Bertolino Francesco, Cabras Stefano, Castellanos Maria Eugenia, Racugno Walter
Department of Mathematics and Informatics, University of Cagliari, via Ospedale 72, Cagliari, Italy.
Department of Mathematics and Informatics, University of Cagliari, via Ospedale 72, Cagliari, Italy
Stat Methods Med Res. 2015 Dec;24(6):1030-43. doi: 10.1177/0962280212437827. Epub 2012 Feb 15.
Multiple hypothesis testing collects a series of techniques usually based on p-values as a summary of the available evidence from many statistical tests. In hypothesis testing, under a Bayesian perspective, the evidence for a specified hypothesis against an alternative, conditionally on data, is given by the Bayes factor. In this study, we approach multiple hypothesis testing based on both Bayes factors and p-values, regarding multiple hypothesis testing as a multiple model selection problem. To obtain the Bayes factors we assume default priors that are typically improper. In this case, the Bayes factor is usually undetermined due to the ratio of prior pseudo-constants. We show that ignoring prior pseudo-constants leads to unscaled Bayes factor which do not invalidate the inferential procedure in multiple hypothesis testing, because they are used within a comparative scheme. In fact, using partial information from the p-values, we are able to approximate the sampling null distribution of the unscaled Bayes factor and use it within Efron's multiple testing procedure. The simulation study suggests that under normal sampling model and even with small sample sizes, our approach provides false positive and false negative proportions that are less than other common multiple hypothesis testing approaches based only on p-values. The proposed procedure is illustrated in two simulation studies, and the advantages of its use are showed in the analysis of two microarray experiments.
多重假设检验收集了一系列通常基于p值的技术，作为来自许多统计检验的现有证据的总结。在假设检验中，从贝叶斯的角度来看，针对备择假设的特定假设的证据，以数据为条件，由贝叶斯因子给出。在本研究中，我们基于贝叶斯因子和p值来处理多重假设检验，将多重假设检验视为一个多重模型选择问题。为了获得贝叶斯因子，我们假设了通常不合适的默认先验。在这种情况下，由于先验伪常数的比率，贝叶斯因子通常是不确定的。我们表明，忽略先验伪常数会导致未缩放的贝叶斯因子，这不会使多重假设检验中的推断程序无效，因为它们是在比较方案中使用的。事实上，利用p值的部分信息，我们能够近似未缩放贝叶斯因子的抽样零分布，并在埃弗龙多重检验程序中使用它。模拟研究表明，在正态抽样模型下，即使样本量较小，我们的方法提供的假阳性和假阴性比例也小于仅基于p值的其他常见多重假设检验方法。在两个模拟研究中对所提出的程序进行了说明，并在两个微阵列实验的分析中展示了其使用的优势。
