Phylogenetic Association Analysis with Conditional Rank Correlation

Summary Phylogenetic association analysis plays a crucial role in investigating the correlation between microbial compositions and specific outcomes of interest in microbiome studies. However, existing methods for testing such associations have limitations related to the assumption of a linear association in high-dimensional settings and the handling of confounding effects. Therefore, there is a need for methods capable of characterizing complex associations, including nonmonotonic relationships. This paper introduces a novel phylogenetic association analysis framework and associated tests to address these challenges by employing conditional rank correlation as a measure of association. These tests account for confounders in a fully nonparametric manner, ensuring robustness against outliers and the ability to detect diverse dependencies. The proposed framework aggregates conditional rank correlations for subtrees using a weighted sum and maximum approach to capture both dense and sparse signals. The significance level of the test statistics is determined by calibrating through a nearest neighbour bootstrapping method, which is straightforward to implement and can accommodate additional datasets when available. The practical advantages of the proposed framework are demonstrated through numerical experiments utilizing both simulated and real microbiome datasets.