Abstract

This article develops p-values for evaluating means of normal populations that make use of indirect or prior information. A p-value of this type is based on a biased frequentist hypothesis test that has optimal average power with respect to a probability distribution that encodes indirect information about the mean parameter, resulting in a smaller p-value if the indirect information is accurate. In a variety of multiparameter settings, we show how to adaptively estimate the indirect information for each mean parameter while still maintaining uniformity of the p-values under their null hypotheses. This is done using a linking model through which indirect information about the mean of one population may be obtained from the data of other populations. Importantly, the linking model does not need to be correct to maintain the uniformity of the p-values under their null hypotheses. This methodology is illustrated in several data analysis scenarios, including small area inference, spatially arranged populations, interactions in linear regression, and generalized linear models. Supplementary materials for this article are available online.

摘要

本文开发了p值，用于评估利用间接或先验信息的正常人群的平均值。这种类型的p值基于有偏的常客假设检验，该检验对于编码关于平均参数的间接信息的概率分布具有最佳平均功率，如果间接信息准确，则导致较小的p值。在各种多参数设置中，我们展示了如何自适应地估计每个平均参数的间接信息，同时仍然保持p的均匀性-在他们的零假设下的值。这是使用链接模型完成的，通过该模型可以从其他人群的数据中获得有关一个​​人群平均值的间接信息。重要的是，链接模型不需要是正确的，也可以在零假设下保持p值的一致性。这种方法在几个数据分析场景中得到了说明，包括小区域推断、空间排列的种群、线性回归中的交互和广义线性模型。本文的补充材料可在线获取。