Relationship Between MiRKAT and Coefficient of Determination in Similarity Matrix Regression

Abstract

The Microbiome Regression-based Kernel Association Test (MiRKAT) is widely used in testing for the association between microbiome compositions and an outcome of interest. The MiRKAT statistic is derived as a variance-component score test in a kernel machine regression-based generalized linear mixed model. In this brief report, we show that the MiRKAT statistic is proportional to the R 2 (coefficient of determination) statistic in a similarity matrix regression, which characterizes the fraction of variability in outcome similarity, explained by microbiome similarity (up to a constant).