Phylogenetic Association Analysis with Conditional Rank Correlation
Shulei Wang, Bo Yuan, Tony Cai, and Hongzhe Li
Phylogenetic association analysis is an essential and powerful tool for studying the association between microbial compositions and the outcome of interest in microbiome studies. However, existing methods for testing such associations are more sensitive to a linear association in a high-dimensional setting and the assumptions of confounding effects. Methods that are capable of characterizing complex association, including non-monotonic association, are therefore needed. This paper proposes a new phylogenetic association analysis framework to address these challenges. The new framework introduces conditional rank correlation as a measure of association to detect a wide range of dependencies, which is robust to the outlier, accounts for confounders in a fully nonparametric way. The new framework aggregates conditional rank correlations for subtrees as the weighted sum and maximum to capture dense and sparse signals. To determine the significance level, we calibrate the test statistics by a nearest neighbor bootstrapping method, which is easy to use and can incorporate extra data sets when available. The practical merits of the new framework are demonstrated by numerical experiments using both simulated and real microbiome data sets.