Identifying Microbial Interaction Networks Based on Irregularly Spaced Longitudinal 16S rRNA sequence data
Though being vital for human health, microbial interactions with their host and with each other are still largely obscure for researchers. To deepen the understanding, the analyses based on longitudinal data are a better choice than the cross-sectional data since the information provided by the former is usually more stable. To this end, in this paper, we first propose an EM-type algorithm to identify microbial interaction network for the irregularly spaced longitudinal measurements. Correlation functions are employed to account for the correlation across the temporal measurements for a given subject. The algorithms take advantage of the efficiency of the popular graphical lasso algorithm and can be implemented straightforwardly. Simulation studies show that the proposed algorithms can significantly outperform the conventional algorithms such as graphical lasso or neighborhood method when the correlation between measurements grows larger. In second part of the paper, based on a 16S rRNA sequence data set of gut microbiome, module-preserving permutation test is proposed to test the independence of the estimated network and the phylogeny of the microbe species. The results demonstrate evidences of strong association between the interaction network and the phylogenetic tree which indicates that the taxa closer in their genomes tend to have more/stronger interactions in their functions. The proposed algorithms can be implemented through R package lglasso at \url{https://github.com/jiezhou-2/lglasso