The Annals of Statistics

Nonparametric Survival Analysis with Time-Dependent Covariate Effects: A Penalized Partial Likelihood Approach

David M. Zucker and Alan F. Karr

Full-text: Open access

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.

Article information

Source
Ann. Statist. Volume 18, Number 1 (1990), 329-353.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176347503

Digital Object Identifier
doi:10.1214/aos/1176347503

Mathematical Reviews number (MathSciNet)
MR1041396

Zentralblatt MATH identifier
0708.62035

JSTOR
links.jstor.org

Subjects
Primary: 60G05: Foundations of stochastic processes
Secondary: 62G05: Estimation 62J02: General nonlinear regression 62M09: Non-Markovian processes: estimation

Keywords
Survival analysis covariate Cox regression model penalized maximum likelihood estimation partial likelihood consistency asymptotic normality

Citation

Zucker, David M.; Karr, Alan F. Nonparametric Survival Analysis with Time-Dependent Covariate Effects: A Penalized Partial Likelihood Approach. Ann. Statist. 18 (1990), no. 1, 329--353. doi:10.1214/aos/1176347503. http://projecteuclid.org/euclid.aos/1176347503.


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