The statistical analysis of recurrent events:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
2007
|
| Series: | Statistics for biology and health
|
| Subjects: | |
| Links: | http://deposit.dnb.de/cgi-bin/dokserv?id=2930933&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015605892&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015605892&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| Physical Description: | XX, 403 S. graph. Darst. 235 mm x 155 mm |
| ISBN: | 9780387698090 0387698094 |
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| 245 | 1 | 0 | |a The statistical analysis of recurrent events |c Richard J. Cook ; Jerald F. Lawless |
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| _version_ | 1819269050941833216 |
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| adam_text | Contents
Preface
........................................................
vii
Glossary
....................................................... xi
1
Introduction
............................................... 1
1.1
The Scope of Recurrent Events
............................ 1
1.2
Some Preliminary Examples
.............................. 2
1.2.1
Mammary Tumors in a Carcinogenicity Study
......... 2
1.2.2
Testing and Debugging a Large Software System
...... 5
1.2.3
Pulmonary Exacerbations in Cystic Fibrosis
.......... 5
1.2.4
Automobile Warranty Claims
....................... 7
1.3
Notation and Frameworks
................................ 9
1.3.1
Methods Based on Event Counts
.................... 11
1.3.2
Methods Based on Waiting or Gap Times
............ 12
1.3.3
More General Models
.............................. 14
1.3.4
Covariates
........................................ 14
1.3.5
Factors Influencing Model Choice
.................... 15
1.4
Selection of Individuals and Observation Schemes
............ 16
1.4.1
The Choice of Time Scale
.......................... 16
1.4.2
Defining Periods At Risk
......................... 18
1.4.3
Initial Conditions and Selecting Individuals for Study
.. 19
1.4.4
Intermittent Observation and Interval Censoring
...... 20
1.5
Multitype Event Data
.................................... 20
1.5.1
Multivariate Event Processes
....................... 20
1.5.2
Recurrent Events with Termination
.................. 20
1.5.3
Recurrent Episodes
................................ 21
1.6
Some Other Aspects of Analysis and Design
................ 23
1.7
Bibliographic Notes
...................................... 24
Contents
Models
and Frameworks for Analysis
of Recurrent Events
....................................... 27
2.1
Mathematical Background
................................ 27
2.2
Poisson
Processes and Models for Event Counts
............. 31
2.2.1
Poisson
Processes
................................. 31
2.2.2
Covariates in
Poisson
Processes
..................... 34
2.2.3
Random Effects in
Poisson
Processes
................. 35
2.2.4
Example: Mammary Tumors in Rats
................. 37
2.3
Renewal Processes and Models for Gap Times
............... 39
2.3.1
Models for Gap Times Between Events
............... 39
2.3.2
Example: Bowel Motility Cycles
..................... 42
2.4
General Intensity-Based Models
........................... 43
2.5
Discrete-Time Models and Time-Varying Covariates
......... 45
2.6
Likelihood for Selection and Observation Schemes
........... 47
2.7
Bibliographic Notes
...................................... 51
2.8
Problems and Supplements
............................... 52
Methods Based on Counts and Rate Functions
............ 59
3.1
Introduction
............................................ 59
3.2
Parametric Maximum Likelihood for
Poisson
Models
......... 61
3.2.1
Score and Information Functions
.................... 61
3.2.2
A General Parametric Rate Function
................ 62
3.2.3
Time Transform Models
............................ 63
3.2.4
Using Survival Software
............................ 64
3.3
Poisson
Models with Piecewise-Constant Rates
.............. 65
3.4
Nonparametric and Semiparametric
Poisson
Models
.......... 68
3.4.1
Nonparametric Inference
........................... 68
3.4.2
Semiparametric Regression
......................... 70
3.4.3
Stratification
..................................... 73
3.4.4
Additive Models
.................................. 75
3.5
Poisson
Models with Random Effects
...................... 76
3.5.1
Formulation
...................................... 76
3.5.2
Models for Zero-Inflated Data
....................... 78
3.5.3
Negative Binomial Models
.......................... 79
3.6
Robust Methods for Rate and Mean Functions
.............. 82
3.6.1
Nonparametric Estimation
.......................... 82
3.6.2
Parametric Estimation
............................. 83
3.6.3
Robust Semiparametric Methods
.................... 84
3.6.4
Robust Methods with Semiparametric Variances
...... 86
3.6.5
Methods Based on Multivariate Failure Time Data
___ 86
3.7
