  In many studies of human diseases, multiple omic datasets are measured.
Typically, these omic datasets are studied one by one with the disease, thus
the relationship between omics are overlooked. Modeling the joint part of
multiple omics and its association to the outcome disease will provide insights
into the complex molecular base of the disease. In this article, we extend
dimension reduction methods which model the joint part of omics to a novel
method that jointly models an outcome variable with omics. We establish the
model identifiability and develop EM algorithms to obtain maximum likelihood
estimators of the parameters for normally and Bernoulli distributed outcomes.
Test statistics are proposed to infer the association between the outcome and
omics, and their asymptotic distributions are derived. Extensive simulation
studies are conducted to evaluate the proposed model. The model is illustrated
by a Down syndrome study where Down syndrome and two omics - methylation and
glycomics - are jointly modeled.
