Boosted Nonparametric Hazards with Time-Dependent Covariates

33 Pages Posted: 28 Jan 2017 Last revised: 29 Jun 2020

See all articles by Donald Lee

Donald Lee

Emory University - Goizueta Business School

Ningyuan Chen

University of Toronto at Mississauga - Department of Management; University of Toronto - Rotman School of Management

Hemant Ishwaran

University College London - Department of Epidemiology and Public Health

Date Written: February 12, 2017

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. We show that 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.

Keywords: survival analysis; gradient boosting; functional data; step-size shrinkage; regression trees; likelihood functional; queuing transition rates; emergency departments

JEL Classification: C14, C24, C34, C41, C44, C53

Suggested Citation

Lee, Donald and Chen, Ningyuan and Ishwaran, Hemant, Boosted Nonparametric Hazards with Time-Dependent Covariates (February 12, 2017). Available at SSRN: https://ssrn.com/abstract=2906586 or http://dx.doi.org/10.2139/ssrn.2906586

Donald Lee (Contact Author)

Emory University - Goizueta Business School ( email )

1300 Clifton Road
Atlanta, GA 30322-2722
United States

Ningyuan Chen

University of Toronto at Mississauga - Department of Management ( email )


Canada

University of Toronto - Rotman School of Management ( email )

105 St. George st
Toronto, ON M5S 3E6
Canada

Hemant Ishwaran

University College London - Department of Epidemiology and Public Health ( email )

1-19 Torrington Place
Miami, FL 33136
United States

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