“Robust Estimation of the Proportion of Treatment Effect Explained by a Surrogate Marker”
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. Previous research on identifying and validating surrogate markers has focused on estimation of the proportion of treatment effect explained by a surrogate marker since a valid surrogate marker should capture a large proportion of the true treatment effect on the primary outcome. However, current methods to estimate the proportion of treatment effect explained usually require restrictive model assumptions that may not hold in practice and thus may lead to biased estimates of this quantity. We propose a nonparametric procedure to estimate the proportion of treatment effect explained by a potential surrogate marker and extend this procedure to a setting with censored time-to-event outcomes. We compare our approach to previously proposed model-based approaches and propose a variance estimation procedure based on perturbation-resampling. 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 by examining potential surrogate markers for diabetes using data from the Diabetes Prevention Program.