Comparison of the binormal and Lehman receiver operating characteristic curves

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In this article, we compared the binormal and the Lehmann receiver operating characteristic (ROC) curves using extensive simulation studies and real data sets related to HIV. We ran a large set of simulation studies with a wide range of distributions, varying sample sizes, and different degrees of overlap between the diseased and non-diseased population distributions. Simulation results suggest that the binormal ROC model performs better for normal data. However, for non-normal data, the Lehman model outperforms the binormal model. The discrepancies between the performances of the two models were more apparent for larger sample sizes or larger degree of separation between the distributions of the diseased and non-diseased subjects. Like the binormal model, the Lehman model provides smooth estimates of ROC curves and a closed-form expression for the area under the ROC curve. Moreover, the Lehmann model can also be used to obtain covariate-adjusted ROC curves and accommodates inference of correlated and longitudinal biomarkers. Thus, the Lehman model should be considered as an alternative when the restrictive distributional assumptions of the binormal model are not met.