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

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  • Yuanpei Cao
  • Wei Lin
  • Hongzhe Li

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.

Suggested Citation

  • Yuanpei Cao & Wei Lin & Hongzhe Li, 2018. "Two-sample tests of high-dimensional means for compositional data," Biometrika, Biometrika Trust, vol. 105(1), pages 115-132.
    • Handle: RePEc:oup:biomet:v:105:y:2018:i:1:p:115-132.
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    File URL: http://hdl.handle.net/10.1093/biomet/asx060
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    Cited by:

    1. Huang, Yuan & Li, Changcheng & Li, Runze & Yang, Songshan, 2022. "An overview of tests on high-dimensional means," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    2. Jiarui Lu & Pixu Shi & Hongzhe Li, 2019. "Generalized linear models with linear constraints for microbiome compositional data," Biometrics, The International Biometric Society, vol. 75(1), pages 235-244, March.

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