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Abstract:
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In some causal inference applications, treatments of interest might be continuous and multidimensional. For example, understanding the causal relationship between severity of radiation therapy, represented by a multidimensional vector of radiation exposure values at different parts of the body, and post-treatment side effects is a problem of clinical interest in oncology. In such circumstances, a more appropriate strategy for making interpretable causal inferences is to reduce the dimension of the treatment. If individual elements of a multidimensional feature vector weakly affect the outcome, but the overall relationship between the feature vector and the outcome is strong, careless approaches to dimension reduction may not preserve this relationship. The literature on sufficient dimension reduction considers strategies that avoid this issue. Methods developed for regression problems, however, do not transfer in a straightforward way to causal inference due to complications arising from confounding. We use semiparametric inference theory for structural models to give a general approach to causal sufficient dimension reduction of a high dimensional treatment.
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