Meta‐analysis is a practical and powerful analytic tool that enables a unified statistical inference across the results from multiple studies. Notably, researchers often report the results on multiple related markers in each study (eg, various α‐diversity indices in microbiome studies). However, univariate meta‐analyses are limited to combining the results on a single common marker at a time, whereas existing multivariate meta‐analyses are limited to the situations where marker‐by‐marker correlations are given in each study. Thus, here we introduce two meta‐analysis methods, multi‐marker meta‐analysis (mMeta) and adaptive multi‐marker meta‐analysis (aMeta), to combine multiple studies throughout multiple related markers with no priori results on marker‐by‐marker correlations. mMeta is a statistical estimator for a pooled estimate and its SE across all the studies and markers, whereas aMeta is a statistical test based on the test statistic of the minimum P‐value among marker‐specific meta‐analyses. mMeta conducts both effect estimation and hypothesis testing based on a weighted average of marker‐specific pooled estimates while estimating marker‐by‐marker correlations non‐parametrically via permutations, yet its power is only moderate. In contrast, aMeta closely approaches the highest power among marker‐specific meta‐analyses, yet it is limited to hypothesis testing. While their applications can be broader, we illustrate the use of mMeta and aMeta to combine microbiome studies throughout multiple α‐diversity indices. We evaluate mMeta and aMeta in silico and apply them to real microbiome studies on the disparity in α‐diversity by the status of human immunodeficiency virus (HIV) infection. The R package for mMeta and aMeta is freely available at https://github.com/hk1785/mMeta.

中文翻译：

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多个相关标志物的 Meta 分析方法：应用到微生物组研究中，并获得多个 α 多样性指数的结果

Meta 分析是一种实用且功能强大的分析工具，可以对多项研究的结果进行统一的统计推断。值得注意的是，研究人员经常在每项研究中报告多个相关标记的结果（例如，微生物组研究中的各种α-多样性指数）。然而，单变量荟萃分析仅限于一次将结果组合在一个共同的标记上，而现有的多变量荟萃分析仅限于在每项研究中给出逐个标记相关性的情况。因此，在这里我们介绍了两种荟萃分析方法，多标记荟萃分析（mMeta）和自适应多标记荟萃分析（aMeta ），以无先验地结合多个相关标记的多项研究逐个标记相关性的结果。mMeta是针对所有研究和标记的汇总估计及其 SE 的统计估计量，而aMeta是基于标记特异性荟萃分析中最小P值的检验统计量的统计检验。mMeta基于标记特定汇总估计的加权平均值进行效果估计和假设检验，同时通过排列以非参数方式估计逐标记相关性，但其功效仅适中。相比之下，aMeta在标记特异性荟萃分析中接近最高功效，但仅限于假设检验。虽然它们的应用范围可能更广泛，但我们说明了mMeta和aMeta在多个α多样性指数中结合微生物组研究。我们在计算机上评估mMeta和aMeta，并将它们应用于真实的微生物组研究，研究人类免疫缺陷病毒 (HIV) 感染状态对α多样性的差异。mMeta和aMeta的 R 包可在 https://github.com/hk1785/mMeta 免费获得。