A debiasing phylogenetic tree-assisted regression model for microbiome data

Abstract

Identifying associations between microbial taxa and sample features has always been a worthwhile issue in microbiome analysis and various regression-based methods have been proposed. These methods can roughly be divided into two types. One considers sparsity characteristic of the microbiome data in the analysis, and the other considers phylogenetic tree to employ evolutionary information. However, none of these methods apply both sparsity and phylogenetic tree thoroughly in the regression analysis with theoretical guarantees. To fill this gap, a phylogenetic tree-assisted regression model accompanied by a Lasso-type penalty is proposed to detect feature-related microbial compositions. Specifically, based on the rational assumption that the smaller the phylogenetic distance between two microbial species, the closer their coefficients in the regression model, the phylogenetic tree is accommodated into the regression model by constructing a Laplacian-type penalty in the loss function. Both linear regression model for continuous outcome and generalized linear regression model for categorical outcome are analyzed in this framework. Additionally, debiasing algorithms are proposed for the coefficient estimators to give more precise evaluation. Extensive numerical simulations and real data analyses demonstrate the higher efficiency of the proposed method.