  Prognostic models in survival analysis are aimed at understanding the
relationship between patients' covariates and the distribution of survival
time. Traditionally, semi-parametric models, such as the Cox model, have been
assumed. These often rely on strong proportionality assumptions of the hazard
that might be violated in practice. Moreover, they do not often include
covariate information updated over time. We propose a new flexible method for
survival prediction: DeepHazard, a neural network for time-varying risks. Our
approach is tailored for a wide range of continuous hazards forms, with the
only restriction of being additive in time. A flexible implementation, allowing
different optimization methods, along with any norm penalty, is developed.
Numerical examples illustrate that our approach outperforms existing
state-of-the-art methodology in terms of predictive capability evaluated
through the C-index metric. The same is revealed on the popular real datasets
as METABRIC, GBSG, and ACTG.
