Abstract：
We consider the problem of testing multiple null hypotheses, where a decision to reject or retain must be made for each one and embedding incorrect decisions into a real-life context may inflict different losses. We argue that traditional methods controlling the Type I error rate may be too restrictive in this situation and that the standard familywise error rate may not be appropriate. Using a decision-theoretic approach, we define suitable loss functions for a given decision rule, where incorrect decisions can be treated unequally by assigning different loss values. Taking expectation with respect to the sampling distribution of the data allows us to control the familywise expected loss instead of the conventional familywise error rate. Different loss functions can be adopted, and we search for decision rules that satisfy certain optimality criteria within a broad class of decision rules for which the expected loss is bounded by a fixed threshold under any parameter configuration. We illustrate the methods with the problem of establishing efficacy of a new medicinal treatment in non-overlapping subgroups of patients.
摘要：
我们考虑测试多个零假设的问题，必须为每个人做出拒绝或保留的决定，并且将不正确的决定嵌入现实生活中可能会造成不同的损失。我们认为，在这种情况下，控制I型错误率的传统方法可能过于严格，并且标准的家庭错误率可能不合适。使用决策理论方法，我们为给定的决策规则定义合适的损失函数，其中错误的决策可以通过分配不同的损失值来不平等地对待。对数据的抽样分布采取期望使我们能够控制按家庭预期的损失，而不是传统的按家庭的错误率。可以采用不同的损失函数，并且我们在广泛的决策规则类别中搜索满足某些最优性标准的决策规则，在任何参数配置下，预期损失都受到固定阈值的限制。我们说明了在非重叠患者亚组中建立新药物治疗功效的方法。
