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{1176347503,
author = {Zucker, David M. and Karr, Alan F.},
title = {Nonparametric Survival Analysis with Time-Dependent Covariate Effects: A Penalized Partial Likelihood Approach},
journal = {Ann. Statist.},
volume = {18},
number = {1},
year = {1990},
pages = { 329-353},
language = {en},
url = {http://dml.mathdoc.fr/item/1176347503}
}
Zucker, David M.; Karr, Alan F. Nonparametric Survival Analysis with Time-Dependent Covariate Effects: A Penalized Partial Likelihood Approach. Ann. Statist., Tome 18 (1990) no. 1, pp. 329-353. http://gdmltest.u-ga.fr/item/1176347503/