A distance based multisample test for high-dimensional compositional data with applications to the human microbiome

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MET HODOLOGY

Open Access

A distance based multisample test for high-dimensional compositional data with applications to the human microbiome Qingyang Zhang*

and Thy Dao

From The 20th International Conference on Bioinformatics & Computational Biology (BIOCOMP 2019) Las Vegas, NV, USA. 29 July–01 August 2019 *Correspondence: [email protected] Department of Mathematical Sciences, University of Arkansas, Fayetteville, AR 72701, USA

Abstract Background: Compositional data refer to the data that lie on a simplex, which are common in many scientific domains such as genomics, geology and economics. As the components in a composition must sum to one, traditional tests based on unconstrained data become inappropriate, and new statistical methods are needed to analyze this special type of data. Results: In this paper, we consider a general problem of testing for the compositional difference between K populations. Motivated by microbiome and metagenomics studies, where the data are often over-dispersed and high-dimensional, we formulate a well-posed hypothesis from a Bayesian point of view and suggest a nonparametric test based on inter-point distance to evaluate statistical significance. Unlike most existing tests for compositional data, our method does not rely on any data transformation, sparsity assumption or regularity conditions on the covariance matrix, but directly analyzes the compositions. Simulated data and two real data sets on the human microbiome are used to illustrate the promise of our method. Conclusions: Our simulation studies and real data applications demonstrate that the proposed test is more sensitive to the compositional difference than the mean-based method, especially when the data are over-dispersed or zero-inflated. The proposed test is easy to implement and computationally efficient, facilitating its application to large-scale datasets. Keywords: Microbiome, Compositional data, High dimensionality, Centered log-ratio transformation, Multisample test, Distance correlation Background

   Data that lie on the simplex S d−1 = (x1 , x2 , ..., xd ), s.t. minj xj ≥ 0, dj=1 xj = 1 are often called (d − 1)-dimensional compositional data, and they arise in many scientific disciplines such as genomics, geology and economics [1–3]. As the components in a composition must sum to one, classic statistical tests including two-sample t-test and

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