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\footnotesize \noindent Statistica Sinica {\bf 23} (2013), 383-408

\footnotesize \noindent doi:http://dx.doi.org/10.5705/ss.2011.151

\vspace{3pc} \normalsize \centerline{\large\bf A FRAILTY MODEL
APPROACH FOR REGRESSION} \vspace{2pt} \centerline{\large\bf ANALYSIS
OF BIVARIATE INTERVAL-CENSORED} \vspace{2pt} \centerline{\large\bf
SURVIVAL DATA} \vspace{.25cm}
\author{Chi-Chung
Wen and Yi-Hau Chen} \vspace{.4cm} \centerline{\it Tamkang
University and Academia Sinica} \vspace{.55cm} 
\begin{quotation}
\noindent {\it Abstract:}
 Owing to the fact that general
semiparametric inference procedures are still underdeveloped for
multivariate interval-censored event time data,  we propose
semiparametric maximum likelihood estimation for the gamma-frailty
Cox model under mixed-case interval censoring.  We establish the
consistency of the semiparametric maximum likelihood estimator
(SPMLE) for the model parameters, including the regression
coefficients and the cumulative hazard functions in the Cox model,
and the variance of the gamma frailty. The SPMLEs of the cumulative
hazard functions are shown to have a $n^{1/3}$-rate of convergence,
while those of the regression coefficients and the frailty variance
have a $n^{1/2}$-rate of convergence; here $n$ denotes the number of
study units. The asymptotic normality of the regression coefficients
and the frailty variance is also established, with the asymptotic
variance given by the inverse of the efficient Fisher information
matrix. A profile-likelihood approach is proposed for estimating the
asymptotic variance. Based on the self-consistency equations and the
contraction principle, we propose a stable and efficient computation
algorithm.  Simulation results reveal that the large sample theories
work quite well in finite samples. We analyze a dataset from an AIDS
clinical trial  by the proposed methods to assess the effects of the
baseline CD4 cell counts on the times to CMV shedding in blood and
urine.\par \vspace{9pt} \noindent {\it Key words and phrases:}
Correlated data, interval censoring, proportional hazards,
self-consistency.\par
\end{quotation}

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