Two-sample tests of high-dimensional means for compositional data

Yuanpei Cao, Wei Lin and Hongzhe Li

Biometrika, 2018, vol. 105, issue 1, 115-132

Abstract: Summary Compositional data are ubiquitous in many scientific endeavours. Motivated by microbiome and metagenomic research, we consider a two-sample testing problem for high-dimensional compositional data and formulate a testable hypothesis of compositional equivalence for the means of two latent log basis vectors. We propose a test through the centred log-ratio transformation of the compositions. The asymptotic null distribution of the test statistic is derived and its power against sparse alternatives is investigated. A modified test for paired samples is also considered. Simulations show that the proposed tests can be significantly more powerful than tests that are applied to the raw and log-transformed compositions. The usefulness of our tests is illustrated by applications to gut microbiome composition in obesity and Crohn’s disease.

Keywords: Basis; Centred log-ratio transformation; Compositional equivalence; Extreme value distribution; Microbiome; Sparse alternative (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (3)

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