Treatment Effect Quantiles in Stratified Randomized Experiments and Matched Observational Studies
分层随机实验与匹配观测研究中的个体处理效应分位数AI 解读 ↓
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分层随机实验与匹配观测研究中的个体处理效应分位数
- 研究问题
- 当个体处理效应存在厚尾或极端值时，如何对其分位数进行随机化推断，并在匹配观测研究中评估未测混杂的影响？
- 方法与思路
- 作者针对分位数原假设的整数规划提出带最优变换的贪心算法，并将分层随机实验的推断扩展到匹配观测研究及敏感性分析。
- 材料陈述的贡献
- 摘要称，算法降低计算成本、保持有效 p 值且比所述整数约束松弛更不保守；推断和敏感性分析对所有效应分位数同时有效。
- 阅读关注点
- 应核对个体效应分位数与结果分位数差的区别、复合原假设的处理、算法保证，以及所有分位数同时有效所需的随机化和匹配条件。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未核实；摘要未说明具体分配机制、算法细节或敏感性模型，不依赖单位分布不等于无需设计假设。
原文摘要
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.