Statistical Methods for Survival Data Analysis / Edition 4

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Praise for the Third Edition ". . . an easy-to read introduction to survival analysis which covers the major concepts and techniques of the subject." - Statistics in Medical Research Updated and expanded to reflect the latest developments, Statistical Methods for Survival Data Analysis, Fourth Edition continues to deliver a comprehensive introduction to the most commonly-used methods for analyzing survival data. Authored by a uniquely well-qualified author team, the Fourth Edition is a critically acclaimed guide to statistical methods with applications in clinical trials, epidemiology, areas of business, and the social sciences. The book features many real-world examples to illustrate applications within these various fields, although special consideration is given to the study of survival data in biomedical sciences. Emphasizing the latest research and providing the most up-to-date information regarding software applications in the field, Statistical Methods for Survival Data Analysis, Fourth Edition also includes: Marginal and random effect models for analyzing correlated censored or uncensored data Multiple types of two-sample and K-sample comparison analysis Updated treatment of parametric methods for regression model fitting with a new focus on accelerated failure time models Expanded coverage of the Cox proportional hazards model Exercises at the end of each chapter to deepen knowledge of the presented material Statistical Methods for Survival Data Analysis is an ideal text for upper-undergraduate and graduate-level courses on survival data analysis. The book is also an excellent resource for biomedical investigators, statisticians, and epidemiologists, as well as researchers in every field in which the analysis of survival data plays a role.

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Editorial Reviews

Defined in a broad sense, survival data refers to data that involve the remaining time until a certain event such as a death, a relapse, or the onset of a disease. Analysis of such data is applicable in such fields as criminology, sociology, marketing, and health insurance, as well as biomedical and reliability research. The many methodologies are presented here. Annotation c. Book News, Inc., Portland, OR (
From the Publisher
"…an easy-to read introduction to survival analysis which covers the major concepts and techniques of the subject." (Statistics in Medical Research, October 2005)

"The book is well written and provides explicit details of the models and methods used." (Journal of the American Statistical Association, June 2004)

"…contains thorough descriptions and illustrations of several useful nonparametric and parametric statistical methods to analyze survival data." (Journal of Statistical Computation & Simulation, May 2004) 

"...a comprehensive and clearly written textbook...a very good reference..." (Short Book Reviews, Vol 24(1), 2004)

"...continues to be application-oriented with a minimum level of mathematics..." (Zentralblatt Math, Vol 1026, 2004)

"This third edition is a significant upgrade...this remains an excellent choice or a basic textbook in survival analysis..." (Technometrics, Vol. 45, No. 4, November 2003)

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Product Details

Meet the Author

ELISA T. LEE, PhD, is Regents Professor and George LynnCross Research Professor of Biostatistics and Epidemiology andDirector of the Center for American Indian Health Research at theUniversity of Oklahoma Health Sciences Center.

JOHN Wenyu WANG, PhD, is Professor of Research at theCenter for American Indian Health Research at the University ofOklahoma Health Sciences Center.

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Table of Contents

Preface xi

1 Introduction 1

1.1 Preliminaries 1

1.2 Censored Data 2

1.3 Scope of the Book 5

2 Functions of Survival Time 8

2.1 Definitions 8

2.2 Relationships of the Survival Functions 15

Exercises 16

3 Examples of Survival Data Analysis 19

3.1 Example 3.1: Comparison of Two Treatments and Three Diets19

3.2 Example 3.2: Comparison of Two Survival Patterns Using LifeTables 26

3.3 Example 3.3: Fitting Survival Distributions to Tumor-Free Times28

3.4 Example 3.4: Comparing Survival of a Cohort with that of aGeneral Population — Relative Survival 30

3.5 Example 3.5: Identification of Risk Factors for Incident Events33

3.6 Example 3.6: Identification of Risk Factors for the Prevalenceof Age-Related Macular Degeneration 38

3.7 Example 3.7: Identification of Significant Risk Factors forIncident Hypertension Using Related Data (Repeated Measurements) ina Longitudinal Study 46

