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28 March 2013 One parameter contaminated binormal model (CBM) for analysis of difficult-to-fit ROC data
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Introduction. Perception experiments collecting rating method ROC data sometimes result in operating points at only relatively high specificities for some treatment-reader combinations. In the extreme, no operating points are internal to the feasible space of many parametric models (i.e. for all points, FP = 0). Dorfman & Berbaum1 developed a contaminated binormal model (CBM) to account for ROC data that have few false-positive reports even though many healthy subjects are sampled. Unfortunately, CBM can give very different ROC curve shapes for similar ROC points and when there are no internal operating points, the ROC curve shape will often differ substantially from that obtained when there are internal operating points. Materials and Methods. We eliminate the CBM limiting case by adding a small constant to each cell of the rating data matrix2,3 and to set μ, the difference between the visible signal and noise distributions, to the same high value for all conditions.1 Results. We illustrate the resulting ROC curves using an example dataset from Schartz et al.4 All observed ROC points become internal. The fitted ROC curves are similar to those of the limiting CBM and empirical ROC, but all curves using the same μ have the same shape and never cross. ROC accuracy parameters such area, partial area, and sensitivity at any fixed specificity correspond perfectly. Conclusions. Constraining the CBM to a fixed large μ provides a more effective way to apply it to difficult-to-fit data.
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Kevin S. Berbaum and Kevin M. Schartz "One parameter contaminated binormal model (CBM) for analysis of difficult-to-fit ROC data", Proc. SPIE 8673, Medical Imaging 2013: Image Perception, Observer Performance, and Technology Assessment, 86730C (28 March 2013);

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