## The Cox Model and Its ApplicationsThis book will be of interest to readers active in the fields of survival analysis, genetics, ecology, biology, demography, reliability and quality control. Since Sir David Cox’s pioneering work in 1972, the proportional hazards model has become the most important model in survival analysis. The success of the Cox model stimulated further studies in semiparametric and nonparametric theories, counting process models, study designs in epidemiology, and the development of many other regression models that could offer more flexible or more suitable approaches in data analysis. Flexible semiparametric regression models are increasingly being used to relate lifetime distributions to time-dependent explanatory variables. Throughout the book, various recent statistical models are developed in close connection with specific data from experimental studies in clinical trials or from observational studies. |

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### Contents

1 | |

2 Elements of Survival Analysis | 9 |

3 The Cox Proportional Hazards Model | 35 |

4 The AFT GPH LT Frailty and GLPH Models | 53 |

5 CrossEffect Models of Survival Functions | 63 |

6 The Simple CrossEffect Model | 71 |

7 GoodnessofFit for the Cox Model | 81 |

8 Remarks on Computations in Parametric and Semiparametric Estimation | 101 |

9 Cox Model for Degradation and Failure Time Data | 109 |

115 | |

121 | |

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AFT model alternative Andersen Ao(s Ao(t asymptotic Bagdonaviˇcius and Nikulin baseline cumulative hazard censoring chemotherapy coefficients considered constant covariates counting process covariate values Cox model cross-effect model cumulative hazard function Dabrowska degradation models degradation process denote depend distribution function example explanatory variables exponential frailty model gamma gastric cancer goodness-of-fit groups hazard rate function HR(t Hsieh model Kaplan–Meier Klein and Moeschberger KM estimates Koutrouvelis 1985 lifetime likelihood function log-logistic log-rank test lung cancer Martinussen and Scheike Meeker and Escobar Nikulin and H.-D.I. nonparametric observed obtained p-dimensional p-value parametric models partial likelihood patients PH model proportional hazards model radiotherapy random variable ratio regression models regression parameters reliability resource SCE model score function semiparametric estimation SpringerBriefs in Statistics Stablein and Koutrouvelis statistical inference step-stresses stress survival analysis survival data survival function treatment two-sample vector Weibull distribution Weibull regression