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\footnotesize \noindent Statistica Sinica {\bf 23} (2013), 359-381

\footnotesize \noindent doi:http://dx.doi.org/10.5705/ss.2010.297

\vspace{3pc} \normalsize \centerline{\large\bf AUGMENTED ESTIMATING
EQUATIONS FOR} \vspace{2pt} \centerline{\large\bf SEMIPARAMETRIC
PANEL COUNT REGRESSION WITH} \vspace{2pt} \centerline{\large\bf
INFORMATIVE OBSERVATION TIMES AND} \vspace{2pt}
\centerline{\large\bf  CENSORING TIME} \vspace{.25cm}
\author{Xiaojing Wang, Shuangge Ma and Jun Yan}
\vspace{.4cm} \centerline{\it Google New York, Yale University and
University of Connecticut} \vspace{.55cm}  
\begin{quotation}
\noindent {\it Abstract:} We propose an augmented estimating
equation (AEE) approach for a semiparametric mean regression model
with panel count data under possibly informative observation schemes
and censoring. On a grid of time points, counts in all the
subintervals of each observation window are treated as missing
values, and are imputed with a robust working model given the
observed count in the window. The observation scheme and the event
process are allowed to be dependent through covariates and an
unobserved frailty, which enters the mean function multiplicatively.
Conditional on covariates, the censoring time and the event process
can be dependent through the frailty. Regression coefficients and
the unspecified baseline mean function are estimated with an
Expectation-Solving (ES) algorithm. Distributions of the observation
times, censoring time, and frailty are all considered as nuisance
and unspecified. With empirical process theory, estimators for both
the parametric and nonparametric component are shown to be
consistent. The regression coefficient estimator is shown to be
asymptotically normal. The cumulative baseline estimator is
self-consistent in that the estimator is automatically
non-decreasing. In simulation studies, the estimator performs well
for moderate sample sizes and appears to be competitive in
comparison with existing estimators under a wide range of practical
settings. The utility of the proposed methods is illustrated with a
bladder tumor study.\par \vspace{9pt} \noindent {\it Key words and
phrases:} Expectation-Solving algorithm, missing data,
semiparametric regression. \par
\end{quotation}

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