Exercises 54

4 Nonparametric Methods of Estimating Survival Functions68

4.1 Product-Limit Estimates of Survivorship Function 69

4.2 N elson–Aalen Estimates of Survivorship Function 82

4.3 Life-Table Analysis 83

4.4 Relative Survival Rates 96

4.5 Standardized Rates and Ratios 98

Exercises 104

5 Nonparametric Methods for Comparing Survival Distributions108

5.1 Comparison of Two Survival Distributions 108

5.2 The Mantel and Haenszel Test 123

5.3 Comparison of K (K > 2) Samples 128

Exercises 130

6 Some Well-Known Parametric Survival Distributions And TheirApplications 133

6.1 Exponential Distribution 133

6.2 Weibull Distribution 138

6.3 Lognormal Distribution 143

6.4 Gamma, Generalized Gamma, and Extended Generalized GammaDistributions 148

6.5 Log-Logistic Distribution 153

6.6 O ther Survival Distributions 155

Exercises 159

7 Estimation Procedures for Parametric Survival DistributionsWithout Covariates 161

7.1 General Maximum Likelihood Estimation Procedure 161

7.2 Exponential Distribution 165

7.3 Weibull Distribution 178

7.4 Lognormal Distribution 180

7.5 The Extended Generalized Gamma Distribution 183

7.6 The Log-Logistic Distribution 184

7.7 Gompertz Distribution 185

7.8 Graphical Methods 186

Exercises 203

8 Tests of Goodness-of-Fit and Distribution Selection206

8.1 Goodness-of-Fit Test Statistics Based on Asymptotic LikelihoodInferences 207

8.2 Tests for Appropriateness of a Family of Distributions210

8.3 Selection of a Distribution by Using BIC or AIC Procedure216

8.4 Tests for a Specific Distribution with Known Parameters217

8.5 Hollander and Proschan’s Test for Appropriateness of aGiven Distribution with Known Parameters 220

Exercises 224

9 Parametric Methods for Comparing Two Survival Distributions226

9.1 Log-Likelihood Ratio Test for Comparing Two SurvivalDistributions 226

9.2 Comparison of Two Exponential Distributions 229

9.3 Comparison of Two Weibull Distributions 234

9.4 Comparison of Two Gamma Distributions 236

Exercises 237

10 Parametric Methods for Regression Model Fitting andIdentification of Prognostic Factors 239

10.1 Preliminary Examination of Data 240

10.2 General Structure of Parametric Regression Models and TheirAsymptotic Likelihood Inference 242

10.3 Exponential AFT Model 246

10.4 Weibull AFT Model 255

10.5 Lognormal AFT Model 258

10.6 The Extended Generalized Gamma AFT Model 261

10.7 Log-Logistic AFT Model 264

10.8 O ther Parametric Regression Models 268

10.9 Model Selection Methods 270

Exercises 279

11 Identification of Risk Factors Related to Survival Time: CoxProportional Hazards Model 282

11.1 The Proportional Hazards Model 282

11.2 The Partial Likelihood Function 285

11.3 Identification of Significant Covariates 302

11.4 Estimation of the Survivorship Function with Covariates309

11.5 Adequacy Assessment of the Proportional Hazards Model317

Exercises 334

12 Identification of Prognostic Factors Related to SurvivalTime: Non-Proportional Hazards Models 337

12.1 Models with Time-Dependent Covariates 337

12.2 Stratified Proportional Hazards Model 346

12.3 Competing Risks Model 350

12.4 Recurrent Event Models 353

12.5 Models for Related Observations 370

Exercises 382

13 Identification of Risk Factors Related to Dichotomous andPolychotomous Outcomes 384

13.1 Univariate Analysis 385

13.2 Logistic and Conditional Logistic Regression Model forDichotomous Outcomes 392

13.3 Models for Polychotomous Outcomes 421

13.4 Models for Related Observations 432

Exercises 440

Appendix 443

References 466

Index 477

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