An adaptive independence test for microbiome community data

Advances in sequencing technologies and bioinformatics tools have vastly improved our ability to collect and analyze data from complex microbial communities. A major goal of microbiome studies is to correlate the overall microbiome composition with clinical or environmental variables. La Rosa et al. recently proposed a parametric test for comparing microbiome populations between two or more groups of subjects. However, this method is not applicable for testing the association between the community composition and a continuous variable. Although multivariate nonparametric methods based on permutations are widely used in ecology studies, they lack interpretability and can be inefficient for analyzing microbiome data. We consider the problem of testing for independence between the microbial community composition and a continuous or many-valued variable. By partitioning the range of the variable into a few slices, we formulate the problem as a problem of comparing multiple groups of microbiome samples, with each group indexed by a slice. To model multivariate and over-dispersed count data, we use the Dirichlet-multinomial distribution. We propose an adaptive likelihood-ratio test by learning a good partition or slicing scheme from the data. A dynamic programming algorithm is developed for numerical optimization. We demonstrate the superiority of the proposed test by numerically comparing it with that of La Rosa et al. and other popular approaches on the same topic including PERMANOVA, the distance covariance test, and the microbiome regression-based kernel association test. We further apply it to test the association of gut microbiome with age in three geographically distinct populations and show how the learned partition facilitates differential abundance analysis.