Evaluating the treatment effects has become an important topic for many applications. However, most existing literature focuses mainly on the average treatment effects. When the individual effects are heavy-tailed or have outlier values, not only may the average effect not be appropriate for summarizing the treatment effects, but also the conventional inference for it can be sensitive and possibly invalid due to poor large-sample approximations. In this paper we focus on quantiles of individual effects, which can be more robust measures of treatment effects in the presence of extreme individual effects. Moreover, our inference for quantiles of individual effects are purely randomization-based, which avoids any distributional assumption on the units. We first consider inference for stratified randomized experiments, extending the recent work of Caughey et al. (2021). The calculation of valid p-values for testing null hypotheses on quantiles of individual effects involves linear integer programming, which is generally NP hard. To overcome this issue, we propose a greedy algorithm with a certain optimal transformation, which has much lower computational cost, still leads to valid p-values and is less conservative than the usual relaxation by dropping the integer constraint. We then extend our approach to matched observational studies and propose sensitivity analysis to investigate to what extent our inference on quantiles of individual effects is robust to unmeasured confounding. Both the randomization inference and sensitivity analysis are simultaneously valid for all quantiles of individual effects, which are actually free lunches added to the conventional analysis assuming constant effects. Furthermore, the inference results can be easily visualized and interpreted.

翻译：评估治疗效果已成为许多应用中的一个重要话题。 但是,大多数现有文献都主要侧重于平均治疗效果。 当个体效应是重尾或超值时,不仅平均效果可能不适合总结治疗效果,而且常规推论可能敏感,而且可能无效,因为大成样近似差差,本文侧重于个体效应的四分位数,这在极端个人效应的情况下可以更有力地衡量治疗效果。此外,我们对个体效应的量化的推论纯粹基于随机化,这避免了对单位的分布性假设。我们首先考虑对分层随机化实验的推论,延长Caughey等人最近的工作(2021年),而对于这种实验的常规推论可能是敏感和无效的。在计算个体效应的四分位数时,我们侧重于线性整数的编程,这通常比较困难。为了克服这一问题,我们建议一种贪婪的算法,以某种最优的转换法,其计算成本要低得多,从而避免对单位的任何分配性假设性假设。我们首先考虑的是分数性实验的推论,而后期性分析比常规分析要更保守。