbations and rhDNase......Page 377
D.5 Artificial Field Repair Data......Page 379
References......Page 382
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