Multi-task Survival Analysis

Collecting labeling information of time-to-event analysis is naturally very time consuming, i.e., one has to wait for the occurrence of the event of interest, which may not always be observed for every instance. By taking advantage of censored instances, survival analysis methods internally consider more samples than standard regression methods, which partially alleviates this data insufficiency problem. Whereas most existing survival analysis models merely focus on a single survival prediction task, when there are multiple related survival prediction tasks, we may benefit from the tasks relatedness. Simultaneously learning multiple related tasks, multi-task learning (MTL) provides a paradigm to alleviate data insufficiency by bridging data from all tasks and improves generalization performance of all tasks involved. Even though MTL has been extensively studied, there is no existing work investigating MTL for survival analysis. In this paper, we propose a novel multi-task survival analysis framework that takes advantage of both censored instances and task relatedness. Specifically, based on two common used task relatedness assumptions, i.e., low-rank assumption and cluster structure assumption, we formulate two concrete models, COX-TRACE and COX-cCMTL, under the proposed framework, respectively. We develop efficient algorithms and demonstrate the performance of the proposed multi-task survival analysis models on the The Cancer Genome Atlas (TCGA) dataset. Our results show that the proposed approaches can significantly improve the prediction performance in survival analysis and can also discover some inherent relationships among different cancer types.