Meta-analysis methods for multiple related markers: Applications to microbiome studies with the results on multiple α-diversity indices

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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

Original languageEnglish (US)
Pages (from-to)2859-2876
Number of pages18
JournalStatistics in Medicine
Issue number12
StatePublished - May 30 2021


  • adaptive meta-analysis
  • meta-analysis for microbiome studies
  • meta-analysis for α-diversity indices
  • multi-marker meta-analysis
  • non-parametric meta-analysis
  • random effects meta-analysis

ASJC Scopus subject areas

  • Epidemiology
  • Statistics and Probability


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