Exploring Pathway-Based Group Lasso for Cancer Survival Analysis: A Special Case of Multi-Task Learning

Motivation: The Cox proportional hazard models are widely used in the study of cancer survival. However, these models often meet challenges such as the large number of features and small sample sizes of cancer data sets. While this issue can be partially solved by applying regularization techniques such as lasso, the models still suffer from unsatisfactory predictive power and low stability. Methods: Here, we investigated two methods to improve survival models. Firstly, we leveraged the biological knowledge that groups of genes act together in pathways and regularized both at the group and gene level using latent group lasso penalty term. Secondly, we designed and applied a multi-task learning penalty that allowed us leveraging the relationship between survival models for different cancers. Results: We observed modest improvements over the simple lasso model with the inclusion of latent group lasso penalty for six of the 16 cancer types tested. The addition of a multi-task penalty, which penalized coefficients in pairs of cancers from diverging too greatly, significantly improved accuracy for a single cancer, lung squamous cell carcinoma, while having minimal effect on other cancer types. Conclusion: While the use of pathway information and multi-tasking shows some promise, these methods do not provide a substantial improvement when compared with standard methods.