## Survival Analysis: A Self-Learning TextThis greatly expanded second edition of Survival Analysis- A Self-learning Text provides a highly readable description of state-of-the-art methods of analysis of survival/event-history data. This text is suitable for researchers and statisticians working in the medical and other life sciences as well as statisticians in academia who teach introductory and second-level courses on survival analysis. The second edition continues to use the unique "lecture-book" format of the first (1996) edition with the addition of three new chapters on advanced topics: Chapter 7: Parametric Models Chapter 8: Recurrent events Chapter 9: Competing Risks. Also, the Computer Appendix has been revised to provide step-by-step instructions for using the computer packages STATA (Version 7.0), SAS (Version 8.2), and SPSS (version 11.5) to carry out the procedures presented in the main text. The original six chapters have been modified slightly to expand and clarify aspects of survival analysis in response to suggestions by students, colleagues and reviewers, and to add theoretical background, particularly regarding the formulation of the (partial) likelihood functions for proportional hazards, stratified, and extended Cox regression models David Kleinbaum is Professor of Epidemiology at the Rollins School of Public Health at Emory University, Atlanta, Georgia. Dr. Kleinbaum is internationally known for innovative textbooks and teaching on epidemiological methods, multiple linear regression, logistic regression, and survival analysis. He has provided extensive worldwide short-course training in over 150 short courses on statistical and epidemiological methods. He is also the author of ActivEpi (2002), an interactive computer-based instructional text on fundamentals of epidemiology, which has been used in a variety of educational environments including distance learning. Mitchel Klein is Research Assistant Professor with a joint appointment in the Department of Environmental and Occupational Health (EOH) and the Department of Epidemiology, also at the Rollins School of Public Health at Emory University. Dr. Klein is also co-author with Dr. Kleinbaum of the second edition of Logistic Regression- A Self-Learning Text (2002). He has regularly taught epidemiologic methods courses at Emory to graduate students in public health and in clinical medicine. He is responsible for the epidemiologic methods training of physicians enrolled in Emorya??s Master of Science in Clinical Research Program, and has collaborated with Dr. Kleinbaum both nationally and internationally in teaching several short courses on various topics in epidemiologic methods. |

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### Contents

Introduction to Survival Analysis | 1 |

Introduction | 2 |

Objectives | 3 |

Presentation | 4 |

Detailed Outline | 34 |

Practice Exercises | 38 |

Test | 40 |

Answers to Practice Exercises | 42 |

Extension of the Cox Proportional Hazards Model for TimeDependent Variables | 211 |

Introduction | 212 |

Objectives | 213 |

Presentation | 214 |

Detailed Outline | 246 |

Practice Exercises | 249 |

Test | 253 |

Answers to Practice Exercises | 255 |

KaplanMeier Survival Curves and the LogRank Test | 45 |

Introduction | 46 |

Objectives | 47 |

Presentation | 48 |

Detailed Outline | 70 |

Practice Exercises | 73 |

Test | 77 |

Answers to Practice Exercises | 79 |

Matrix Formula for the LogRank Statistic for Several Groups | 82 |

The Cox Proportional Hazards Model and Its Characteristics | 83 |

Introduction | 84 |

Objectives | 85 |

Presentation | 86 |

Detailed Outline | 117 |

Practice Exercises | 119 |

Test | 123 |

Answers to Practice Exercises | 127 |

Evaluating the Proportional Hazards Assumption | 131 |

Introduction | 132 |

Objectives | 133 |

Presentation | 134 |

Detailed Outline | 158 |

Practice Exercises | 161 |

Test | 164 |

Answers to Practice Exercises | 167 |

The Stratified Cox Procedure | 173 |

Introduction | 174 |

Objectives | 175 |

Presentation | 176 |

Detailed Outline | 198 |

Practice Exercises | 201 |

Test | 204 |

Answers to Practice Exercises | 207 |

Parametric Survival Models | 257 |

Introduction | 258 |

Objectives | 259 |

Presentation | 260 |

Detailed Outline | 313 |

Practice Exercises | 319 |

Test | 324 |

Answers to Practice Exercises | 327 |

Recurrent Event Survival Analysis | 331 |

Introduction | 332 |

Objectives | 333 |

Presentation | 334 |

Detailed Outline | 371 |

Practice Exercises | 377 |

Test | 381 |

Answers to Practice Exercises | 389 |

Competing Risks Survival Analysis | 391 |

Introduction | 392 |

Abbreviated Outline | 394 |

Objectives | 395 |

Presentation | 396 |

Detailed Outline | 440 |

Practice Exercises | 447 |

Test | 452 |

Answers to Practice Exercises | 458 |

Survival Analysis on the Computer | 463 |

A STATA | 465 |

B SAS | 508 |

C SPSS | 542 |

Test Answers | 557 |

References | 581 |

### Common terms and phrases

adjusted survival curves AFT model assess the PH baseline hazard bladder cancer cell type censored chi-square CLINIC Coef coefficients competing risks confidence interval consider covariates Cox PH model data layout dataset denotes effect estimated hazard ratio event-type exponential extended Cox model follow-up formula frailty models graph hazard function hazard model heaviside functions interaction model Kaplan-Meier KM curves LM model Log likelihood log WBC log-log curves log-logistic log-rank test marginal approach model containing no-interaction model null hypothesis obtained ordered failure output p-value parameter patients PH assumption placebo predictors PROC product terms proportional hazards Proportional Hazards Model recurrent events regression remission data risk set satisfy the PH SC model shown SPSS strata stratified Cox model stratum survival analysis survival estimates survival function survival plots SURVT test statistic time-dependent variables tion transplant vival Wald test Weibull distribution