## The Annals of Statistics

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

#### 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

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