The Connection Between R-Learning and Inverse-Variance Weighting for Estimation of Heterogeneous Treatment Effects

TL;DR

This paper reveals the connection between R-Learning and inverse-variance weighting in estimating heterogeneous treatment effects, showing that weight choice is crucial for performance and demonstrating the advantages of IVWs.

Contribution

It establishes that R-Learning implicitly uses inverse-variance weights and provides theoretical convergence rates for IVWs in CATE estimation.

Findings

IVWs improve stability over inverse-propensity weights

Simulations show IVWs outperform other weighting methods

Derived the fastest known convergence rates for IVWs

Abstract

Many methods for estimating conditional average treatment effects (CATEs) can be expressed as weighted pseudo-outcome regressions (PORs). Previous comparisons of POR techniques have paid careful attention to the choice of pseudo-outcome transformation. However, we argue that the dominant driver of performance is actually the choice of weights. For example, we point out that R-Learning implicitly performs a POR with inverse-variance weights (IVWs). In the CATE setting, IVWs mitigate the instability associated with inverse-propensity weights, and lead to convenient simplifications of bias terms. We demonstrate the superior performance of IVWs in simulations, and derive convergence rates for IVWs that are, to our knowledge, the fastest yet shown without assuming knowledge of the covariate distribution.