  Building classification models that predict a binary class label on the basis
of high dimensional multi-omics datasets poses several challenges, due to the
typically widely differing characteristics of the data layers in terms of
number of predictors, type of data, and levels of noise. Previous research has
shown that applying classical logistic regression with elastic-net penalty to
these datasets can lead to poor results (Liu et al., 2018). We implement a
two-step approach to multi-omic logistic regression in which variable selection
is performed on each layer separately and a predictive model is then built
using the variables selected in the first step. Here, our approach is compared
to other methods that have been developed for the same purpose, and we adapt
existing software for multi-omic linear regression (Zhao and Zucknick, 2020) to
the logistic regression setting. Extensive simulation studies show that our
approach should be preferred if the goal is to select as many relevant
predictors as possible, as well as achieving prediction performances comparable
to those of the best competitors. Our motivating example is a cardiometabolic
syndrome dataset comprising eight 'omic data types for 2 extreme phenotype
groups (10 obese and 10 lipodystrophy individuals) and 185 blood donors. Our
proposed approach allows us to identify features that characterise
cardiometabolic syndrome at the molecular level. R code is available at
https://github.com/acabassi/logistic-regression-for-multi-omic-data.
