An adjustment for a post-randomization variable in the comparison of two treatments for survival

A method is proposed to infer the randomized treatment effect on survival after an adjustment for a post-randomization variable. The post-randomization variable is made independent of the treatment assignment and is considered a surrogate for baseline prognostic factors. The relationship between the post-randomization surrogate and baseline prognostic factors for survival is considered smooth, but otherwise unknown. The effect of these factors on survival is modelled using the Cox proportional hazards model with a semi-parametric relative risk function. Likelihood based estimates and tests for the treatment effect are demonstrated. An example from a randomized clinical trial in cancer illustrates the methodology.