Statistical Methods for Survival Data Analysis by Elisa T.Lee, John Wenyu Wang

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Statistical Methods for Survival Data Analysis by Elisa T.Lee, John Wenyu Wang

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Statistical Methods for Survival Data Analysis by Elisa T.Lee John Wenyu Wang

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 Also

Updated and expanded to reflect the latest developments, Statistical Methods for Survival Data Analysis, Fourth Editioncontinues 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. Also

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 Also
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 Also
Expanded coverage of the Cox proportional hazards model
Exercises at the end of each chapter to deepen knowledge of the presented material Also

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. Also

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Table of Contents

Preface xi

1 Introduction 1

1.1 Preliminaries 1 Also

1.2 Censored Data 2

1.3 Scope of the Book 5 Also

2 Functions of Survival Time 8

2.1 Definitions 8

2.2 Relationships of the Survival Functions 15 Also

Exercises 16

3 Examples of Survival Data Analysis 19

3.1 Example 3.1: Comparison of Two Treatments and Three Diets 19 Also

3.2 Example 3.2: Comparison of Two Survival Patterns Using Life Tables 26

3.3 Example 3.3: Fitting Survival Distributions to Tumor-Free Times 28

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

3.5 Example 3.5: Identification of Risk Factors for Incident Events 33

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

3.7 Example 3.7: Identification of Significant Risk Factors for Incident Hypertension Using Related Data (Repeated Measurements) in a Longitudinal Study 46 Also

Exercises 54

4 Nonparametric Methods of Estimating Survival Functions 68

4.1 Product-Limit Estimates of Survivorship Function 69

4.2 N elson–Aalen Estimates of Survivorship Function 82 Also

4.3 Life-Table Analysis 83

4.4 Relative Survival Rates 96 Also

4.5 Standardized Rates and Ratios 98

Exercises 104

5 Nonparametric Methods for Comparing Survival Distributions 108

5.1 Comparison of Two Survival Distributions 108

5.2 The Mantel and Haenszel Test 123 Also

5.3 Comparison of K (K > 2) Samples 128

Exercises 130 Also

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6 Some Well-Known Parametric Survival Distributions And Their Applications 133

6.1 Exponential Distribution 133

6.2 Weibull Distribution 138 Also

6.3 Lognormal Distribution 143

6.4 Gamma, Generalized Gamma, and Extended Generalized Gamma Distributions 148 Also

6.5 Log-Logistic Distribution 153

6.6 O ther Survival Distributions 155

Exercises 159 Also

7 Estimation Procedures for Parametric Survival Distributions Without Covariates 161

7.1 General Maximum Likelihood Estimation Procedure 161

7.2 Exponential Distribution 165

7.3 Weibull Distribution 178 Also

7.4 Lognormal Distribution 180

7.5 The Extended Generalized Gamma Distribution 183

7.6 The Log-Logistic Distribution 184 Also

7.7 Gompertz Distribution 185

7.8 Graphical Methods 186

Exercises 203 Also

8 Tests of Goodness-of-Fit and Distribution Selection 206

8.1 Goodness-of-Fit Test Statistics Based on Asymptotic Likelihood Inferences 207

8.2 Tests for Appropriateness of a Family of Distributions 210

8.3 Selection of a Distribution by Using BIC or AIC Procedure 216 Also

8.4 Tests for a Specific Distribution with Known Parameters 217

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

Exercises 224 Also

9 Parametric Methods for Comparing Two Survival Distributions 226

9.1 Log-Likelihood Ratio Test for Comparing Two Survival Distributions 226

9.2 Comparison of Two Exponential Distributions 229 Also

9.3 Comparison of Two Weibull Distributions 234

9.4 Comparison of Two Gamma Distributions 236

Exercises 237 Also

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10 Parametric Methods for Regression Model Fitting and Identification of Prognostic Factors 239

10.1 Preliminary Examination of Data 240 Also

10.2 General Structure of Parametric Regression Models and Their Asymptotic Likelihood Inference 242

10.3 Exponential AFT Model 246

10.4 Weibull AFT Model 255 Also

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 Also

10.9 Model Selection Methods 270

Exercises 279

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

11.1 The Proportional Hazards Model 282 Also

11.2 The Partial Likelihood Function 285

11.3 Identification of Significant Covariates 302

11.4 Estimation of the Survivorship Function with Covariates 309 Also

11.5 Adequacy Assessment of the Proportional Hazards Model 317

Exercises 334

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

12.1 Models with Time-Dependent Covariates 337 Also

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 Also

Exercises 382

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13 Identification of Risk Factors Related to Dichotomous and Polychotomous Outcomes 384

13.1 Univariate Analysis 385 Also

13.2 Logistic and Conditional Logistic Regression Model for Dichotomous Outcomes 392

13.3 Models for Polychotomous Outcomes 421

13.4 Models for Related Observations 432 Also

Exercises 440

Appendix 443

References 466

Index 477

Author Information

ELISA T. LEE, PhD, is Regents Professor and George Lynn Cross Research Professor of Biostatistics and Epidemiology and Director of the Center for American Indian Health Research at the University of Oklahoma Health Sciences Center. Also

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

Reviews

“In summary, this book continues to improve, and the fourth edition is a welcome addition to the available books on survival analysis. The expanded sections on modelling and the addition of R software examples are particularly helpful.” (International Statistical Review, 1 October 2015) Also