A Bayesian method for detecting pairwise associations in compositional data

TitleA Bayesian method for detecting pairwise associations in compositional data
Publication TypeJournal Article
Year of Publication2017
AuthorsSchwager E, Mallick H, Ventz S, Huttenhower C
JournalPLoS Comput Biol
Volume13
Issue11
Paginatione1005852
Date Published2017 Nov
ISSN1553-7358
KeywordsAlgorithms, Bayes Theorem, Computational Biology, Computer Simulation, Ecology, Humans, Markov Chains, Microbiota, Models, Biological, Proteobacteria
Abstract

Compositional data consist of vectors of proportions normalized to a constant sum from a basis of unobserved counts. The sum constraint makes inference on correlations between unconstrained features challenging due to the information loss from normalization. However, such correlations are of long-standing interest in fields including ecology. We propose a novel Bayesian framework (BAnOCC: Bayesian Analysis of Compositional Covariance) to estimate a sparse precision matrix through a LASSO prior. The resulting posterior, generated by MCMC sampling, allows uncertainty quantification of any function of the precision matrix, including the correlation matrix. We also use a first-order Taylor expansion to approximate the transformation from the unobserved counts to the composition in order to investigate what characteristics of the unobserved counts can make the correlations more or less difficult to infer. On simulated datasets, we show that BAnOCC infers the true network as well as previous methods while offering the advantage of posterior inference. Larger and more realistic simulated datasets further showed that BAnOCC performs well as measured by type I and type II error rates. Finally, we apply BAnOCC to a microbial ecology dataset from the Human Microbiome Project, which in addition to reproducing established ecological results revealed unique, competition-based roles for Proteobacteria in multiple distinct habitats.

DOI10.1371/journal.pcbi.1005852
Alternate JournalPLoS Comput Biol
PubMed ID29140991
PubMed Central IDPMC5706738
Grant ListR01 HG005220 / HG / NHGRI NIH HHS / United States
T32 GM074897 / GM / NIGMS NIH HHS / United States
U54 DE023798 / DE / NIDCR NIH HHS / United States
U54 DK102557 / DK / NIDDK NIH HHS / United States