Relative Contrast Estimation and Inference for Treatment Recommendation

TL;DR

This paper introduces a novel method for estimating and inferring relative treatment effects, which are scale-invariant and potentially more suitable than absolute effects in resource-constrained treatment prioritization scenarios.

Contribution

It models scale-invariant contrasts between treatment effects using a single index model with identifiability constraints, and develops an efficient estimation procedure with theoretical guarantees.

Findings

Proposed method outperforms existing approaches in simulations.

Theoretical analysis confirms efficiency and identifiability.

Numerical studies demonstrate practical advantages of the approach.

Abstract

When there are resource constraints, it is important to rank or estimate treatment benefits according to patient characteristics. This facilitates prioritization of assigning different treatments. Most existing literature on individualized treatment rules targets absolute conditional treatment effect differences as the metric for benefits. However, there can be settings where relative differences may better represent such benefits. In this paper, we consider modeling such relative differences that form scale-invariant contrasts between conditional treatment effects. We show that all scale-invariant contrasts are monotonic transformations of each other. Therefore we posit a single index model for a particular relative contrast. Identifiability of the model is enforced via an intuitive $l_2$ norm constraint on index parameters. We then derive estimating equations and efficient scores via semiparametric efficiency theory. Based on the efficient score and its variant, we propose a two-step approach that consists of minimizing a doubly robust loss function and a subsequent one-step efficiency augmentation procedure to achieve efficiency bound. Careful theoretical and numerical studies are provided to show the superiority of the proposed approach.