Integrating gene set analysis and nonlinear predictive modeling of disease phenotypes using a Bayesian multitask formulation

Identifying molecular signatures of disease phenotypes is studied using two mainstream approaches: (i) Predictive modeling methods such as linear classification and regression algorithms are used to find signatures predictive of phenotypes from genomic data, which may not be robust due to limited sample size or highly correlated nature of genomic data. (ii) Gene set analysis methods are used to find gene sets on which phenotypes are linearly dependent by bringing prior biological knowledge into the analysis, which may not capture more complex nonlinear dependencies. Thus, formulating an integrated model of gene set analysis and nonlinear predictive modeling is of great practical importance. In this study, we propose a Bayesian binary classification framework to integrate gene set analysis and nonlinear predictive modeling. We then generalize this formulation to multitask learning setting to model multiple related datasets conjointly. Our main novelty is the probabilistic nonlinear formulation that enables us to robustly capture nonlinear dependencies between genomic data and phenotype even with small sample sizes. We demonstrate the performance of our algorithms using repeated random subsampling validation experiments on two cancer and two tuberculosis datasets by predicting important disease phenotypes from genome-wide gene expression data. We are able to obtain comparable or even better predictive performance than a baseline Bayesian nonlinear algorithm and to identify sparse sets of relevant genes and gene sets on all datasets. We also show that our multitask learning formulation enables us to further improve the generalization performance and to better understand biological processes behind disease phenotypes