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\footnotesize \noindent Statistica Sinica {\bf 22} (2012), 1457-1477

\footnotesize \noindent doi:http://dx.doi.org/10.5705/ss.2011.088

\vspace{3pc} \normalsize \centerline{\large\bf JACKKNIFE EMPIRICAL
LIKELIHOOD BASED} \vspace{2pt} \centerline{\large\bf  CONFIDENCE
INTERVALS} \vspace{2pt} \centerline{\large\bf  FOR PARTIAL AREAS
UNDER ROC CURVES} \vspace{.25cm}
\author{Gianfranco Adimari and Monica Chiogna}
\vspace{.4cm} \centerline{\it University of Padova} \vspace{.55cm}
\begin{quotation}
\noindent {\it Abstract:} The partial area under the ROC curve
(partial AUC)  summarizes the accuracy of a diagnostic or screening
test over a relevant region of the ROC curve and represents a useful
tool for the evaluation and comparison of tests. In this paper, we
propose a jackknife empirical likelihood method for making inference
on   partial AUCs. Following the idea  in
%Jing, Yuan, and Zhou (2009),
\cite{jing:09}, we combine the empirical likelihood function with
suitable jackknife pseudo-values obtained from a nonparametric
estimator of the normalized partial AUC. This leads to a jackknife
empirical likelihood function for  normalized partial AUCs, for
which a Wilks-type result is obtained. Such a pseudo-likelihood can
be used, in a standard way, to construct confidence intervals or
perform tests of hypotheses.  We also give some simulation results
that indicate that the jackknife empirical likelihood based
confidence intervals compare favorably with alternatives in terms of
coverage probability. The proposed method is extended to inference
on the difference between two partial AUCs. Finally, an application
to the Wisconsin Breast Cancer Data is discussed.\par \vspace{9pt}
\noindent {\it Key words and phrases:} Diagnostic tests, jackknife
pseudo-values, nonparametric statistical methods,
pseudo-likelihoods. \par
\end{quotation}
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