Abstract

Standardization has been a widely adopted practice in multiple testing, for it takes into account the variability in sampling and makes the test statistics comparable across different study units. However, despite conventional wisdom to the contrary, we show that there can be a significant loss in information from basing hypothesis tests on standardized statistics rather than the full data. We develop a new class of heteroscedasticity-adjusted ranking and thresholding (HART) rules that aim to improve existing methods by simultaneously exploiting commonalities and adjusting heterogeneities among the study units. The main idea of HART is to bypass standardization by directly incorporating both the summary statistic and its variance into the testing procedure. A key message is that the variance structure of the alternative distribution, which is subsumed under standardized statistics, is highly informative and can be exploited to achieve higher power. The proposed HART procedure is shown to be asymptotically valid and optimal for false discovery rate (FDR) control. Our simulation results demonstrate that HART achieves substantial power gain over existing methods at the same FDR level. We illustrate the implementation through a microarray analysis of myeloma.

摘要

标准化在多重测试中已被广泛采用，因为它考虑了抽样的可变性，并使不同研究单元的测试统计数据具有可比性。然而，尽管与传统观念相反，我们表明，基于标准化统计而不是完整数据的假设检验可能会导致信息显着丢失。我们开发了一类新的异方差调整排序和阈值 (HART) 规则，旨在通过同时利用研究单元之间的共性和调整异质性来改进现有方法。HART 的主要思想是通过将汇总统计量及其方差直接合并到测试过程中来绕过标准化。一个关键信息是替代分布的方差结构，它包含在标准化统计数据中，信息量很大，可以用来实现更高的功率。所提出的 HART 程序被证明是渐近有效的，并且对于错误发现率 (FDR) 控制是最优的。我们的仿真结果表明，HART 在相同 FDR 级别上比现有方法实现了显着的功率增益。我们通过骨髓瘤的微阵列分析来说明实施。