Aggregating multiple effects is often encountered in large-scale data analysis where the fraction of significant effects is generally small. Many existing methods cannot handle it effectively because of lack of computational accuracy for small p-values. The Cauchy combination test (abbreviated as CCT) ( J Am Statist Assoc, 2020, 115(529):393-402) is a powerful and computational effective test to aggregate individual $p$-values under arbitrary correlation structures. This work revisits CCT and shows three key contributions including that (i) the tail probability of CCT can be well approximated by a standard Cauchy distribution under much more relaxed conditions placed on individual p-values instead of the original test statistics; (ii) the relaxation conditions are shown to be satisfied for many popular copulas formulating bivariate distributions; (iii) the power of CCT is no less than that of the minimum-type test as the number of tests goes to infinity with some regular conditions. These results further broaden the theories and applications of CCT. The simulation results verify the theoretic results and the performance of CCT is further evaluated with data from a prostate cancer study.
翻译:在大规模数据分析中往往会遇到多重效应的集合,因为重要效应的一小部分一般是很小的,许多现有方法无法有效处理这些效应,因为缺乏对小p价值的计算准确性。Cauchy组合试验(作为CCT进行) (J Am Statistist Assoc, 2020, 115 (529): 393-402) 是一个强大和计算有效的试验,在任意相关结构下对单个美元价值进行汇总。这项工作重新审视了CCT,并显示出三个主要贡献,包括:(一) CCT的尾部概率可以被标准CAuchy分布在对单个p-value所设定的更为宽松的条件下,而不是在最初的测试统计中加以比较容易得多地估计。 (二) 事实证明,对于编制双变分布的许多流行的 Cogulas (J Am Statististist Assoc, 2020, 115 (529): 393-402) 是一个强大的和计算有效的试验,在任意性关系结构下,CCT的力量不少于最低类型试验的数目,因为试验的数量与某些经常条件不相同。这些结果进一步扩大了CCT的理论和应用。这些结果进一步扩大了CCT的理论和应用。模拟结果对CCT的结果核查结果和CCT的实验结果进行了核查,对CCT的实验结果和表现进行了进一步评价。