DirichletMultinomial

DirichletMultinomial models variability in microbial metagenomic count data using Dirichlet multinomial mixtures to infer taxa probability vectors, cluster samples into metacommunities, and assess associations with conditions or treatments.

Key Features:

• Probabilistic Modeling: Represents microbial communities as vectors of taxa probabilities drawn from Dirichlet mixture components parameterized by component-specific hyperparameters.
• Metacommunity Clustering: Clusters samples into metacommunities (enterotypes/envirotypes) via multinomial sampling from Dirichlet mixture components.
• Treatment Impact and Classification: Assesses associations between microbial compositions and conditions or interventions and supports classification by component membership.
• Evidence Framework and Laplace Approximation: Fits DMM models within an evidence framework and estimates model evidence using the Laplace approximation.

Scientific Applications:

• Human Gut Microbiome Studies: Applied to human gut genus-frequency data from obese and lean twins to identify four clusters—two Bacteroides-dominated homogeneous clusters and two higher-variance clusters—and found no significant overall effect of body mass but an increased probability that obesity derives from high-variance clusters.
• Anna Karenina Principle (AKP) and Inflammatory Bowel Disease: Supports the AKP by showing disturbed states exhibit greater variability, exemplified by an inflammatory bowel disease study where ileal Crohn's disease is associated with more variable community compositions.

Methodology:

Fits Dirichlet multinomial mixture models to taxa count matrices, models taxa probability vectors per mixture component, uses multinomial sampling for sample generation, and estimates model evidence via the Laplace approximation within an evidence framework.