Marginal and hazard ratio specific random data generation: Applications to semi-parametric bootstrapping

Cox's partial likelihood for censored time-to-event data can be interpreted as a permutation probability, whereby covariate values are permuted to the observed times-to-event and censoring times. This interpretation facilitates a simple method for jointly generating times-to-event and covariate tuples with considerable flexibility, including time dependence of the hazard ratio and specification of both the marginal time-to-event and covariate distributions. This interpretation also facilitates a method for semi-parametric bootstrapping of hazard ratio estimators.