A family of multiplicative survival models incorporating a long-term survivorship parameter c as a function of covariates

A family of multiplicative survival models is obtained for the analysis of clinical trial data in which a substantial proportion c of patients respond favorably to treatment with longterm survivorship. The model (MWSM) representing the hazard function for all patients as a function of c and a Weibull density is developed in which the distributional parameters and c are regressed on covariates and estimated by the method of maximum likelihood. The MWSM hazard function is monotonically increasing, peaking, then decreasing thereafter if the shape parameter exceeds unity, and is monotonically decreasing otherwise. Mortality rates with similar behavior have been empirically observed in cancer clinical trial data. A nonproportional or proportional hazards model results depending upon whether or not any Weibull parameter is regressed on covariates. Tests of hypotheses and confidence intervals for c and p-quantiles are obtained.