The Coxlogit model: Feature selection from survival and classification data

This paper proposes a novel approach to select features that are jointly predictive of survival times and classification within subgroups. Both tasks are common but generally tackled independently in clinical data analysis. Here we propose an embedded feature selection to select common markers, i.e. genes, for both tasks seen as a multi-objective optimization. The Coxlogit model relies on a Cox proportional hazard model and a logistic regression that are constrained to share the same weights. Such model is further regularized through an elastic net penalty to enforce a common sparse support and to prevent overfitting. The model is estimated through a coordinate ascent algorithm maximizing a regularized log-likelihood. This Coxlogit approach is validated on synthetic and real breast cancer data. Those experiments illustrate that the proposed approach offers similar predictive performances than a Cox model for survival times or a logistic regression for classification. Yet the proposed approach is shown to outperform those standard techniques at selecting discriminant features that are informative for both tasks simultaneously.