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\noindent Statistica Sinica {\bf 16}(2006), 267-285

\vspace{3pc} \normalsize
\centerline{\large\bf NONPARAMETRIC SURVIVAL ANALYSIS ON}
\vspace{2pt}
\centerline{\large\bf TIME-DEPENDENT COVARIATE EFFECTS}
\vspace{2pt}
\centerline{\large\bf IN CASE-COHORT SAMPLING DESIGN}
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\author{Haimeng Zhang and Chunfeng Huang}
\vspace{.4cm}
\centerline{\it Concordia College and North Dakota State University}
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\begin{quotation}
\noindent {\it 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.\par
\vspace{9pt}
\noindent {\it Key words and phrases:}
Asymptotic normality, case-cohort sampling, Cox
model, consistency, maximum penalized
pseudolikelihood estimator, survival analysis.\par
\end{quotation}

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