The Annals of Applied Statistics

A phylogenetic scan test on a Dirichlet-tree multinomial model for microbiome data

Yunfan Tang, Li Ma, and Dan L. Nicolae

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In this paper, we introduce the phylogenetic scan test (PhyloScan) for investigating cross-group differences in microbiome compositions using the Dirichlet-tree multinomial (DTM) model. DTM models the microbiome data through a cascade of independent local DMs on the internal nodes of the phylogenetic tree. Each of the local DMs captures the count distributions of a certain number of operational taxonomic units at a given resolution. Since distributional differences tend to occur in clusters along evolutionary lineages, we design a scan statistic over the phylogenetic tree to allow nodes to borrow signal strength from their parents and children. We also derive a formula to bound the tail probability of the scan statistic, and verify its accuracy through simulations. The PhyloScan procedure is applied to the American Gut dataset to identify taxa associated with diet habits. Empirical studies performed on this dataset show that PhyloScan achieves higher testing power in most cases.

Article information

Ann. Appl. Stat., Volume 12, Number 1 (2018), 1-26.

Received: October 2016
Revised: March 2017
First available in Project Euclid: 9 March 2018

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Zentralblatt MATH identifier

Dirichlet-multinomial microbiome Dirichlet-tree multinomial phylogenetic tree PhyloScan scan statistics union probability


Tang, Yunfan; Ma, Li; Nicolae, Dan L. A phylogenetic scan test on a Dirichlet-tree multinomial model for microbiome data. Ann. Appl. Stat. 12 (2018), no. 1, 1--26. doi:10.1214/17-AOAS1086.

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Supplemental materials

  • Theorem proofs. This supplementary file contains proofs of independence of DTM p-value under the global null (Theorem 1) and error bound of PhyloScan statistic approximation (Theorem 2).