Semiparametric Causal Sufficient Dimension Reduction Of Multidimensional Treatments

TL;DR

This paper introduces a semiparametric approach for reducing the dimensionality of multidimensional treatments in causal inference, ensuring the preservation of cause-effect relationships, with applications demonstrated in radiation oncology.

Contribution

It develops a novel semiparametric method for causal sufficient dimension reduction of multidimensional treatments, addressing confounding and preserving causal effects.

Findings

Method effectively reduces treatment dimensions while maintaining causal relationships.

Simulation studies validate the approach's accuracy and robustness.

Application to radiation oncology data demonstrates practical utility.

Abstract

Cause-effect relationships are typically evaluated by comparing 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 multidimensional. For example, understanding the causal relationship between severity of radiation therapy, summarized by a multidimensional 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 multidimensional treatment vector weakly affect the outcome, but the overall relationship between treatment and outcome is strong, careless approaches to dimension reduction may not preserve this relationship. Further, methods developed for regression problems do not directly transfer to causal inference due to confounding complications. In this paper, we use semiparametric inference theory for structural models to give a general approach to causal sufficient dimension reduction of a multidimensional treatment such that the cause-effect relationship between treatment and outcome is preserved. We illustrate the utility of our proposals through simulations and a real data application in radiation oncology.