{'fraction_non_alphanumeric': 0.03244078269824923, 'fraction_numerical': 0.0020597322348094747, 'mean_word_length': 5.865724381625442, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 1, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Meta‐analysis methods for multiple related markers: Applications to microbiome studies with the results on multiple α‐diversity indices

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.