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March, 1990 Nonparametric Survival Analysis with Time-Dependent Covariate Effects: A Penalized Partial Likelihood Approach
David M. Zucker, Alan F. Karr
Ann. Statist. 18(1): 329-353 (March, 1990). DOI: 10.1214/aos/1176347503

Abstract

Techniques are developed for nonparametric analysis of data under a Cox-regression-like model permitting time-dependent covariate effects determined by a regression function $\beta_0(t)$. Estimators resulting from maximization of an appropriate penalized partial likelihood are shown to exist and a computational approach is outlined. Weak uniform consistency (with a rate of convergence) and pointwise asymptotic normality of the estimators are established under regularity conditions. A consistent estimator of a common baseline hazard function is presented and used to construct a consistent estimator of the asymptotic variance of the estimator of the regression function. Extensions to multiple covariates, general relative risk functions and time-dependent covariates are discussed.

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David M. Zucker. Alan F. Karr. "Nonparametric Survival Analysis with Time-Dependent Covariate Effects: A Penalized Partial Likelihood Approach." Ann. Statist. 18 (1) 329 - 353, March, 1990. https://doi.org/10.1214/aos/1176347503

Information

Published: March, 1990
First available in Project Euclid: 12 April 2007

zbMATH: 0708.62035
MathSciNet: MR1041396
Digital Object Identifier: 10.1214/aos/1176347503

Subjects:
Primary: 60G05
Secondary: 62G05, 62J02, 62M09

Rights: Copyright © 1990 Institute of Mathematical Statistics

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Vol.18 • No. 1 • March, 1990
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