Analysis of accelerated hazards models

The proportional hazards model for survival time data usually assumes that the covariates of interest take constant effects proportionally on an unspecified baseline hazard function. However, it may not be applicable when the assumption of constant proportionality is violated. In a two-arm randomized clinical trial, for example, the treatment is often expected to be fully effective only after a certain lag period. Some alternatives, such as the accelerated failure time model, have been developed in statistical literature. This article introduces an accelerated hazards model when there is a scale change relationship between the hazard functions. An estimating equation is proposed to estimate the parameter semiparametrically. The methodology is demonstrated within a two-sample framework. Several extensions of the model are also considered. Real clinical trial data are used to investigate the model's practical use.