Sufficient Dimension Reduction for Interactions

TL;DR

This paper introduces a method for dimension reduction in regression that captures interaction effects between predictors and other variables, aiding personalized treatment strategies.

Contribution

It extends traditional dimension reduction to focus on subspaces sufficient for explaining predictor interactions, relevant for precision medicine applications.

Findings

Develops a new dimension reduction approach for interactions

Demonstrates improved modeling of interaction effects

Applicable to personalized treatment decision-making

Abstract

Dimension reduction lies at the heart of many statistical methods. In regression, dimension reduction has been linked to the notion of sufficiency whereby the relation of the response to a set of predictors is explained by a lower dimensional subspace in the predictor space. In this paper, we consider the notion of a dimension reduction in regression on subspaces that are sufficient to explain interaction effects between predictors and another variable of interest. The motivation for this work is from precision medicine where the performance of an individualized treatment rule, given a set of pretreatment predictors, is determined by interaction effects.