Supervised group Lasso with applications to microarray data analysis

Abstract

Background: A tremendous amount of efforts have been devoted to identifying genes for diagnosis and prognosis of diseases using microarray gene expression data. It has been demonstrated that gene expression data have cluster structure, where the clusters consist of co-regulated genes which tend to have coordinated functions. However, most available statistical methods for gene selection do not take into consideration the cluster structure.

Results: We propose a supervised group Lasso approach that takes into account the cluster structure in gene expression data for gene selection and predictive model building. For gene expression data without biological cluster information, we first divide genes into clusters using the K-means approach and determine the optimal number of clusters using the Gap method. The supervised group Lasso consists of two steps. In the first step, we identify important genes within each cluster using the Lasso method. In the second step, we select important clusters using the group Lasso. Tuning parameters are determined using V-fold cross validation at both steps to allow for further flexibility. Prediction performance is evaluated using leave-one-out cross validation. We apply the proposed method to disease classification and survival analysis with microarray data.

Conclusion: We analyze four microarray data sets using the proposed approach: two cancer data sets with binary cancer occurrence as outcomes and two lymphoma data sets with survival outcomes. The results show that the proposed approach is capable of identifying a small number of influential gene clusters and important genes within those clusters, and has better prediction performance than existing methods.

Figure 1

Gap statistics as a function of number of clusters. Red solid line: Colon data; Green dashed line: Nodal data.

Figure 2

Paths of parameter estimates for Lasso, GLasso and SGLasso. Red lines, cluster 1; Blue lines, cluster 2; Green lines, cluster 3. Solid lines, β₁, β₄ and β₇; Dashed lines, β₂, β₅, and β₈; Dashed-Dotted lines, β₃, β₆, and β₉. The grey lines show the selected tuning parameters. C1, C2 and C3 in the lower-left panel denote clusters 1, 2 and 3, respectively.