Analysis of time-to-event data using a flexible mixture model under a constraint of proportional hazards

Cox proportional hazards (PH) model evaluates the effects of interested covariates under PH assumption without specified the baseline hazard. In clinical trial applications, however, the explicitly estimated hazard or cumulative survival function for each treatment group helps to assess and interpret the meaning of treatment difference. In this paper, we propose to use a flexible mixture model under the PH constraint to fit the underline survival functions. Simulations are conducted to evaluate its performance and show that the proposed mixture PH model is very similar to the Cox PH model in terms of estimating the hazard ratio, bias, confidence interval coverage, type-I error and testing power. Application to several real clinical trial examples demonstrates that the results from this approach are almost identical to the results from Cox PH model. The explicitly estimated hazard function for each treatment group provides additional useful information and helps the interpretation of hazard comparisons.