We present a multivariate one-sided sensitivity analysis for matched observational studies, appropriate when the researcher has specified that a given causal mechanism should manifest itself in effects on multiple outcome variables in a known direction. The test statistic can be thought of as the solution to an adversarial game, where the researcher determines the best linear combination of test statistics to combat nature's presentation of the worst-case pattern of hidden bias. The corresponding optimization problem is convex, and can be solved efficiently even for reasonably sized observational studies. Asymptotically the test statistic converges to a chi-bar-squared distribution under the null, a common distribution in order restricted statistical inference. The test attains the largest possible design sensitivity over a class of coherent test statistics, and facilitates one-sided sensitivity analyses for individual outcome variables while maintaining familywise error control through is incorporation into closed testing procedures.

中文翻译：

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匹配观察性研究中的多变量单边测试作为对抗性游戏

我们为匹配的观察性研究提供了多变量单边敏感性分析，适用于当研究人员指定给定的因果机制应该在已知方向上对多个结果变量的影响中表现出来。测试统计量可以被认为是对抗性游戏的解决方案，在这种博弈中，研究人员确定测试统计量的最佳线性组合，以对抗大自然对隐藏偏见的最坏情况模式的呈现。相应的优化问题是凸的，即使对于合理规模的观测研究也可以有效解决。渐近地，测试统计量收敛到零下的卡条平方分布，这是一种常见的分布，以限制统计推断。