Interval of Uncertainty: An Alternative Approach for the Determination of Decision Thresholds, with an Illustrative Application for the Prediction of Prostate Cancer

Often, for medical decisions based on test scores, a single decision threshold is determined and the test results are dichotomized into positive and negative diagnoses. It is therefore important to identify the decision threshold with the least number of misclassifications. The proposed method uses trichotomization: it defines an Uncertain Interval around the point of intersection between the two distributions of individuals with and without the targeted disease. In this Uncertain Interval the diagnoses are intermixed and the numbers of correct and incorrect diagnoses are (almost) equal. This Uncertain Interval is considered to be a range of test scores that is inconclusive and does not warrant a decision. It is expected that defining such an interval with some precision, prevents a relatively large number of false decisions, and therefore results in an increased accuracy or correct classifications rate (CCR) for the test scores outside this Uncertain Interval. Clinical data and simulation results confirm this. The results show that the CCR is systematically higher outside the Uncertain Interval when compared to the CCR of the decision threshold based on the maximized Youden index. For strong tests with a very small overlap between the two distributions, it can be difficult to determine an Uncertain Interval. In simulations, the comparison with an existing method for test-score trichotomization, the Two-graph Receiver Operating Characteristic (TG-ROC), showed smaller differences between the two distributions for the Uncertain Interval than for TG-ROC's Intermediate Range and consequently a more improved CCR outside the Uncertain Interval. The main conclusion is that the Uncertain Interval method offers two advantages: 1. Identification of patients for whom the test results are inconclusive; 2. A higher estimated rate of correct decisions for the remaining patients.