Some Useful Tests for Rate Functions
...................... 88
3.7.1
Tests for Trend
................................... 88
3.7.2
Tests for Multiplicative Covariate Effects
............. 90
3.7.3
Generalized Residuals, Martingales, and Assessment
of Fit
............................................ 92
Contents xvii
3.7.4 Tests
for Extra-Poisson
Variation.................... 97
3.7.5
Two-Sample Test Statistics Based on Rates
........... 97
3.8
Applications and Illustrations
.............................100
3.8.1
Rat Mammary Tumor Data
........................100
3.8.2
A Trial of Treatment for Herpes Simplex Virus
........105
3.8.3
Fitting and Prediction from a Software Debugging
Model
...........................................107
3.8.4
Comparing Warranty Claim Histories
................110
3.9
Bibliographic Notes
......................................112
3.10
Problems and Supplements
...............................114
Analysis of Gap Times
.....................................121
4.1
Renewal Processes and Related Methods
of Analysis
.............................................121
4.2
Extensions of Renewal Models
............................126
4.2.1
Conditional Analysis of Successive Gap Times
........126
4.2.2
Models with Random Effects
........................128
4.2.3
Joint Gap Time Distributions
.......................129
4.2.4
Modulated Renewal Processes
.......................132
4.3
Examples
...............................................133
4.3.1
Bowel Motility Cycles
..............................133
4.3.2
Pulmonary Exacerbations and rhDNase Treatment
.... 134
4.4
Estimation of Marginal Gap Time Probabilities
.............137
4.4.1
Nonparametric Estimation of Marginal Gap Time
Distributions
.....................................139
4.4.2
Estimation for Marginal Regression Models
...........143
4.4.3
Pulmonary Exacerbations in Cystic Fibrosis
..........143
4.5
Left Truncation of First Gap Times and Initial Conditions
___146
4.5.1
Initial Conditions and Renewal Processes
.............147
4.5.2
Initial Conditions and General Gap Time Analysis
.....150
4.6
Bibliographic Notes
......................................152
4.7
Problems and Supplements
...............................153
General Intensity-Based Models
...........................161
5.1
Time Scales and Intensity Modeling
........................161
5.2
Parametric Analysis for Two Useful Models
.................163
5.2.1
Log-Linear Intensity Models
........................163
5.2.2
A Trend-Renewal Model
...........................165
5.2.3
Model Checking
...................................167
5.2.4
An Illustration: Air-Conditioning System Failures
.....167
5.3
Semiparametric Markov Analysis
..........................171
5.3.1
Models with Dependence on Prior Counts
............171
5.3.2
Markov Nonparametric Estimation
..................173
5.3.3
Models with Covariates
............................175
5.3.4
Analysis of Outbreaks Due to Herpes Simplex Virus
... 177
xviii Contents
5.4 Semiparametric
Modulated Renewal Analysis
...............183
5.4.1
Analysis Based on the Cox Model
...................183
5.4.2
Illustration:
Cerebrospinal
Fluid Shunts
..............185
5.5
Some Additional Illustrations
.............................189
5.5.1
Pulmonary Exacerbations in the Study of rhDNase
-----190
5.5.2
Analysis of Asthma Exacerbations
...................193
5.6
Bibliographic Notes
......................................200
5.7
Problems and Supplements
...............................201
6
Multitype Recurrent Events
...............................205
6.1
Multivariate Event Data
.................................205
6.2
Intensity-Based Methods
.................................206
6.2.1
Notation and Intensity Functions
....................206
6.2.2
Remarks on Intensity-Based Models
.................207
6.3
Random Effect Models for Multitype Events
................209
6.4
Robust Methods for Multitype Events
......................212
6.4.1
Methods Based on Working Independence Assumptions
212
6.4.2
Robust Methods with Covariance Functions
..........214
6.5
Alternating Two-State Processes
..........................216
6.6
Recurrent Events with a Terminal Event
...................218
6.6.1
Intensity-Based Approaches
.........................219
6.6.2
Random Effects Models
............................220
6.6.3
Robust Methods for Marginal Features
...............222
6.6.4
Partially Conditional Methods
......................224
6.7
Applications and Illustrations
.............................227
6.7.1
Cerebrospinal
Fluid Shunt Failures
..................227
6.7.2
Exacerbations in Patients with Chronic Bronchitis
.....232
6.7.3
Skeletal Complications in Metastatic Cancer
..........236
6.7.4
Relationships Between Skeletal Complications
.........241
6.8
Bibliographic Notes
......................................246
6.9
Problems and Supplements
...............................247
7
Observation Schemes Giving Incomplete or Selective Data
