Boosted Nonparametric Hazards with Time-Dependent Covariates

Annals of Statistics 49:4:2101-2128 (2021)

28 Pages Posted: 28 Jan 2017 Last revised: 30 Sep 2021

See all articles by Donald K.K. Lee

Donald K.K. Lee

Emory University - Goizueta Business School; Emory University - Dept of Biostatistics & Bioinformatics

Ningyuan Chen

University of Toronto - Rotman School of Management

Hemant Ishwaran

University College London - Department of Epidemiology and Public Health

Date Written: 2021

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 K.K. and Lee, Donald K.K. and Chen, Ningyuan and Ishwaran, Hemant, Boosted Nonparametric Hazards with Time-Dependent Covariates (2021). Annals of Statistics 49:4:2101-2128 (2021), Available at SSRN: https://ssrn.com/abstract=2906586 or http://dx.doi.org/10.2139/ssrn.2906586

Donald K.K. Lee (Contact Author)

Emory University - Goizueta Business School ( email )

1300 Clifton Road
Atlanta, GA 30322-2722
United States

Emory University - Dept of Biostatistics & Bioinformatics ( email )

Atlanta, GA 30322
United States

Ningyuan Chen

University of Toronto - Rotman School of Management ( email )

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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