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）可表征处理变量对结局分布不同分位点上的潜在异质性因果效应。在非随机研究中，倾向性评分（PS）方法常用于估计QTEs。实证与理论研究表明，PS模型中协变量的过度调整与不足调整均会导致处理效应估计产生偏倚和效率损失。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，与处理变量和结局相关的协变量可能随结局分布的不同分位数而变化。然而，既往研究在估计不同QTEs时忽视了在PS模型中分别调整不同的协变量。本文提出分位数回归结果自适应套索（QROAL）方法，用于选择能够提供QTEs无偏且有效估计的协变量。该方法的一个显著特征是采用线性分位数回归模型构建惩罚权重，从而在估计不同QTEs时实现对PS模型中协变量的选择性调整。模拟研究表明，本文提出的方法在变量选择方面优于结果自适应套索（OAL）方法。此外，在一系列同质性和异质性情景中，所提方法在均方根误差指标上均展现出优于OAL方法的性能。最后，我们将QROAL方法应用于中国健康与养老追踪调查（CHARLS）数据集，以探究吸烟状态对抑郁症状严重程度的影响。