Statistica Sinica 16(2006), 267-285

NONPARAMETRIC SURVIVAL ANALYSIS ON

TIME-DEPENDENT COVARIATE EFFECTS

IN CASE-COHORT SAMPLING DESIGN

Haimeng Zhang and Chunfeng Huang

Concordia College and North Dakota State University

Abstract: A nonparametric analysis of time-dependent covariate effects on failures determined by a regression function $\beta_0(t)$ in Cox's regression model based on case-cohort sampling design is developed. The analysis is carried out through maximizing appropriate penalized pseudolikelihoods. Weak uniform consistency and pointwise asymptotic normality of the resulting estimators are investigated under regularity conditions. Further generalization of the results is also discussed in the paper.

Key words and phrases: Asymptotic normality, case-cohort sampling, Cox model, consistency, maximum penalized pseudolikelihood estimator, survival analysis.