Sufficient Dimension Reduction for Interactions and Its Application to Optimizing Individualized Dose Rules

• Activity Number: 125 - Novel Approaches for Estimating and Evaluating Treatment Rules with Applications in Mental Health Research
• Type: Topic Contributed
• Date/Time: Monday, August 3, 2020 : 1:00 PM to 2:50 PM
• Sponsor: Mental Health Statistics Section
• Author(s): Hyung Park* and Eva Petkova and Thaddeus Tarpey and R. Todd Ogden
• Companies: New York University and NYU School of Medicine and NYU School of Medicine and Columbia University
• Keywords: Sufficient dimension reduction; Interaction effect; Projection-pursuit regression; ensor product P-splines

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 work, we consider the notion of a dimension reduction in regression on subspaces that are sufficient to explain interaction effects between a set of predictors and another variable of interest, leading to a parsimonious parametrization of projection-pursuit regression models specifically defined for the interaction effects. The motivation for this work is from precision medicine where the performance of an individualized does rule, given a set of patient’s characteristics, is determined by interaction effects between dose and patient’s characteristics.