Supplemental Tables S2 -- S3 confirm that distributions realized during the proportional odds and NPO1 simulations were approximately centered at the levels designated above for \(\alpha_{j-1}\), \(\beta_{j-1}\), and \(AUC\). Supplemental Table S4 shows, however, that for the NPO2 condition the medians of the realized distributions for \(\alpha_{j-1}\) and \(\beta_{j-1}\) differed by as much as 29 percent from their designated values, even as the realized AUCs were centered on their designated values. Tables S5 -- S7 display the median, 2.5th and 97.5th percentiles, and the percent-bias of cutpoints selected by each criterion across sample sizes \(n\). Percent-biases are the median of percent-differences between realized cutpoints (selected and parametric) and designated cutpoints. The ROC curve-based cutpoint selection criteria exhibited a range of biases. Among both proportional (Table S5) and non-proportional (Tables S6 and S7) odds conditions, absolute values of the percent-biases ranged from 2.8 -- 144.2 percent. Total Accuracy demonstrated the best performance with biases ranging from 2.8 -- 11.7 percent, while the other criteria performed considerably worse.
Forgoing ROC curve analysis and calculating cutpoints from the MLE regression parameters yielded small, often negligible absolute percent-biases \(\left( \lt 2.3 \ \text{percent} \right)\) for both proportional and non-proportional odds conditions. In addition, across all sample sizes, parametric cutpoints consistently out-performed ROC curve-based cutpoint selection criteria.
Notably, for the NPO2 condition (Supplemental Table S7), the differences in the realized cumulative logit parameters did not entail discrepancies in realized cutpoints compared to the other simulation conditions, whether the cutpoints were selected by criteria or calculated parametrically.