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Diagnostic systems designed to detect possibly multiple lesions per patient (e.g. multiple polyps during CT colonoscopy) are often evaluated in “free-response” studies that allow for diagnostic responses unconstrained in their number and locations. Analysis of free-response studies requires extensions of the traditional receiver operating characteristic (ROC) analysis, which are termed free-response ROC (FROC) methodology. Despite substantial developments in this area, FROC tools and approaches are much more cumbersome than traditional ROC methods. Alternative approaches that use well-known ROC tools (e.g. ROI-ROC) require defining and physically delineating regions of interest (ROI) and combine FROC data within ROIs. We propose an approach that allows analyzing FROC data using conventional ROC tools without delineating the actual ROIs or reducing data. The design parameters of FROC study are used to make FROC data analyzable using ROC tools and to calibrate the corresponding FROC and ROC curves on both conceptual and numerical levels. Differences in the performance indices of the nonparametric FROC and the new approach are shown to be asymptotically negligible and typically rather small in practice. Data from a large multi-reader study of colon cancer detection are used to illustrate the new approach.

Receiver operating characteristic analysis provides an important methodology for assessing traditional (e.g., imaging technologies and clinical practices) and new (e.g., genomic studies, biomarker development) diagnostic problems. The area under the clinically/practically relevant part of the receiver operating characteristic curve (partial area or partial area under the receiver operating characteristic curve) is an important performance index summarizing diagnostic accuracy at multiple operating points (decision thresholds) that are relevant to actual clinical practice. A robust estimate of the partial area under the receiver operating characteristic curve is provided by the area under the corresponding part of the empirical receiver operating characteristic curve. We derive a closed-form expression for the jackknife variance of the partial area under the empirical receiver operating characteristic curve. Using the derived analytical expression, we investigate the differences between the jackknife variance and a conventional variance estimator. The relative properties in finite samples are demonstrated in a simulation study. The developed formula enables an easy way to estimate the variance of the empirical partial area under the receiver operating characteristic curve, thereby substantially reducing the computation burden, and provides important insight into the structure of the variability. We demonstrate that when compared with the conventional approach, the jackknife variance has substantially smaller bias, and leads to a more appropriate type I error rate of the Wald-type test. The use of the jackknife variance is illustrated in the analysis of a data set from a diagnostic imaging study.