Accurate prognosis of patients with cancer is important for the stratification of patients, the optimization of treatment strategies, and the design of clinical trials. Both clinical features and molecular data can be used for this purpose, for instance, to predict the survival of patients censored at specific time points. Multi-omics data, including genome-wide gene expression, methylation, protein expression, copy number alteration, and somatic mutation data, are becoming increasingly common in cancer studies. To harness the rich information in multi-omics data, we developed GDP (Group lass regularized Deep learning for cancer Prognosis), a computational tool for survival prediction using both clinical and multi-omics data. GDP integrated a deep learning framework and Cox proportional hazard model (CPH) together, and applied group lasso regularization to incorporate gene-level group prior knowledge into the model training process. We evaluated its performance in both simulated and real data from The Cancer Genome Atlas (TCGA) project. In simulated data, our results supported the importance of group prior information in the regularization of the model. Compared to the standard lasso regularization, we showed that group lasso achieved higher prediction accuracy when the group prior knowledge was provided. We also found that GDP performed better than CPH for complex survival data. Furthermore, analysis on real data demonstrated that GDP performed favorably against other methods in several cancers with large-scale omics data sets, such as glioblastoma multiforme, kidney renal clear cell carcinoma, and bladder urothelial carcinoma. In summary, we demonstrated that GDP is a powerful tool for prognosis of patients with cancer, especially when large-scale molecular features are available.
Efficient Asynchronous Semi-stochastic Block Coordinate Descent Methods for Large-Scale SVD