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In diagnostic trials, clustered data are
obtained when several subunits of the same patient are observed. Within-cluster
correlations need to be taken into account when analyzing such clustered data.
A nonparametric method has been proposed by Obuchowski (1997) to estimate the
Receiver Operating Characteristic curve area (AUC) for such clustered data.
However, Obuchowski’s estimator gives equal weight to all pairwise rankings
within and between cluster. In this paper, we modify Obuchowski’s estimate by
allowing weights for the pairwise rankings vary across clusters. We consider
the optimal weights for estimating one AUC as well as two AUCs’ difference. Our
results in this paper show that the optimal weights depends on not only the
within-patient correlation but also the proportion of patients that have both
unaffected and affected units. More importantly, we show that the loss of efficiency
using equal weight instead of our optimal weights can be severe when there is a
large within-cluster correlation and the proportion of patients that have both
unaffected and affected units is small.