Testing Relationship between Treatment and Survival Time with an Intermediate Event†

Consider a clinical trial in which the main end-point is survival. Suppose after the start of the study an intermediate event occurs which may be influenced by a covariate(or treatment). In many clinical studies the occurrence of an intermediate event may change the survival distribution. This investigation develops two-stage model which, in the first stage, models the effect of covariate on the intermediate event and models the relationship between survival time and covariate as well as the intermediate event. In this paper, the two-stage model is presented in order to model intermediate event and a test based on this model is also provided. A numerical simulations are carried out to evaluate its overall significance level.