Estimation of the proportion of treatment effect explained by a high-dimensional surrogate.

Clinical studies examining the effectiveness of a treatment with respect to some primary outcome often require long-term follow-up of patients and/or costly or burdensome measurements of the primary outcome of interest. Identifying a surrogate marker for the primary outcome of interest may allow one to evaluate a treatment effect with less follow-up time, less cost, or less burden. While much clinical and statistical work has focused on identifying and validating surrogate markers, available approaches tend to focus on settings in which only a single surrogate marker is of interest. Limited work has been done to accommodate the high-dimensional surrogate marker setting where the number of potential surrogates is greater than the sample size. In this article, we develop methods to estimate the proportion of treatment effect explained by high-dimensional surrogates. We study the asymptotic properties of our proposed estimator, propose inference procedures, and examine finite sample performance via a simulation study. We illustrate our proposed methods using data from a randomized study comparing a novel whey-based oral nutrition supplement with a standard supplement with respect to change in body fat percentage over 12 weeks, where the surrogate markers of interest are gene expression probesets.

Estimation and inference for the indirect effect in high-dimensional linear mediation models.

Mediation analysis is difficult when the number of potential mediators is larger than the sample size. In this paper we propose new inference procedures for the indirect effect in the presence of high-dimensional mediators for linear mediation models. We develop methods for both incomplete mediation, where a direct effect may exist, and complete mediation, where the direct effect is known to be absent. We prove consistency and asymptotic normality of our indirect effect estimators. Under complete mediation, where the indirect effect is equivalent to the total effect, we further prove that our approach gives a more powerful test compared to directly testing for the total effect. We confirm our theoretical results in simulations, as well as in an integrative analysis of gene expression and genotype data from a pharmacogenomic study of drug response. We present a novel analysis of gene sets to understand the molecular mechanisms of drug response, and also identify a genome-wide significant noncoding genetic variant that cannot be detected using standard analysis methods.