Comparing and combining biomarkers as principal surrogates for time-to-event clinical endpoints

Principal surrogate endpoints are useful as targets for phase I and II trials. In many recent trials, multiple post-randomization biomarkers are measured. However, few statistical methods exist for comparison of or combination of biomarkers as principal surrogates, and none of these methods to our knowledge utilize time-to-event clinical endpoint information. We propose a Weibull model extension of the semi-parametric estimated maximum likelihood method that allows for the inclusion of multiple biomarkers in the same risk model as multivariate candidate principal surrogates. We propose several methods for comparing candidate principal surrogates and evaluating multivariate principal surrogates. These include the time-dependent and surrogate-dependent true and false positive fraction, the time-dependent and the integrated standardized total gain, and the cumulative distribution function of the risk difference. We illustrate the operating characteristics of our proposed methods in simulations and outline how these statistics can be used to evaluate and compare candidate principal surrogates. We use these methods to investigate candidate surrogates in the Diabetes Control and Complications Trial.