. 251
7.1
Intermittent Observation During Followup
..................251
7.1.1
Methods Based on
Poisson
Processes
.................252
7.1.2
Robust Estimation of Rate and Mean Functions
.......254
7.1.3
Illustration: Superficial Tumors of the Bladder
........256
7.1.4
Interval-Count Data for Multiple Events
.............260
7.1.5
Illustration: Joint Damage in Psoriatic Arthritis
.......263
7.2
Dependent Censoring or Inspections
.......................264
7.2.1
Dependent Censoring and Weighted Estimating
Functions
........................................264
7.2.2
Rate or Mean Function Estimation with Event-
Dependent Censoring
..............................268
7.2.3
Intermittent Observation
...........................270
Contents xix
7.3
Event-Dependent Selection
...............................273
7.3.1
Some Examples
...................................273
7.3.2
Supplementary Information on Selection
..............281
7.4
Bibliographic Notes
......................................284
7.5
Problems and Supplements
...............................286
8
Other Topics
..............................................293
8.1
Event Processes with Marks
..............................293
8.2
Models for Cumulative Costs
..............................295
8.2.1
Introduction
......................................295
8.2.2
Estimation for Cost Processes
.......................297
8.2.3
Examples
........................................299
8.3
Prediction
..............................................302
8.3.1
Introduction
......................................302
8.3.2
Predictive Probabilities and Calibration
..............304
8.3.3
Some Examples of Prediction
.......................306
8.4
Recurrent Events in Randomized Trials
....................311
8.4.1
Specification and Testing of Treatment Effects
........311
8.4.2
Trial Design for Mixed
Poisson
Processes
.............315
8.4.3
Use of Baseline Count Data
.........................316
8.4.4
Interim Monitoring with Recurrent Events
............320
8.5
Clustered Data
..........................................324
8.6
Missing Covariate Values
.................................327
8.7
Covariate Measurement Error
.............................329
8.8
Bayesian Methods
.......................................331
8.9
Bibliographic Notes
......................................332
8.10
Problems and Supplements
...............................333
A Estimation and Statistical Inference
.......................337
A.I Maximum Likelihood
....................................337
АЛЛ
Introduction
......................................337
A.1.2 Asymptotic
Pivotais
...............................338
A.
1.3
Confidence Regions or Intervals
.....................340
A.1.4 Tests of Hypotheses
...............................341
A.2 Estimating Functions
....................................342
В
Computational Methods
...................................345
B.I Software for Recurrent Events
.............................345
B.2 Optimization Methods
...................................346
B.3 Simulation and Resampling Methods
.......................346
С
Code and Remarks for Selected Examples
.................349
С Л
Tumorgenicity
Data Analysis of Chapter
3..................349
C.I.I
Poisson
Analysis with Weibull Baseline Rate
..........349
СЛ.2
Poisson
Analysis with Piecewise-Constant Rates
.......351
xx Contents
С.
1.3 Nonparametric and Semiparametric
Poisson
Analysis
..353
С.
1.4
Semiparametric Mixed
Poisson
Analysis
..............353
С.
1.5
Robust Semiparametric Analysis
....................354
C.2 Code for rhDNase Data Analyses of Chapter
4..............355
C.3 Code for Chronic Bronchitis Trial of Chapter
6..............358
D
Datasets...................................................
363
D.I Bladder Cancer Data
....................................363
D.2 Bowel Motility Data
.....................................364
D.3 Pulmonary Exacerbations and rhDNase
....................365
D.4 Software Debugging Data
.................................367
D.5 Artificial Field Repair Data
...............................367
References
.....................................................371
Author Index
..................................................391
Subject Index
.................................................397
Recurrent event data arise in diverse fields such as medicine, public health, insurance, social science,
economics, manufacturing and reliability. The purpose of this book is to present models and
statistical methods for the analysis of recurrent event data. No single comprehensive treatment of
these areas currently exists. The authors provide broad but detailed coverage of the major approaches
to analysis, while also emphasizing the modeling assumptions that they are based on. Thus, they
consider important models such as
Poisson
and renewal processes, with extensions to incorporate
covariates or random effects.
