A mixture model combining logistic regression with proportional hazards regression

A model is proposed for the analysis of censored data which combines a logistic formulation for the probability of occurrence of an event with a proportional hazards specification for the time of occurrence of the event. The proposed model is a semiparametric generalization of a parametric model due to Farewell (1982). Estimates of the regression parameters are obtained by maximizing a Monte Carlo approximation of a marginal likelihood and the EM algorithm is used to estimate the baseline survivor function. We present some simulation results to verify the validity of the suggested estimation procedure. It appears that the semiparametric estimates are reasonably efficient with acceptable bias whereas the parametric estimates can be highly dependent on the parametric assumptions.