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**Bender, R.; Augustin, Thomas and Blettner, Maria (2003): Generating Survival Times to Simulate Cox Proportional Hazards Models. Collaborative Research Center 386, Discussion Paper 338 [PDF, 159kB]**

## Abstract

This paper discusses techniques to generate survival times for simulation studies regarding Cox proportional hazards models. In linear regression models, the response variable is directly connected with the considered covariates, the regression coefficients and the simulated random errors. Thus, the response variable can be generated from the regression function, once the regression coefficients and the error distribution are specified. However, in the Cox model, which is formulated via the hazard function, the effect of the covariates have to be translated from the hazards to the survival times, because the usual software packages for estimation of Cox models require the individual survival time data. A general formula describing the relation between the hazard and the corresponding survival time of the Cox model is derived. It is shown how the exponential, the Weibull and the Gompertz distribution can be used to generate appropriate survival times for simulation studies. Additionally, the general relation between hazard and survival time can be used to develop own distributions for special situations and to handle flexibly parameterized proportional hazards models. The use of other distributions than the exponential distribution only is indispensable to investigate the characteristics of the Cox proportional hazards model, especially in non-standard situations, where the partial likelihood depends on the baseline hazard.

Item Type: | Paper |
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Keywords: | Cox proportional hazards model; exponential distribution; Gompertz distribution; simulation; survival times; Weibull distribution |

Faculties: | Mathematics, Computer Science and Statistics > Statistics > Collaborative Research Center 386 Special Research Fields > Special Research Field 386 |

Subjects: | 500 Science > 510 Mathematics |

URN: | urn:nbn:de:bvb:19-epub-1716-2 |

Language: | English |

Item ID: | 1716 |

Date Deposited: | 10. Apr 2007 |

Last Modified: | 04. Nov 2020, 12:45 |