Robust estimation of the proportion of treatment effect explained by surrogate marker information

In randomized treatment studies where the primary outcome requires long follow-up of patients and/or expensive or invasive obtainment procedures, the availability of a surrogate marker that could be used to estimate the treatment effect and could potentially be observed earlier than the primary outcome would allow researchers to make conclusions regarding the treatment effect with less required follow-up time and resources. The Prentice criterion for a valid surrogate marker requires that a test for treatment effect on the surrogate marker also be a valid test for treatment effect on the primary outcome of interest. Based on this criterion, methods have been developed to define and estimate the proportion of treatment effect on the primary outcome that is explained by the treatment effect on the surrogate marker. These methods aim to identify useful statistical surrogates that capture a large proportion of the treatment effect. However, current methods to estimate this proportion usually require restrictive model assumptions that may not hold in practice and thus may lead to biased estimates of this quantity. In this paper, we propose a nonparametric procedure to estimate the proportion of treatment effect on the primary outcome that is explained by the treatment effect on a potential surrogate marker and extend this procedure to a setting with multiple surrogate markers. We compare our approach with previously proposed model-based approaches and propose a variance estimation procedure based on a perturbation-resampling method. Simulation studies demonstrate that the procedure performs well in finite samples and outperforms model-based procedures when the specified models are not correct. We illustrate our proposed procedure using a data set from a randomized study investigating a group-mediated cognitive behavioral intervention for peripheral artery disease participants.