  In this article, we propose a new method named fused mixed graphical model
(FMGM), which can infer network structures for dichotomous phenotypes. We
assumed that the interplay of different omics markers is associated with
disease status and proposed an FMGM-based method to detect the associated omics
marker network difference. The statistical models of the networks were based on
a pairwise Markov random field model, and penalty functions were added to
minimize the effect of sparseness in the networks. The fast proximal gradient
method (PGM) was used to optimize the target function. Method validity was
measured using synthetic datasets that simulate power-law network structures,
and it was found that FMGM showed superior performance, especially in terms of
F1 scores, compared with the previous method inferring the networks
sequentially (0.392 and 0.546). FMGM performed better not only in identifying
the differences (0.217 and 0.410) but also in identifying the networks (0.492
and 0.572). The proposed method was applied to multi-omics profiles of
6-month-old infants with and without atopic dermatitis (AD), and different
correlations were found between the abundance of microbial genes related to
carotenoid biosynthesis and RNA degradation according to disease status,
suggesting the importance of metabolism related to oxidative stress and
microbial RNA balance.

Methodology;Quantitative Methods