  This paper presents an original approach for jointly fitting survival times
and classifying samples into subgroups. The Coxlogit model is a generalized
linear model with a common set of selected features for both tasks. Survival
times and class labels are here assumed to be conditioned by a common risk
score which depends on those features. Learning is then naturally expressed as
maximizing the joint probability of subgroup labels and the ordering of
survival events, conditioned to a common weight vector. The model is estimated
by minimizing a regularized log-likelihood through a coordinate descent
algorithm.
  Validation on synthetic and breast cancer data shows that the proposed
approach outperforms a standard Cox model or logistic regression when both
predicting the survival times and classifying new samples into subgroups. It is
also better at selecting informative features for both tasks.
