Microorganisms such as bacteria do not exist in isolation but form complex ecologies with various interactions. The environment, such as the age or diet of the host, can greatly impact the composition and structure of these microbial communities. Differential analysis of microbial community structures aims to elucidate such systematic changes during an adaptive response to changes in the environment. In this paper, we propose a flexible Markov random field model for learning the microbial community structure and introduce a testing framework for detecting the difference between networks, also known as differential network analysis. Our global test for differential networks is particularly powerful against sparse alternatives. In addition, we develop a multiple testing procedure with false discovery rate control to infer the structure of the differential network. The proposed method is applied to a gut microbiome study on UK twins to detect the microbial interactions associated with the age of the host.
Keywords High dimensional logistic regression; Differential network; Multiple testing; Microbiome; Microbial community.