Overlap, matching, or entropy weights: what are we weighting for?

TL;DR

This paper compares equipoise estimators like overlap, matching, and entropy weights to inverse probability weights, highlighting their advantages in handling positivity issues and providing guidance on their appropriate use in treatment effect estimation.

Contribution

The paper clarifies the rationale, differences, and appropriate contexts for using equipoise estimators versus IPW, supported by simulations and a healthcare data example.

Findings

Equipoise estimators are flexible and interpretable alternatives to IPW.

They perform better under positivity violations in treatment assignment.

Comparison with IPW trimming highlights differences in estimands and applicability.

Abstract

There has been a recent surge in statistical methods for handling the lack of adequate positivity when using inverse probability weights (IPW). However, these nascent developments have raised a number of questions. Thus, we demonstrate the ability of equipoise estimators (overlap, matching, and entropy weights) to handle the lack of positivity. Compared to IPW, the equipoise estimators have been shown to be flexible and easy to interpret. However, promoting their wide use requires that researchers know clearly why, when to apply them and what to expect. In this paper, we provide the rationale to use these estimators to achieve robust results. We specifically look into the impact imbalances in treatment allocation can have on the positivity and, ultimately, on the estimates of the treatment effect. We zero into the typical pitfalls of the IPW estimator and its relationship with the estimators of the average treatment effect on the treated (ATT) and on the controls (ATC). Furthermore, we also compare IPW trimming to the equipoise estimators. We focus particularly on two key points: What fundamentally distinguishes their estimands? When should we expect similar results? Our findings are illustrated through Monte-Carlo simulation studies and a data example on healthcare expenditure.