C-mix: A high-dimensional mixture model for censored durations, with applications to genetic data

Simon Bussy, Agathe Guilloux, Anne-Sophie Jannot, Stéphane Gaïffas

Abstract:

We introduce a supervised learning mixture model for censored durations (C-mix) to simultaneously detect subgroups
of patients with different prognosis and order them based on their risk. Our method is applicable in a high-dimensional
setting, i.e. with a large number of biomedical covariates. Indeed, we penalize the negative log-likelihood by the ElasticNet, which leads to a sparse parameterization of the model and automatically pinpoints the relevant covariates for the
survival prediction. Inference is achieved using an efficient Quasi-Newton Expectation Maximization algorithm, for which
we provide convergence properties. The statistical performance of the method is examined on an extensive Monte Carlo
simulation study and finally illustrated on three publicly available genetic cancer datasets with high-dimensional
covariates. We show that our approach outperforms the state-of-the-art survival models in this context, namely both
the CURE and Cox proportional hazards models penalized by the Elastic-Net, in terms of C-index, AUC(t) and survival
prediction. Thus, we propose a powerful tool for personalized medicine in cancerology.