Statistical Methods for Survival Data Analysis

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收藏 2006-10-27

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
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 (K2) 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
viii 
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 Appropriateness of 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 Regression Models
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
 ix
11.7 Log-Logistic Regression Model, 280
11.8 Other Parametric Regression Models, 283
11.9 Model Selection Methods, 286
Bibliographical Remarks, 295
Exercises, 295
12 Identification of Prognostic Factors Related to Survival Time:
Cox Proportional Hazards Model 298
12.1 Partial Likelihood Function for Survival Times, 298
12.2 Identification of Significant Covariates, 314
12.3 Estimation of the Survivorship Function with Covariates, 319
12.4 Adequacy Assessment of the Proportional Hazards Model, 326
Bibliographical Remarks, 336
Exercises, 337
13 Identification of Prognostic Factors Related to Survival Time:
Nonproportional Hazards Models 339
13.1 Models with Time-Dependent Covariates, 339
13.2 Stratified Proportional Hazards Models, 348
13.3 Competing Risks Model, 352
13.4 Recurrent Events Models, 356
13.5 Models for Related Observations, 374
Bibliographical Remarks, 376
Exercises, 376
14 Identification of Risk Factors Related to Dichotomous
and Polychotomous Outcomes 377
14.1 Univariate Analysis, 378
14.2 Logistic and Conditional Logistic Regression Models
for Dichotomous Responses, 385
14.3 Models for Polychotomous Outcomes, 413
Bibliographical Remarks, 425
Exercises, 425
Appendix A Newton--Raphson Method 428
Appendix B Statistical Tables 433
References 488
Index 511