Gene and pathway identification with L_p penalized Bayesian logistic regression

Background: Identifying genes and pathways associated with diseases such as cancer has been a subject of considerable research in recent years in the area of bioinformatics and computational biology. It has been demonstrated that the magnitude of differential expression does not necessarily indicate biological significance. Even a very small change in the expression of particular gene may have dramatic physiological consequences if the protein encoded by this gene plays a catalytic role in a specific cell function. Moreover, highly correlated genes may function together on the same pathway biologically. Finally, in sparse logistic regression with Lp (p < 1) penalty, the degree of the sparsity obtained is determined by the value of the regularization parameter. Usually this parameter must be carefully tuned through cross-validation, which is time consuming. Results: In this paper, we proposed a simple Bayesian approach to integrate the regularization parameter out analytically using a new prior. Therefore, there is no longer a need for parameter selection, as it is eliminated entirely from the model. The proposed algorithm (BLpLog) is typically two or three orders of magnitude faster than the original algorithm and free from bias in performance estimation. We also define a novel similarity measure and develop an integrated algorithm to hunt the regulatory genes with low expression changes but having high correlation with the selected genes. Pathways of those correlated genes were identified with DAVID http://david.abcc.ncifcrf.gov/. Conclusion: Experimental results with gene expression data demonstrate that the proposed methods can be utilized to identify important genes and pathways that are related to cancer and build a parsimonious model for future patient predictions.