Cox Regression with Correlation Based Regularization for Electronic Health Records

Survival Regression models play a vital role in analyzing time-to-event data in many practical applications ranging from engineering to economics to healthcare. These models are ideal for prediction in complex data problems where the response is a time-to-event variable. An event is defined as the occurrence of a specific event of interest such as a chronic health condition. Cox regression is one of the most popular survival regression model used in such applications. However, these models have the tendency to over fit the data which is not desirable for healthcare applications because it limits their generalization to other hospital scenarios. In this paper, we address these challenges for the cox regression model. We combine two unique correlation based regularizers with cox regression to handle correlated and grouped features which are commonly seen in many practical problems. The proposed optimization problems are solved efficiently using cyclic coordinate descent and Alternate Direction Method of Multipliers algorithms. We conduct experimental analysis on the performance of these algorithms over several synthetic datasets and electronic health records (EHR) data about heart failure diagnosed patients from a hospital. We demonstrate through our experiments that these regularizers effectively enhance the ability of cox regression to handle correlated features. In addition, we extensively compare our results with other regularized linear and logistic regression algorithms. We validate the goodness of the features selected by these regularized cox regression models using the biomedical literature and different feature selection algorithms.