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arXiv · 2607.27633

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

Hao Wu·Chun Li·Bryan E. Shepherd
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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.

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BibTeXRIS

Hao Wu, Chun Li, Bryan E. Shepherd. 2026-08-11. Doubly Robust Estimators of Quantile Treatment Effects With Semiparametric Cumulative Probability Models. https://arxiv.org/abs/2607.27633

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