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\footnotesize \noindent Statistica Sinica {\bf 22} (2012), 337-357

\footnotesize \noindent doi:http://dx.doi.org/10.5705/ss.2009.303

\vspace{3pc} \normalsize \centerline{\large\bf A PATTERN-MIXTURE
MODEL FOR HAPLOTYPE} \vspace{2pt} \centerline{\large\bf ANALYSIS OF
LONGITUDINAL TRAITS} \vspace{2pt} \centerline{\large\bf WITH
NON-IGNORABLE DROPOUT} \vspace{.25cm}
\author{Hongying Li and Rongling Wu}
\vspace{.4cm} \centerline{\it University of Florida and Pennsylvania
State University} \vspace{.55cm}
\begin{quotation}
\noindent {\it Abstract:} Current statistical methods allow the
characterization of DNA sequence variants associated with
interpersonal differences in a complex biological response. However,
this process is significantly hindered when some subjects have to
drop out early due to physiological side effects or limited
duration. Here, we derive a pattern-mixture model for detecting
functional nucleotide combinations (or haplotypes) responsible for
longitudinal responses by making full use of information from those
dropout data. The model was formulated within the maximum likelihood
context, with the model parameters, haplotype frequencies, and
haplotype effects estimated by implementing the EM and
Newton-Raphson algorithms. {One advantage of the model is to
generate and address a number of clinically meaningful hypotheses
about the genetic control mechanisms of longitudinal responses and
time-to-event processes}. By analyzing a pharmacogenomic data set,
the model identified significant haplotype effects on heart rate
increases in response to increasing doses of dobutamine. The
statistical properties of the model and its usefulness and
utilization were investigated through computer simulation. The new
model can be used to unravel the genetic architecture of
interpersonal variation in complex longitudinal responses with
incomplete data and ultimately to materialize the idea of clinical
genomics.
\par
\vspace{9pt} \noindent {\it Key words and phrases:} Drug response,
EM algorithm, functional mapping, longitudinal trait, non-ignorable
dropout, pattern mixture, quantitative trait nucleotides. \par
\end{quotation}

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