Transfer Learning for Survival Analysis via Efficient L2,1-Norm Regularized Cox Regression

In survival analysis, the primary goal is to monitor several entities and model the occurrence of a particular event of interest. In such applications, it is quite often the case that the event of interest may not always be observed during the study period and this gives rise to the problem of censoring which cannot be easily handled in the standard regression approaches. In addition, obtaining sufficient labeled training instances for learning a robust prediction model is a very time consuming process and can be extremely difficult in practice. In this paper, we propose a transfer learning based Cox method, called Transfer-Cox, which uses auxiliary data to augment learning when there are insufficient amount of training examples. The proposed method aims to extract "useful" knowledge from the source domain and transfer it to the target domain, thus potentially improving the prediction performance in such time-to-event data. The proposed method uses the l_2,1-norm penalty to encourage multiple predictors to share similar sparsity patterns, thus learns a shared representation across source and target domains, potentially improving the model performance on the target task. To speedup the computation, we apply the screening approach and extend the strong rule to sparse survival analysis models in multiple high-dimensional censored datasets. We demonstrate the performance of the proposed transfer learning method using several synthetic and high-dimensional microarray gene expression benchmark datasets and compare with other related competing state-of-the-art methods. Our results show that the proposed screening approach significantly improves the computational efficiency of the proposed algorithm without compromising the prediction performance. We also demonstrate the scalability of the proposed approach and show that the time taken to obtain the results is linear with respect to both the number of instances and features.