Abstract
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.
Highlights
In diagnostic trials, clustered data are obtained when several subunits of the same patient are observed
In a study by Masaryk et al (1991) [2], two radiologists evaluated 65 carotid arteries in 36 patients using three-dimensional Magnetic Resonance Angiography(MRA), a potential screeening tool for athe- rosclerosis of the carorid arteries. These patients underwent intra-arterial digital subtraction angiography (DSA), which is considered the gold standard for characterizing the degree of stenosis
Correlation exists for outcomes between two unaffected units, between two affected units, and between an unaffected and an affected unit from the same cluster, and between the outcomes of the two diagnostic tests from the same cluster
Summary
In diagnostic trials, clustered data are obtained when several subunits of the same patient are observed. In the presence of various within-cluster correlations, these differences would affect the contribution of a cluster to the overall variance of the AUC estimator and weights should vary across clusters. We modify Obuchowski’s estimator by allowing the weight assigned to each pairwise ranking to vary across clusters, and derive the optimal weights that minimize the variance of the AUC estimator. Our results in this paper show that the optimal weights depends on the within-cluster correlation and the proportion of clusters that have both unaffected and affected units. We show that the gain of efficiency in comparison with two simple weighting schemes can be doubled when there is a large within-cluster correlation and the proportion of clusters that have both unaffected and affected units is small.
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