AI 中文总结
针对现有分位数处理效应（QTE）估计方法对模型误设敏感的问题，提出基于半参数累积概率模型（CPM）的双重稳健QTE估计框架，开发两种估计策略并通过模拟和HIV数据验证其有效性。
AI 中文摘要
因果推断文献传统上聚焦于估计潜在结局的均值，而在生物医学研究中，评估处理如何影响整个结局分布可提供额外信息。分位数处理效应（Quantile Treatment Effect, QTE）捕捉这类分布差异，尤其适用于结局呈偏态分布的情况。然而，现有估计QTE的方法需对结局做分布假设，因此对模型误设敏感。受一项存在偏态结局（其中一个结局受检测限限制）的HIV研究启发，我们提出一种基于累积概率模型（Cumulative Probability Model, CPM）的双重稳健框架以估计QTE，CPM是一种基于秩的半参数线性转换模型。我们开发两种基于CPM的估计策略：（1）逆累积分布函数（Cumulative Distribution Function, CDF）方法，该方法首先利用有效影响函数（Efficient Influence Function, EIF）估计潜在结局的边际CDF，再通过反转分布的加权分位数插值得到边际分位数；（2）直接方法，该方法求解潜在边际分位数的EIF。所提估计量具有双重稳健性且渐近正态。我们进一步将该框架扩展至概率处理效应（Probability Treatment Effects, PTEs）及其条件对应形式。针对统计推断，我们研究多种方差估计方法，包括基于EIF的估计量、三明治估计量及非参数自助法。模拟研究表明，在干扰模型误设下，经验三明治估计量与非参数自助法可提供双重稳健的方差估计，且具有稳定的有限样本表现。所提方法通过大量蒙特卡洛模拟进行评估，并通过HIV数据应用予以说明。
英文摘要
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.
CommentsSupplementary material included. Revised manuscript with updated notation and minor corrections
