Exact Tests of Zero Variance Component in Presence of Multiple VarianceComponents with Application to Longitudinal Microbiome Study

In the metagenomics studies, testing the association of microbiome composition and clinical conditions translates to testing the nullity of variance components. Computationally efficient score tests have been the major tools. But they can only apply to the null hypothesis with a single variance component and when sample sizes are large. Therefore, they are not applicable to longitudinal microbiome studies. In this paper, we propose exact tests (score test, likelihood ratio test, and restricted likelihood ratio test) to solve the problems of (1) testing the association of the overall microbiome composition in a longitudinal design and (2) detecting the association of one specific microbiome cluster while adjusting for the effects from related clusters. Our approach combines the exact tests for null hypothesis with a single variance component with a strategy of reducing multiple variance components to a single one. Simulation studies demonstrate that our method has correct type I error rate and superior power compared to existing methods at small sample sizes and weak signals. Finally, we apply our method to a longitudinal pulmonary microbiome study of human immunodeficiency virus (HIV) infected patients and reveal two interesting genera Prevotella and Veillonella associated with forced vital capacity. Our findings shed lights on the impact of lung microbiome to HIV complexities. The method is implemented in the open source, high-performance computing language Julia and is freely available at https://github.com/JingZhai63/VCmicrobiome.