Evaluating multiple surrogate markers with censored data.

The utilization of surrogate markers offers the opportunity to reduce the length of required follow-up time and/or costs of a randomized trial examining the effectiveness of an intervention or treatment. There are many available methods for evaluating the utility of a single surrogate marker including both parametric and nonparametric approaches. However, as the dimension of the surrogate marker increases, a completely nonparametric procedure becomes infeasible due to the curse of dimensionality. In this paper, we define a quantity to assess the value of multiple surrogate markers in a time-to-event outcome setting and propose a robust estimation approach for censored data. We focus on surrogate markers that are measured at some landmark time, t0 , which occurs earlier than the end of the study. Our approach is based on a dimension reduction procedure with an option to incorporate weights to guard against potential misspecification of the working model, resulting in three different proposed estimators, two of which can be shown to be double robust. We examine the finite sample performance of the estimators under various scenarios using a simulation study. We illustrate the estimation and inference procedures using data from the Diabetes Prevention Program (DPP) to examine multiple potential surrogate markers for diabetes.