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\footnotesize \noindent Statistica Sinica {\bf 24} (2014), 415-428

\footnotesize \noindent

\vspace{3pc} \normalsize \centerline{\large\bf OPTIMAL DESIGNS FOR
TWO-PARAMETER NONLINEAR} \vspace{2pt} \centerline{\large\bf  MODELS
WITH APPLICATION TO SURVIVAL MODELS} \vspace{.25cm}
\author{Maria Konstantinou, Stefanie Biedermann and Alan Kimber}
\vspace{.4cm} \centerline{\it %Statistical Sciences Research Institute,
University of Southampton} \vspace{.55cm}  
\begin{quotation}
\noindent {\it Abstract:} Censoring occurs in many industrial or
biomedical `time to event' experiments. Finding efficient designs
for such experiments can be problematic since the statistical models
involved are usually nonlinear, making the optimal choice of design
parameter dependent. We provide analytical characterisations of
locally $D$- and $c$-optimal designs for a class of models, thus
reducing the numerical effort for design search substantially. We
also investigate standadised maximin $D$- and $c$-optimal designs.
We illustrate our results using the natural proportional hazards
parameterisation of the exponential regression model. Different
censoring mechanisms are incorporated and the robustness of designs
against parameter misspecification is assessed.
\par
\vspace{9pt} \noindent {\it Key words and phrases:} $c$-optimality,
$D$-optimality, proportional hazards, survival analysis. \par
\end{quotation}

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