Modeling Survival Data: Extending the Cox Model

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Springer Science & Business Media, Aug 11, 2000 - Mathematics - 350 pages
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This is a book for statistical practitioners, particularly those who design and analyze studies for survival and event history data. Its goal is to extend the toolkit beyond the basic triad provided by most statistical packages: the Kaplan-Meier estimator, log-rank test, and Cox regression model. Building on recent developments motivated by counting process and martingale theory, it shows the reader how to extend the Cox model to analyse multiple/correlated event data using marginal and random effects (frailty) models. It covers the use of residuals and diagnostic plots to identify influential or outlying observations, assess proportional hazards and examine other aspects of goodness of fit. Other topics include time-dependent covariates and strata, discontinuous intervals of risk, multiple time scales, smoothing and regression splines, and the computation of expected survival curves. A knowledge of counting processes and martingales is not assumed as the early chapters provide an introduction to this area. The focus of the book is on actual data examples, the analysis and interpretation of the results, and computation. The methods are now readily available in SAS and S-Plus and this book gives a hands-on introduction, showing how to implement them in both packages, with worked examples for many data sets. The authors call on their extensive experience and give practical advice, including pitfalls to be avoided. Terry Therneau is Head of the Section of Biostatistics, Mayo Clinic, Rochester, Minnesota. He is actively involved in medical consulting, with emphasis in the areas of chronic liver disease, physical medicine, hematology, and laboratory medicine, and is an author on numerous papers in medical and statistical journals. He wrote two of the original SAS procedures for survival analysis (coxregr and survtest), as well as the majority of the S-Plus survival functions. Patricia Grambsch is Associate Professor in the Division of Biostatistics, School of Public Health, University of Minnesota. She has collaborated extensively with physicians and public health researchers in chronic liver disease, cancer prevention, hypertension clinical trials and psychiatric research. She is a fellow the American Statistical Association and the author of many papers in medical and statistical journals.
 

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Contents

Introduction
1
12 Overview
2
13 Counting processes
3
Estimating the Survival and Hazard Functions
7
212 Estimating the survival function
13
22 Counting processes and martingales
17
221 Modeling the counting process
18
222 Martingale basics
19
85 Ordered multiple events
185
852 Fitting the models
187
VII
190
VIII
196
IX
205
X
211
86 Multistate models
216
862 Crohns disease
217

23 Properties of the NelsonAalen estimator
26
232 Efficiency
28
24 Tied data
31
The Cox Model
39
32 Stratified Cox models
44
33 Handling ties
48
34 Wald score and likelihood ratio tests
53
341 Confidence intervals
57
35 Infinite coefficients
58
36 Sample size determination
61
361 The impact of strata on sample size
67
37 The counting process form of a Cox model
68
371 Timedependent covariates
69
372 Discontinuous intervals of risk
74
575 Alternate time scales
75
374 Summary
76
Residuals
79
42 Martingale residuals
80
422 Overall tests of goodnessoffit
81
424 Usage
82
43 Deviance residuals
83
45 Score residuals
84
46 Schoenfeld residuals
85
Functional Form
87
511 Stage Dl prostate cancer
88
512 PBC data
90
I
92
II
95
III
96
IV
99
V
102
VI
107
56 Timedependent covariates
111
57 Martingale residuals under misspecified models
115
572 Relation to functional form
118
58 Penalized models
120
582 SPlus functions
122
583 Spline fits
124
59 Summary
126
Testing Proportional Hazards
127
62 Timedependent coefficients
130
63 Veterans Administration data
135
64 Limitations
140
643 Stratified models
141
65 Strategies for nonproportional data
142
66 Causes of nonproportionality
148
Influence
153
72 Variance
159
73 Case weights
161
Multiple Events per Subject
169
82 Robust variance and computation
170
822 Connection to other work
173
83 Selecting a model
174
84 Unordered outcomes
175
842 Diabetic retinopathy study
177
843 UDCA in patients with PBC
179
844 Colon cancer data
183
87 Combination models
227
88 Summary
229
Frailty Models
231
92 Computation
232
93 Examples
238
94 Unordered events
240
942 Familial aggregation of breast cancer
241
95 Ordered events
243
952 Survival of kidney catheters
245
953 Chronic granulotamous disease
250
96 Formal derivations
251
962 EM solution for shared frailty
252
963 Gamma frailty
253
964 Gaussian frailty
255
965 Correspondence of the profile likelihoods
256
97 Sparse computation
258
98 Concluding remarks
259
Expected Survival
261
102 Individual survival Cox model
263
1021 Natural history of PBC
264
1022 Mean survival
266
1024 Timedependent covariates
268
103 Cohort survival population
272
1033 Ederer estimate
273
1034 Hakulinen estimate
274
1035 Conditional expected survival
275
1036 Example
276
104 Cohort survival Cox model
279
1042 Naive estimate
280
1044 Hakulinen and conditional estimates
281
1045 Comparing observed to expected for the UDCA trial
283
Introduction to SAS and SPlus
289
A1 SAS
290
A2 SPlus
294
SAS Macros
301
B2 phlev
303
B3 schoen
304
B4 surv
305
B5 survtd
307
B6 survexp
308
S Functions
309
C3 gamterms
310
C4 plotterm
311
Data Sets
313
D2 Primary biliary cirrhosis
314
D3 Sequential PBC
316
D4 rIFNg in patients with chronic granulomatous disease
318
D5 rhDNase for the treatment of cystic fibrosis
320
Test Data
323
E1 2 Efron approximation
326
E1 3 Exact partial likelihood
329
E2 Test data 2
330
E22 Efron approximation
332
References
333
Index
346
Copyright

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Page 345 - Stage Dl prostatic adenocarcinoma: significance of nuclear DNA ploidy patterns studied by flow cytometry. Mayo Clin. Proc., 63: 103-112.
Page 340 - Mantel-Haenszel analysis of litter-matched time-to-response data, With modifications for recovery of interlitter information.
Page 342 - RL Prentice, BJ Williams and AV Peterson, On the regression analysis of multivariate failure time data, Biometrika, vol.
Page 342 - Ricci P, Therneau TM, Malinchoc M et al. A prognostic model for the outcome of liver transplantation in patients with cholestatic liver disease. Hepatology 1997; 25: 672.
Page 342 - M. Pugh, J. Robbins, S. Lipsitz, and D. Harrington, Inference in the Cox proportional hazards model with missing covariate data.
Page 343 - D. Schoenfeld. Chi-squared goodness-of-fit tests for the proportional hazards regression model.

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About the author (2000)

Patricia M. Grambsch is Associate Professor in the Division of Biostatistics, School of Public Health, University of Minnesota.

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