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Updated: Oct 9, 2025

Establishing a Competing Risk Regression Nomogram Model for Survival Data
Published on: October 23, 2020
BOOSTED NONPARAMETRIC HAZARDS WITH TIME-DEPENDENT COVARIATES
Donald K K Lee1, Ningyuan Chen2, Hemant Ishwaran3
1Goizueta Business School and Department of Biostatistics & Bioinformatics, Emory University.
Abstract:
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. To avoid overfitting, boosting employs several regularization devices. One of them is step-size restriction, but the rationale for this is somewhat mysterious from the viewpoint of consistency. Our work brings some clarity to this issue by revealing that step-size restriction is a mechanism for preventing the curvature of the risk from derailing convergence.
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