Statistical methods for survival data analysis

535 Pages·2003·4.05 MB·English

by  Elisa T. Lee, John Wang

Statistical Methods for
Survival Data Analysis

Statistical Methods for
Survival Data Analysis
Third Edition
ELISA T. LEE
JOHN WENYU WANG
Department of Biostatistics and Epidemiology and
Center for American Indian Health Research
College of Public Health
University of Oklahoma Health Sciences Center
Oklahoma City, Oklahoma
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Lee,ElisaT.
Statisticalmethodsforsurvivaldataanalysis.--3rded./ElisaT.LeeandJohnWenyuWang.
p.cm.--(Wileyseriesinprobabilityandstatistics)
Includesbibliographicalreferencesandindex.
ISBN0-471-36997-7(cloth:alk.paper)
1.Medicine--Research--Statisticalmethods.2.Failuretimedataanalysis.3.
Prognosis--Statisticalmethods.I.Wang,JohnWenyu.II.Title.III.Series.
R853.S7L432003
610(cid:1).72--dc21 2002027025
PrintedintheUnitedStatesofAmerica.
10987654321
To the memory of our parents
Mr. Chi-Lan Tan and Mrs. Hwei-Chi Lee Tan
(E.T.L.)
Mr. Beijun Zhang and Mrs. Xiangyi Wang
(J.W.W.)

Contents
Preface xi
1 Introduction
1.1 Preliminaries, 1
1.2 Censored Data, 1
1.3 Scope of the Book, 5
Bibliographical Remarks, 7
2 Functions of Survival Time 8
2.1 Definitions, 8
2.2 Relationships of the Survival Functions, 15
Bibliographical Remarks, 17
Exercises, 17
3 Examples of Survival Data Analysis 19
3.1 Example 3.1: Comparison of Two Treatments and Three
Diets, 19
3.2 Example 3.2: Comparison of Two Survival Patterns
Using Life Tables, 26
3.3 Example 3.3: Fitting Survival Distributions to Remission
Data, 29
3.4 Example 3.4: Relative Mortality and Identification of
Prognostic Factors, 32
3.5 Example 3.5: Identification of Risk Factors, 40
Bibliographical Remarks, 47
Exercises, 47
vii
viii 
4 Nonparametric Methods of Estimating Survival Functions 64
4.1 Product-Limit Estimates of Survivorship Function, 65
4.2 Life-Table Analysis, 77
4.3 Relative, Five-Year, and Corrected Survival Rates, 94
4.4 Standardized Rates and Ratios, 97
Bibliographical Remarks, 102
Exercises, 102
5 Nonparametric Methods for Comparing Survival Distributions 106
5.1 Comparison of Two Survival Distributions, 106
5.2 Mantel—Haenszel Test, 121
5.3 Comparison of K (K(cid:2)2) Samples, 125
Bibliographical Remarks, 131
Exercises, 131
6 Some Well-Known Parametric Survival Distributions
and Their Applications 134
6.1 Exponential Distribution, 134
6.2 Weibull Distribution, 138
6.3 Lognormal Distribution, 143
6.4 Gamma and Generalized Gamma Distributions, 148
6.5 Log-Logistic Distribution, 154
6.6 Other Survival Distributions, 155
Bibliographical Remarks, 160
Exercises, 160
7 Estimation Procedures for Parametric Survival Distributions
without Covariates 162
7.1 General Maximum Likelihood Estimation Procedure, 162
7.2 Exponential Distribution, 166
7.3 Weibull Distribution, 178
7.4 Lognormal Distribution, 180
7.5 Standard and Generalized Gamma Distributions, 188
7.6 Log-Logistic Distribution, 195
7.7 Other Parametric Survival Distributions, 196
Bibliographical Remarks, 196
Exercises, 197
 ix
8 Graphical Methods for Survival Distribution Fitting 198
8.1 Introduction, 198
8.2 Probability Plotting, 200
8.3 Hazard Plotting, 209
8.4 Cox—Snell Residual Method, 215
Bibliographical Remarks, 219
Exercises, 219
9 Tests of Goodness of Fit and Distribution Selection 221
9.1 Goodness-of-Fit Test Statistics Based on Asymptotic
Likelihood Inferences, 222
9.2 Tests for Appropriatenessof a Family of Distributions, 225
9.3 Selection of a Distribution Using BIC
or AIC Procedures, 230
9.4 Tests for a Specific Distribution with
Known Parameters, 233
9.5 Hollander and Proschan’s Test for Appropriateness
of a Given Distribution with Known Parameters, 236
Bibliographical Remarks, 238
Exercises, 240
10 Parametric Methods for Comparing Two Survival Distributions 243
10.1 Likelihood Ratio Test for Comparing Two Survival
Distributions, 243
10.2 Comparison of Two Exponential Distributions, 246
10.3 Comparison of Two Weibull Distributions, 251
10.4 Comparison of Two Gamma Distributions, 252
Bibliographical Remarks, 254
Exercises, 254
11 Parametric Methods for Regression Model Fitting and
Identification of Prognostic Factors 256
11.1 Preliminary Examination of Data, 257
11.2 General Structure of Parametric RegressionModels
and Their Asymptotic Likelihood Inference, 259
11.3 Exponential Regression Model, 263
11.4 Weibull Regression Model, 269
11.5 Lognormal Regression Model, 274
11.6 Extended Generalized Gamma Regression Model, 277