Identification of prognostic genes and gene sets for early-stage non-small cell lung cancer using bi-level selection methods.

In contrast to feature selection and gene set analysis, bi-level selection is a process of selecting not only important gene sets but also important genes within those gene sets. Depending on the order of selections, a bi-level selection method can be classified into three categories - forward selection, which first selects relevant gene sets followed by the selection of relevant individual genes; backward selection which takes the reversed order; and simultaneous selection, which performs the two tasks simultaneously usually with the aids of a penalized regression model. To test the existence of subtype-specific prognostic genes for non-small cell lung cancer (NSCLC), we had previously proposed the Cox-filter method that examines the association between patients' survival time after diagnosis with one specific gene, the disease subtypes, and their interaction terms. In this study, we further extend it to carry out forward and backward bi-level selection. Using simulations and a NSCLC application, we demonstrate that the forward selection outperforms the backward selection and other relevant algorithms in our setting. Both proposed methods are readily understandable and interpretable. Therefore, they represent useful tools for the researchers who are interested in exploring the prognostic value of gene expression data for specific subtypes or stages of a disease.