A single-index model with a surface-link for optimizing individualized dose rules

TL;DR

This paper introduces a single-index model with a surface-link to effectively model and estimate nonlinear interaction effects between covariates and continuous treatments, aiming to optimize individualized dose rules in observational studies.

Contribution

It proposes a novel single-index regression approach with a surface-link for modeling complex interaction effects, enhancing personalized treatment decision-making.

Findings

Effective modeling of nonlinear covariate-treatment interactions

Application to real-world dose optimization problems

Simulation results demonstrate improved estimation accuracy

Abstract

This paper focuses on the problem of modeling and estimating interaction effects between covariates and a continuous treatment variable on an outcome, using a single-index regression approach. The primary motivation is to estimate an optimal individualized dose rule in an observational study. To model possibly nonlinear interaction effects between patients' covariates and a continuous treatment variable, we employ a two-dimensional penalized spline regression on an index-treatment domain, where the index is defined as a linear projection of the covariates. The method is illustrated using two applications as well as simulation experiments. A unique contribution of this work is in the parsimonious (single-index) parametrization specifically defined for the interaction effect term.