Doubly Robust Estimators of Quantile Treatment Effects With Semiparametric Cumulative Probability Models

2026-07-29

AI Summary

This study addresses the limitations of traditional causal inference methods, which primarily focus on average potential outcomes and struggle to capture treatment effects across the entire outcome distribution—particularly when outcomes are skewed or subject to detection limits. Existing quantile treatment effect estimators are often sensitive to model misspecification under such conditions. To overcome this, the authors propose two novel strategies based on a semiparametric cumulative probability model (CPM), introducing double robustness for the first time in this context. The first approach employs an inverse cumulative distribution function, while the second directly solves the efficient influence function for marginal quantiles. Both methods are extended to estimate probabilistic treatment effects and their conditional variants. The proposed estimators exhibit robustness and asymptotic normality, with simulations demonstrating strong finite-sample performance and stable variance estimation even under model misspecification. Their practical utility is further confirmed through successful application to real-world HIV data.

Abstract

The causal inference literature has traditionally focused on estimating the mean of the potential outcome, whereas evaluating how a treatment affects the entire outcome distribution can provide additional information in biomedical research. Quantile treatment effect (QTE) captures such distributional differences, particularly when outcomes are skewed. However, existing approaches for estimating QTE make distributional assumptions about the outcome and are thus sensitive to model misspecification. Motivated by an HIV study with skewed outcomes, one of which is subject to detection limits, we propose a doubly robust framework for estimating QTE based on the cumulative probability model (CPM), which is a rank-based, semiparametric linear transformation model. We develop two CPM-based estimation strategies: (1) an inverse-cumulative distribution function (CDF) approach that first estimates the marginal CDF of potential outcomes using the efficient influence function (EIF) and then obtains marginal quantiles via weighted quantile interpolation by inverting the distribution, and (2) a direct approach that solves the EIF of potential marginal quantiles. The proposed estimators are doubly robust and asymptotically normal. We further extend the framework to probability treatment effects (PTEs) and their conditional counterparts. For statistical inference, we investigate several variance estimation procedures, including EIF-based estimators, sandwich estimators, and the nonparametric bootstrap. Simulation studies illustrate that the empirical sandwich estimator and the nonparametric bootstrap provide doubly robust variance estimation with stable finite-sample performance under nuisance model misspecification. The proposed methods are evaluated through extensive Monte Carlo simulations and illustrated using an HIV data application.

Problem

• Quantile Treatment Effect
• Model Misspecification
• Doubly Robust
• Cumulative Probability Model
• Skewed Outcomes

Innovation

• doubly robust
• quantile treatment effect
• cumulative probability model
• efficient influence function
• semiparametric