Semiparametric transformation models for semicompeting survival data

Semicompeting risk outcome data (e.g., time to disease progression and time to death) are commonly collected in clinical trials. However, analysis of these data is often hampered by a scarcity of available statistical tools. As such, we propose a novel semiparametric transformation model that improves the existing models in the following two ways. First, it estimates regression coefficients and association parameters simultaneously. Second, the measure of surrogacy, for example, the proportion of the treatment effect that is mediated by the surrogate and the ratio of the overall treatment effect on the true endpoint over that on the surrogate endpoint, can be directly obtained. We propose an estimation procedure for inference and show that the proposed estimator is consistent and asymptotically normal. Extensive simulations demonstrate the valid usage of our method. We apply the method to a multiple myeloma trial to study the impact of several biomarkers on patients' semicompeting outcomes--namely, time to progression and time to death.