Strategies for graphical threshold determination

Determining a threshold for a quantitative variable (arising in biological measurements for instance) is a common problem in medical decision making. We define seven commonly used strategies: each one leads to an optimal determination. To these strategies correspond relevant empirical curves: the ROC curve for strategies involving the sensitivity or the specificity, the predictive ROC curve (P-ROC curve) for strategies involving the positive and negative predicting values, and the well classified frequencies curve (WCF curve) for classification strategies where all misclassifications have the same importance. For one of the considered strategies, there also exists a theoretical formula for the optimal threshold, elicited within a classical probabilistic model, which gives a considerable advantage to this strategy. These strategies are applied to a stimulated example containing 702 cases, where we see that they lead to different optimal threshold values. Finally, we briefly review a practical application in the determination of thresholds for glycemia measurements, leading to the choice of one of them as the optimal one to consider in the gestational diabetes mellitus prediction.