Estimating the Average Treatment Effect under Limited Overlap via Polynomial Approximation and Extrapolation

2026-08-10

AI Summary

In observational studies with limited covariate overlap, conventional inverse probability weighting (IPW) estimators of the average treatment effect (ATE) often exhibit substantial bias and unreliable confidence intervals due to violations of the strong overlap assumption. This work proposes a robust IPW approach based on polynomial extrapolation: by constructing a sequence of surrogate estimators indexed by a tuning parameter, it fits a polynomial function to these estimates and extrapolates to the target ATE, thereby substantially reducing reliance on strong overlap while preserving the original ATE definition. Theoretical analysis establishes that the proposed estimator remains consistent and asymptotically normal under weaker overlap conditions. Simulation studies demonstrate that it achieves markedly improved estimation accuracy and confidence interval coverage compared to standard IPW.

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 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 a class of estimands can be expressed 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 function, 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.

Problem

• Average Treatment Effect
• Limited Overlap
• Observational Studies
• Propensity Score
• Covariate Overlap

Innovation

• Average Treatment Effect
• Limited Overlap
• Polynomial Extrapolation
• Inverse Probability Weighting
• Covariate Balance