Quantile treatment effects (QTEs) can characterize the potentially heterogeneous causal effect of a treatment on different points of the entire outcome distribution. Propensity score (PS) methods are commonly employed for estimating QTEs in non-randomized studies. Empirical and theoretical studies have shown that insufficient and unnecessary adjustment for covariates in PS models can lead to bias and efficiency loss in estimating treatment effects. Striking a balance between bias and efficiency through variable selection is a crucial concern in casual inference. It is essential to acknowledge that the covariates related treatment and outcome may vary across different quantiles of the outcome distribution. However, previous studies have overlooked to adjust for different covariates separately in the PS models when estimating different QTEs. In this article, we proposed the quantile regression outcome-adaptive lasso (QROAL) method to select covariates that can provide unbiased and efficient estimates of QTEs. A distinctive feature of our proposed method is the utilization of linear quantile regression models for constructing penalty weights, enabling covariate selection in PS models separately when estimating different QTEs. We conducted simulation studies to show the superiority of our proposed method over the outcome-adaptive lasso (OAL) method in variable selection. Moreover, the proposed method exhibited favorable performance compared to the OAL method in terms of root mean square error in a range of settings, including both homogeneous and heterogeneous scenarios. Additionally, we applied the QROAL method to datasets from the China Health and Retirement Longitudinal Study (CHARLS) to explore the impact of smoking status on the severity of depression symptoms.

翻译：分位数处理效应（QTEs）可刻画处理变量在整个结果分布不同分位点上可能存在的异质性因果效应。在非随机化研究中，倾向性评分（PS）方法常被用于估计QTEs。实证与理论研究均表明，在PS模型中纳入不足或过多的协变量会导致处理效应估计产生偏倚并损失效率。通过变量选择在偏倚与效率之间取得平衡是因果推断中的关键问题。值得注意的是，与处理和结果相关的协变量可能随结果分布的不同分位数而变化。然而，以往研究在估计不同QTEs时忽视了在PS模型中分别调整不同协变量。本文提出分位数回归结果自适应套索（QROAL）方法，以筛选能够提供QTEs无偏且高效估计的协变量。该方法的一大特色在于利用线性分位数回归模型构建惩罚权重，从而在估计不同QTEs时能够分别对PS模型中的协变量进行选择。我们通过模拟研究证明，所提方法在变量选择方面优于结果自适应套索（OAL）方法。此外，在同质与异质等多种场景设置下，所提方法在均方根误差方面较OAL方法表现出更优性能。我们还将QROAL方法应用于中国健康与养老追踪调查（CHARLS）数据集，以探究吸烟状况对抑郁症状严重程度的影响。