More general intensity-based models are also considered, as well as simpler models that focus on. rate
or mean functions. Parametric nonparametric and semtparametric methodologies are all covered,
with clear descriptions of procedures for estimation, testing and model checking. Important practical
topics such as observation schemes and selection of individuals for stady, the planning of randomized
experiments, events of several types, and the prediction of future events are considered.
Methods of modeling and analysis are illustrated through many examples taken from health research
and industry. The objectives and interpretations of different analyses are discussed in detail, and
issues of robustness are addressed. Statistical analysis of the examples is carried out with S-PLUS
software and code is given for some examples.
This book is directed at graduate students, researchers, and applied statisticians working in industry,
government or
academia.
Some familiarity with survival analysis is beneficial since survival software
is used to carry out many of the analyses considered. This book can be used as a textbook for a
graduate course on the analysis of recurrent events or as a reference for a more general course on
event history analysis. Problems are given at the end of chapters to reinforce the material presented
and to provide additional background or extensions to certain topics.
Richard i. Cook is Professor in the Department of Statistics and Actuarial Science at the
University of Waterloo and Canada Research Chair in Statistical Methods for Health Research.
He is an Associate Editor for the Lifetime Data Analysis.
Jeraid F, Lawless is Professor in the Department of Statistics and Actuarial Science at the University
of Waterloo. He is a former Editor of Technometrics and from
1994-2004
held the General Motors
Canada-NSERC Industrial Research Chair in Quality and Productivity. He is the author of Statistical
Models and Methods for Lifetime Data, Second Edition
(2003),
|
| any_adam_object | 1 |
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| discipline | Allgemeines Biologie Wirtschaftswissenschaften Medizin |
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| id | DE-604.BV022397173 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T12:54:29Z |
| institution | BVB |
| isbn | 9780387698090 0387698094 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015605892 |
| oclc_num | 255964659 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-578 DE-1102 DE-384 |
| owner_facet | DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-578 DE-1102 DE-384 |
| physical | XX, 403 S. graph. Darst. 235 mm x 155 mm |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Springer |
| record_format | marc |
| series2 | Statistics for biology and health |
| spellingShingle | Cook, Richard J. 1965- Lawless, Jerald F. The statistical analysis of recurrent events Statistik Biometry Life change events Statistical methods Research Methodology Statistics Ereignisdaten (DE-588)4197073-1 gnd Medizinische Statistik (DE-588)4127563-9 gnd Biostatistik (DE-588)4729990-3 gnd Statistische Analyse (DE-588)4116599-8 gnd Wiederholung (DE-588)4065972-0 gnd |
| subject_GND | (DE-588)4197073-1 (DE-588)4127563-9 (DE-588)4729990-3 (DE-588)4116599-8 (DE-588)4065972-0 |
| title | The statistical analysis of recurrent events |
| title_auth | The statistical analysis of recurrent events |
| title_exact_search | The statistical analysis of recurrent events |
| title_full | The statistical analysis of recurrent events Richard J. Cook ; Jerald F. Lawless |
| title_fullStr | The statistical analysis of recurrent events Richard J. Cook ; Jerald F. Lawless |
| title_full_unstemmed | The statistical analysis of recurrent events Richard J. Cook ; Jerald F. Lawless |
| title_short | The statistical analysis of recurrent events |
| title_sort | the statistical analysis of recurrent events |
| topic | Statistik Biometry Life change events Statistical methods Research Methodology Statistics Ereignisdaten (DE-588)4197073-1 gnd Medizinische Statistik (DE-588)4127563-9 gnd Biostatistik (DE-588)4729990-3 gnd Statistische Analyse (DE-588)4116599-8 gnd Wiederholung (DE-588)4065972-0 gnd |
| topic_facet | Statistik Biometry Life change events Statistical methods Research Methodology Statistics Ereignisdaten Medizinische Statistik Biostatistik Statistische Analyse Wiederholung |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2930933&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015605892&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015605892&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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