139,99 €
Mehr erfahren.
- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
This book aims to promote regression methods for analyzing lifetime (or time-to-event) data that are based on a representation of the underlying process, and are therefore likely to offer greater scientific insight compared to purely empirical methods. In contrast to the rich statistical literature, the regression methods actually employed in lifetime data analysis are limited, particularly in the biomedical field where D. R. Cox's famous semi-parametric proportional hazards model predominates. Practitioners should become familiar with more flexible models. The first hitting time regression models (or threshold regression) presented here represent observed events as the outcome of an underlying stochastic process. One example is death occurring when the patient's health status falls to zero, but the idea has wide applicability - in biology, engineering, banking and finance, and elsewhere. The central topic is the model based on an underlying Wiener process, leading to lifetimes following the inverse Gaussian distribution. Introducing time-varying covariates and many other extensions are considered. Various applications are presented in detail.
Sie lesen das E-Book in den Legimi-Apps auf:
Seitenzahl: 314
Veröffentlichungsjahr: 2017
Ähnliche
Table of Contents
Cover
Title
Copyright
Preface
1 Introduction to Lifetime Data and Regression Models
1.1. Basics
1.2. The classic lifetime distribution: the Weibull distribution
1.3. Regression models for lifetimes
1.4. Proportional hazards models
1.5. Checking the proportional hazards assumption
1.6. Accelerated failure time models
1.7. Checking the accelerated failure time assumption
1.8. Proportional odds models
1.9. Proportional mean residual life models
1.10. Proportional reversed hazard rate models
1.11. The accelerated hazards model
1.12. The additive hazards model
1.13. PH, AFT and PO distributions
1.14. Cox’s semi-parametric PH regression model
1.15. PH versus AFT
1.16. Residuals
1.17. Cured fraction or long-term survivors
1.18. Frailty
1.19. Models for discrete lifetime data
1.20. Conclusions
2 First Hitting Time Regression Models
2.1. Introduction
2.2. First hitting time models
2.3. First hitting time regression models based on an underlying Wiener process
2.4. Long-term survivors
2.5. FHT versus PH
2.6. Randomized drift in the Wiener process
2.7. First hitting time regression models based on an underlying Ornstein-Uhlenbeck process
2.8. The Birnbaum-Saunders distribution
2.9. Gamma processes
2.10. The inverse Gaussian process
2.11. Degradation and markers
3 Model Fitting and Diagnostics
3.1. Introduction
3.2. Fitting the FHT regression model by maximum likelihood
3.3. The stthreg package
3.4. The threg package
3.5. The invGauss package
3.6. Fitting FHT regressions using the EM algorithm
3.7. Bayesian methods
3.8. Checking model fit
3.9. Issues in fitting inverse Gaussian FHT regression models
3.10. Influence diagnostics for an inverse Gaussian FHT regression model
3.11. Variable selection
4 Extensions to Inverse Gaussian First Hitting Time Regression Models
4.1. Introduction
4.2. Time-varying covariates
4.3. Recurrent events
4.4. Individual random effects
4.5. First hitting time regression model for recurrent events with random effects
4.6. Multiple outcomes
4.7. Extensions of the basic FHT model in a study of low birth weights: a mixture model and a competing risks model
4.8. Semi-parametric modeling of covariate effects
4.9. Semi-parametric model for data with a cured fraction
4.10. Semi-parametric time-varying coefficients
4.11. Bivariate Wiener processes for markers and outcome
5 Relationship of First Hitting Time Models to Proportional Hazards and Accelerated Failure Time Models
5.1. Introduction
5.2. FHT and PH models: direct comparisons by case studies
5.3. FHT and PH models: theoretical connections
5.4. FHT and AFT models: theoretical connections
6 Applications
6.1. Introduction
6.2. Lung cancer risk in railroad workers
6.3. Lung cancer risk in railroad workers: a case-control study
6.4. Occupational exposure to asbestos
6.5. Return to work after limb injury
6.6. An FHT mixture model for a randomized clinical trial with switching
6.7. Recurrent exacerbations in COPD
6.8. Normalcy and discrepancy indexes for birth weight and gestational age
6.9. Hip fractures
6.10. Annual risk of death in cystic fibrosis
6.11. Disease resistance in cows
6.12. Balka, Desmond and McNicholas: an application of their cure rate models
6.13. Progression of cervical dilation
Bibliography
Index
End User License Agreement
Guide
Cover
Table of Contents
Begin Reading
Pages
C1
ii
iii
iv
v
ix
x
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
G1
G2
G3
G4
G5
e1
To my children:
Mark, Helen and Stephen
Mathematical Models and Methods in Reliability Set
coordinated byNikolaos Limnios and Bo Henry Lindqvist
Volume 4
First Hitting Time Regression Models
Lifetime Data Analysis Based on Underlying Stochastic Processes
Chrysseis Caroni
First published 2017 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.
Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:
ISTE Ltd27-37 St George’s RoadLondon SW19 4EUUKwww.iste.co.uk
John Wiley & Sons, Inc.111 River StreetHoboken, NJ 07030USAwww.wiley.com
© ISTE Ltd 2017
The rights of Chrysseis Caroni to be identified as the author of this work have been asserted by her in accordance with the Copyright, Designs and Patents Act 1988.
Library of Congress Control Number: 2017938379
British Library Cataloguing-in-Publication Data
A CIP record for this book is available from the British Library
ISBN 978-1-84821-889-5
Preface
The analysis of lifetime (or time-to-event) data is one of the busiest fields of statistics. This is partly due to the interesting theoretical issues that come up, which tend to be rather different from those that are seen in other areas, and, above all, due to the enormous range of its practical applications. One major field of application is in engineering and technology, where the subject is usually known as reliability. Reliability is concerned with how long a machine or a machine component will operate before it requires replacement or repair. The other major field of application is in biostatistics. A classic example of this field of application is the study of patients’ survival after therapy. Other important fields of application include finance and banking, as well as other areas.
In biostatistics, information about the individuals in the study may be available in the form of covariates (e.g. age and gender). Exploiting this information may improve prediction of lifetimes (a younger patient will generally do better than an older one). Covariates are usually included in statistical models in the form of regression models. Lifetime data analysis contains a rich range of regression models, which will be presented in this book. Many biostatistical texts restrict their attention almost exclusively to a famous regression model introduced by D.R. Cox; this is the model that predominates in statistical practice. However, there is much to be said for using models that are not simply empirical (as Cox’s model is) but are substantive in the sense that they provide a description of the underlying process. The emphasis of this book is on models of this type, in particular the one based on the concept that a lifetime ends when an underlying stochastic process reaches a boundary for the first time.
It is a pleasure to acknowledge my debt to several people who helped to inspire my interest in lifetime data analysis, through their own work, their willingness to discuss matters with me and respond to my queries, and their invitations to participate in conferences and visit their institutions. In this respect, I wish to record my gratitude especially to Mei-Ling Ting Lee, Alex Whitmore and Nikolaos Limnios. In addition, I thank Alan Kimber and Martin Crowder who first got me interested in lifetime data. Finally, Polychronis Economou and Dimitris Stogiannis, first as doctoral students and then as collaborators, have aided my work in many ways.
Chrysseis CARONI
May 2017
Table 1.1.
