Effect modification means the size of a treatment effect varies with an observed covariate. Generally speaking, a larger treatment effect with more stable error terms is less sensitive to bias. Thus, we might be able to conclude that a study is less sensitive to unmeasured bias by using these subgroups experiencing larger treatment effects. Lee et al. (2018) proposed the submax method that leverages the joint distribution of test statistics from subgroups to draw a firmer conclusion if effect modification occurs. However, one version of the submax method uses M-statistics as the test statistics and is implemented in the R package submax (Rosenbaum, 2017). The scaling factor in the M-statistics is computed using all observations combined across subgroups. We show that this combining can confuse effect modification with outliers. We propose a novel group M-statistic that scores the matched pairs in each subgroup to tackle the issue. We examine our novel scoring strategy in extensive settings to show the superior performance. The proposed method is applied to an observational study of the effect of a malaria prevention treatment in West Africa.

翻译：效应修饰是指处理效应的大小随观测协变量而变化。一般而言，处理效应越大且误差项越稳定，其对偏倚的敏感性越低。因此，通过利用那些经历较大处理效应的子群，我们或许能够得出研究对未测量偏倚较不敏感的结论。Lee等人（2018）提出的submax方法利用了来自各子群的检验统计量的联合分布，以便在效应修饰发生时得出更确凿的结论。然而，submax方法的一个版本使用M统计量作为检验统计量，并在R包submax中实现（Rosenbaum, 2017）。M统计量中的尺度因子是使用跨子群合并的所有观测值计算的。我们证明这种合并可能导致效应修饰与异常值混淆。为解决此问题，我们提出了一种新颖的群组M统计量，用于对每个子群中的匹配对进行评分。我们在多种设置下检验了这种新颖的评分策略，以展示其优越性能。所提出的方法被应用于一项关于西非疟疾预防治疗效果观察性研究。