## Survival Analysis: Techniques for Censored and Truncated DataApplied statisticians in many fields frequently analyze time-to-event data. While the statistical tools presented in this book are applicable to data from medicine, biology, public health, epidemiology, engineering, economics and demography, the focus here is on applications of the techniques to biology and medicine. The analysis of survival experiments is complicated by issues of censoring and truncation. The use of counting process methodology has allowed for substantial advances in the statistical theory to account for censoring and truncation in survival experiments. This book makes these complex techniques accessible to applied researchers without the advanced mathematical background. The authors present the essentials of these techniques, as well as classical techniques not based on counting processes, and apply them to data. The second edition contains some new material as well as solutions to the odd-numbered revised exercises. New material consists of a discussion of summary statistics for competing risks probabilities in Chapter 2 and the estimation process for these probabilities in Chapter 4. A new section on tests of the equality of survival curves at a fixed point in time is added in Chapter 7. In Chapter 8 an expanded discussion is presented on how to code covariates and a new section on discretizing a continuous covariate is added. A new section on Lin and Ying's additive hazards regression model is presented in Chapter 10. We now proceed to a general discussion of the usefulness of this book incorporating the new material with that of the first edition. |

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### Contents

1 | |

Chapter 2Basic Quantities and Models | 21 |

Chapter 3Censoring and Truncation | 63 |

Chapter 4Nonparametric Estimation of Basic Quantities | 91 |

Chapter 5Estimation of Basic Quantities | 139 |

Chapter 6Topics in Univariate Estimation | 165 |

Chapter 7Hypothesis Testing | 201 |

Chapter 8Semiparametric Proportional Hazards Regression | 243 |

Chapter 12Inference for Parametric Regression Models | 393 |

Chapter 13Multivariate Survival Analysis | 425 |

Appendix ANumerical Techniques for Maximization | 443 |

Appendix BLargeSample Tests Based on Likelihood Theory | 450 |

C | 462 |

C | 468 |

Appendix DData on 137 Bone Marrow Transplant Patients | 484 |

515 | |

Chapter 9Refinements of the Semiparametric Proportional | 295 |

Chapter 10Additive Hazards Regression Models | 329 |

Regression Diagnostics | 353 |

525 | |

531 | |

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### Common terms and phrases

ˆS(t algorithm AML high-risk AML low-risk aneuploid baseline hazard rate bone marrow transplant censored observations Chapter chi-squared distribution coefficients competing risks compute confidence bands confidence interval constructed counting process Cox model cumulative hazard rate cumulative incidence defined degrees of freedom deviance residuals disease-free survival example exponential factors females Figure given graft-versus-host disease hazard function individual infection kernel laryngeal cancer left-truncated lifetime linear log likelihood log logistic log normal Log rank males martingale martingale residual matrix maximum likelihood estimates median method mortality Nelson–Aalen estimator normal distribution null hypothesis number of deaths p-value parameters partial likelihood platelet platelet recovery Practical Notes prior probability Product-Limit estimator proportional hazards model regression model relapse relative risk remission sample Stage standard error stratified survival curves survival function Table test statistic test the hypothesis Theoretical Notes time-dependent covariates variance vector Wald test Weibull distribution weight function ZP(t