A Surrogate Measure for Time-Varying Biomarkers in Randomized Clinical Trials

Clinical trials with rare or distant outcomes are usually designed to be large in size and long term. The resource-demand and time-consuming characteristics limit the feasibility and efficiency of the studies. There are motivations to replace rare or distal clinical endpoints by reliable surrogate markers, which could be earlier and easier to collect. However, statistical challenges still exist to evaluate and rank potential surrogate markers. In this paper, we define a generalized proportion of treatment effect for survival settings. The measure's definition and estimation do not rely on any model assumption. It is equipped with a consistent and asymptotically normal non-parametric estimator. Under proper conditions, the measure reflects the proportion of average treatment effect mediated by the surrogate marker among the group that would survive to mark the measurement time under both intervention and control arms.