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\footnotesize
\noindent Statistica Sinica {\bf 16}(2006), 235-253

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\centerline{\large\bf CORRECTED SCORE ESTIMATOR FOR JOINT MODELING}
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\centerline{\large\bf OF LONGITUDINAL AND FAILURE TIME DATA}
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\author{C. Y. Wang}
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\centerline{\it Fred Hutchinson Cancer Research Center}
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\begin{quotation}
\noindent {\it Abstract:}
We consider Cox proportional hazards regression when longitudinal
measurements are available.   In some applications, one major goal is
to estimate the effect of the underlying change of the longitudinal
measurements on survival.   One general approach considers regression
analysis when some covariate variables are the underlying regression
coefficients of another random effects
model.  For each subject, the covariate variables to the primary
regression model are not observed, but can be estimated from the observed
longitudinal measurements.  This set-up is often called joint
modeling in the literature, but it can be treated as two-stage modeling.
In this paper, a corrected score estimator is investigated.
Comparisons are made with a naive estimator, a regression calibration
estimator, a risk set regression calibration estimator, and a
conditional score estimator.  Similar to the conditional score estimator,
the corrected score estimator does not need the assumption of an
underlying distribution of the random effects
for each subject.  Under some regularity conditions, the proposed
corrected score estimator is shown to be consistent and asymptotically
normally distributed.   Simulation results under various
random effects distributions are presented.\par
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\noindent {\it Key words and phrases:}
Empirical process,  estimating equation,
  measurement error,  proportional hazards, random effects.\par
\end{quotation}

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