Semiparametric Causal Sufficient Dimension Reduction Of High Dimensional Treatments

Abstract

Cause-effect relationships are typically evaluated by comparing the outcome responses to binary treatment values, representing two arms of a hypothetical randomized controlled trial. However, in certain applications, treatments of interest are continuous and high dimensional. For example, understanding the causal relationship between severity of radiation therapy, represented by a high dimensional vector of radiation exposure values and post-treatment side effects is a problem of clinical interest in radiation oncology. An appropriate strategy for making interpretable causal conclusions is to reduce the dimension of treatment. If individual elements of a high dimensional treatment vector weakly affect the outcome, but the overall relationship between the treatment variable and the outcome is strong, careless approaches to dimension reduction may not preserve this relationship. Moreover, methods developed for regression problems do not transfer in a straightforward way to causal inference due to confounding complications between the treatment and outcome. In this paper, we use semiparametric inference theory for structural models to give a general approach to causal sufficient dimension reduction of a high dimensional treatment such that the cause-effect relationship between the treatment and outcome is preserved. We illustrate the utility of our proposal through simulations and a real data application in radiation oncology