Inference for microbe-metabolite association networks using a latent graph model

Correlation networks are commonly used to infer associations between microbes and metabolites. The resulting $p$-values are then corrected for multiple comparisons using existing methods such as the Benjamini & Hochberg (BH) procedure to control the false discovery rate (FDR). However, most existing methods for FDR control assume the $p$-values are weakly dependent. Consequently, they can have low power in recovering microbe-metabolite association networks that exhibit important topological features, such as the presence of densely associated modules. We propose a novel inference procedure that is both powerful for detecting significant associations in the microbe-metabolite network and capable of controlling the FDR. Power enhancement is achieved by modeling latent structures in the form of a bipartite stochastic block model. We develop a variational expectation-maximization (EM) algorithm to estimate the model parameters and incorporate the learned graph in the testing procedure. In addition to FDR control, this procedure provides a clustering of microbes and metabolites into modules, which is useful for interpretation. We demonstrate the merit of the proposed method in simulations and an application to bacterial vaginosis.