Estimating the average treatment effect under limited overlap via Polynomial Approximation and Extrapolation

Abstract

Estimating the average treatment effect (ATE) remains a fundamental challenge in observational studies in the presence of poor or limited covariate overlap. Although the inverse probability weighting (IPW) estimator is a widely used approach for estimating the ATE, its performance can deteriorate substantially when overlap is limited, often resulting in increased finite sample bias and unreliable confidence intervals. One common strategy is to shift attention from the original target estimand, the ATE, to alternative estimands such as a class of weighted ATEs that are less sensitive to extreme propensity scores; however, doing so changes the scientific question of interest. In this manuscript, we propose a novel ATE estimator that preserves the original target estimand, the ATE, while improving robustness to limited overlap. A key idea is that this class of estimands can be represented by a polynomial function of a hyperparameter characterizing the estimands. Exploiting this structure, the proposed method computes IPW estimators for a sequence of such estimands, models these estimates using a polynomial regression, and extrapolates to recover the ATE. We show that the estimator has consistency and asymptotic normality under weaker overlap conditions than required for the standard IPW estimator. Simulation studies demonstrate that the proposed method improves estimation accuracy and interval performance in settings with limited overlap. In addition to its theoretical and empirical advantages, the proposed approach has a clear interpretation and is easy to implement using standard statistical software.