CAT: a conditional association test for microbiome data using a permutation approach.

In microbiome analysis, researchers often seek to identify taxonomic features associated with an outcome of interest. However, microbiome features are intercorrelated and linked by phylogenetic relationships, making it challenging to assess the association between an individual feature and an outcome. This paper proposes a novel conditional association test, CAT, that can account for other features and phylogenetic relatedness when testing the association between a feature and an outcome. CAT adopts a permutation approach, measuring the importance of a feature in predicting the outcome by permuting operational taxonomic unit/amplicon sequence variant counts belonging to that feature from the data and quantifying how much the association with the outcome is weakened through the change in the coefficient of determination $R^{2}$. Compared with marginal association tests, it focuses on the added value of a feature in explaining outcome variation that is not captured by other features. By leveraging global tests including PERMANOVA and MiRKAT-based methods, CAT allows association testing for continuous, binary, categorical, count, survival, and correlated outcomes. We demonstrate through simulation studies that CAT can provide a direct quantification of feature importance that is distinct from that of marginal association tests, and illustrate CAT with applications to two real-world studies on the microbiome in melanoma patients: one examining the role of the microbiome in shaping immunotherapy response, and one investigating the association between the microbiome and survival outcomes. Our results illustrate the potential of CAT to inform the design of microbiome interventions aimed at improving clinical outcomes.