Within heterogeneous treatment effect (HTE) analysis, various estimands have been proposed to capture the effect of a treatment conditional on covariates. Recently, the conditional quantile comparator (CQC) has emerged as a promising estimand, offering quantile-level summaries akin to the conditional quantile treatment effect (CQTE) while preserving some interpretability of the conditional average treatment effect (CATE). It achieves this by summarising the treated response conditional on both the covariates and the untreated response. Despite these desirable properties, the CQC's current estimation is limited by the need to first estimate the difference in conditional cumulative distribution functions and then invert it. This inversion obscures the CQC estimate, hampering our ability to both model and interpret it. To address this, we propose the first direct estimator of the CQC, allowing for explicit modelling and parameterisation. This explicit parameterisation enables better interpretation of our estimate while also providing a means to constrain and inform the model. We show, both theoretically and empirically, that our estimation error depends directly on the complexity of the CQC itself, improving upon the existing estimation procedure. Furthermore, it retains the desirable double robustness property with respect to nuisance parameter estimation. We further show our method to outperform existing procedures in estimation accuracy across multiple data scenarios while varying sample size and nuisance error. Finally, we apply it to real-world data from an employment scheme, uncovering a reduced range of potential earnings improvement as participant age increases.

翻译：在异质性处理效应分析中，已有多种估计量被提出用于捕捉协变量条件下的处理效应。最近，条件分位数比较器作为一种有前景的估计量出现，它提供了类似于条件分位数处理效应的分位数水平汇总，同时保留了条件平均处理效应的部分可解释性。这是通过汇总同时以协变量和未处理响应为条件的已处理响应来实现的。尽管具有这些理想特性，CQC的现有估计方法受限于需要先估计条件累积分布函数的差异再进行反演。这种反演过程模糊了CQC估计值，阻碍了我们对其进行建模和解释的能力。为解决此问题，我们提出了首个CQC的直接估计器，允许进行显式建模和参数化。这种显式参数化能够提升估计结果的可解释性，同时为约束和指导模型提供了途径。我们从理论和实证两方面证明，我们的估计误差直接取决于CQC本身的复杂度，从而改进了现有估计程序。此外，该方法在关于干扰参数估计方面保持了理想的双重稳健特性。我们进一步证明，在多种数据场景下，当样本量和干扰误差变化时，我们的方法在估计精度上优于现有程序。最后，我们将其应用于就业计划的实际数据，发现随着参与者年龄增长，潜在收入提升的范围呈现收窄趋势。