Boosted nonparametric hazards with time-dependent covariates

Understand

Given functional data from a survival process with time-dependent covariates, we derive a smooth convex representation for its nonparametric log-likelihood functional and obtain its functional gradient.

• From this, we devise a generic gradient boosting procedure for estimating the hazard function nonparametrically.
• An illustrative implementation of the procedure using regression trees is described to show how to recover the unknown hazard.
• The generic estimator is consistent if the model is correctly specified; alternatively, an oracle inequality can be demonstrated for tree-based models.