Cumulative ROC curves for discriminating three or more ordinal outcomes with cutpoints on a shared continuous measurement scale

Abstract

Cumulative receiver operator characteristic (ROC) curve analysis extends classic ROC curve analysis to discriminate three or more ordinal outcome levels on a shared continuous scale. The procedure combines cumulative logit regression with a cumulative extension to the ROC curve and performs as expected with ternary (three-level) ordinal outcomes under a variety of simulated conditions (unbalanced data, proportional and non-proportional odds, areas under the ROC curve [AUCs] from 0.70 to 0.95). Simulations also compared several criteria for selecting cutpoints to discriminate outcome levels: the Youden Index, Matthews Correlation Coefficient, Total Accuracy, and Markedness. Total Accuracy demonstrated the least absolute percent-bias. Cutpoints computed from maximum likelihood regression parameters demonstrated bias that was often negligible. The procedure was also applied to publicly available data related to computer imaging and biomarker exposure science, yielding good to excellent AUCs, as well as cutpoints with sensitivities and specificities of commensurate quality. Implementation of cumulative ROC curve analysis and extension to more than three outcome levels are straightforward. The author’s programs for ternary ordinal outcomes are publicly available.