A Minimax Optimal Ridge-Type Set Test for Global Hypothesis With Applications in Whole Genome Sequencing Association Studies

Testing a global hypothesis for a set of variables is a fundamental problem in statistics with a wide range of applications. A few well-known classical tests include the Hotelling’s <i>T</i> ² test, the <i>F</i>-test, and the empirical Bayes based score test. These classical tests, however, are not robust to the signal strength and could have a substantial loss of power when signals are weak or moderate, a situation we commonly encounter in contemporary applications. In this article, we propose a minimax optimal ridge-type set test (MORST), a simple and generic method for testing a global hypothesis. The power of MORST is robust and considerably higher than that of the classical tests when the strength of signals is weak or moderate. In the meantime, MORST only requires a slight increase in computation compared to these existing tests, making it applicable to the analysis of massive genome-wide data. We also provide the generalizations of MORST that are parallel to the traditional Wald test and Rao’s score test in asymptotic settings. Extensive simulations demonstrated the robust power of MORST and that the Type I error of MORST was well controlled. We applied MORST to the analysis of the whole-genome sequencing data from the Atherosclerosis Risk in Communities study, where MORST detected 20%–250% more signal regions than the classical tests. Supplementary materials for this article are available online.

针对一组变量开展全局假设检验是统计学中的基础性问题，拥有广泛的应用场景。若干经典知名检验方法包括霍特林T²检验（Hotelling’s T² test）、F检验，以及基于经验贝叶斯的得分检验。然而，这类经典检验方法对信号强度缺乏鲁棒性，当信号较弱或处于中等强度时，其检验效能会出现显著损失——而这正是当代应用中十分常见的情形。本文提出一种极小化极大最优岭型集合检验（minimax optimal ridge-type set test, MORST），这是一种简洁通用的全局假设检验方法。当信号强度偏弱或中等时，MORST的检验效能具备鲁棒性，且显著优于经典检验方法。与此同时，相较于现有检验方法，MORST仅需小幅增加计算量，即可适用于大规模全基因组数据分析。我们还推导了MORST在渐近场景下的推广形式，其对应于传统沃尔德检验（Wald test）与劳得分检验（Rao’s score test）。大量模拟实验证实了MORST的鲁棒检验效能，且其一类错误（Type I error）得到了良好控制。我们将MORST应用于社区动脉粥样硬化风险研究（Atherosclerosis Risk in Communities study）的全基因组测序数据分析，结果显示MORST相较于经典检验方法多检出20%至250%的信号区域。本文的补充材料可在线获取。