A regression survival model for testing the proportional hazards hypothesis

A semi-parametric generalization of the proportional hazards regression model is defined, whereby the hazard functions can cross for different values of the covariates. In the two-sample comparison, it includes in particular the case of two Weibull distributions differing in scale and shape parameters. A global test of the proportional hazards assumption is proposed against such defined alternatives. Its power in the two-sample case is compared to that of previously described tests by using simulation experiments. Survival data of patients with breast carcinoma, including several prognostic factors, are presented as an illustration.