Nonparametric Survival Analysis on Time-Dependent Covariate

A nonparametric analysis of time dependent covariate eects on failures determined by a regression function 0(t) in Cox's regression model based on case-cohort sampling design is devel- oped. 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.