Stabilized Inverse Probability Weighting via Isotonic Calibration

Lars van der Laan, Ziming Lin, Marco Carone, Alex Luedtke

Keywords: inverse probability weighting, calibration, isotonic regression, propensity, balancing

TL;DR: We propose a post-hoc calibration algorithm using isotonic regression to construct well-calibrated, stabilized inverse propensity weights from user-supplied, cross-fitted propensity score estimates.

Abstract: Inverse weighting with an estimated propensity score is widely used by estimation methods in causal inference to adjust for confounding bias. However, directly inverting propensity score estimates can lead to instability, bias, and excessive variability due to large inverse weights, especially when treatment overlap is limited. In this work, we propose a post-hoc calibration algorithm for inverse propensity weights that generates well-calibrated, stabilized weights from user-supplied, cross-fitted propensity score estimates. Our approach employs a variant of isotonic regression with a loss function specifically tailored to the inverse propensity weights. Through theoretical analysis and empirical studies, we demonstrate that isotonic calibration improves the performance of doubly robust estimators of the average treatment effect.

Submission Number: 88