Compositionally Aware Phylogenetic Beta-Diversity Measures Better Resolve Microbiomes Associated with Phenotype.

Microbiome data have several specific characteristics (sparsity and compositionality) that introduce challenges in data analysis. The integration of prior information regarding the data structure, such as phylogenetic structure and repeated-measure study designs, into analysis, is an effective approach for revealing robust patterns in microbiome data. Past methods have addressed some but not all of these challenges and features: for example, robust principal-component analysis (RPCA) addresses sparsity and compositionality; compositional tensor factorization (CTF) addresses sparsity, compositionality, and repeated measure study designs; and UniFrac incorporates phylogenetic information. Here we introduce a strategy of incorporating phylogenetic information into RPCA and CTF. The resulting methods, phylo-RPCA, and phylo-CTF, provide substantial improvements over state-of-the-art methods in terms of discriminatory power of underlying clustering ranging from the mode of delivery to adult human lifestyle. We demonstrate quantitatively that the addition of phylogenetic information improves effect size and classification accuracy in both data-driven simulated data and real microbiome data. Microbiome data analysis can be difficult because of particular data features, some unavoidable and some due to technical limitations of DNA sequencing instruments. The first step in many analyses that ultimately reveals patterns of similarities and differences among sets of samples (e.g., separating samples from sick and healthy people or samples from seawater versus soil) is calculating the difference between each pair of samples. We introduce two new methods to calculate these differences that combine features of past methods, specifically being able to take into account the principles that most types of microbes are not in most samples (sparsity), that abundances are relative rather than absolute (compositionality), and that all microbes have a shared evolutionary history (phylogeny). We show using simulated and real data that our new methods provide improved classification accuracy of ordinal sample clusters and increased effect size between sample groups on beta-diversity distances.