A principled approach to setting optimal diagnostic thresholds: where ROC and indifference curves meet

Clinical decisions often rely on diagnostic tests, and selecting the right diagnostic threshold is a key challenge. Prior research has shown that diagnostic thresholds influence patient outcomes and healthcare resource use. It was already known that Receiver Operating Characteristic (ROC) curves describe test performance across thresholds. However, no prior work had resolved how to translate ROC data into optimal decision thresholds. This gap motivated the current study to explore how prior odds and test characteristics interact to determine optimal thresholds. The uncertainty around threshold selection has led to the use of rules of thumb, which lack general applicability. No prior work had clearly demonstrated how to integrate prior probabilities with diagnostic test properties. This paper aims to address this gap by proposing a principled method for threshold selection.

This study aims to provide a framework for selecting optimal diagnostic thresholds using a combination of ROC curves and indifference curves. The specific problem is that existing methods for threshold selection are either rule-based or lack theoretical grounding. The motivation comes from the need to align diagnostic thresholds with patient-specific factors like disease prevalence and test importance. The authors propose that diagnostic thresholds should be chosen based on expected utility maximization. This approach considers both test performance and clinical context. The goal is to move beyond graphical interpretations that do not account for prior odds. The study seeks to clarify how likelihood ratios can guide threshold selection. It also aims to contrast this optimal rule with common but limited threshold rules of thumb.

The authors use a mathematical framework to derive diagnostic thresholds that maximize expected utility. They define the optimal threshold as the product of prior odds and a sensitivity-to-specificity ratio. This threshold corresponds to the point on the ROC curve where the slope equals this product. The study contrasts this optimal rule with two popular threshold rules of thumb. These rules are evaluated for their general applicability and graphical interpretation. Indifference curves are introduced to represent combinations of sensitivity and specificity with equal utility. These curves are tangent to the ROC curve at the optimal threshold. The study uses graphical and mathematical analysis to demonstrate how these curves interact. The approach is grounded in decision theory and health economics principles.

The optimal diagnostic threshold is determined by the product of prior odds and the relative importance of sensitivity versus specificity. This threshold corresponds to the point on the ROC curve where the slope equals this product. Indifference curves show combinations of sensitivity and specificity with equal utility. These curves are tangent to the ROC curve at the optimal threshold. The two popular threshold rules of thumb yield optimal thresholds only in special cases. The optimal rule is supported by a theoretical framework that integrates prior odds and test characteristics. The study demonstrates that likelihood ratios are the canonical decision variable in this context. The indifference curve framework provides a new way to visualize optimal thresholds. The results suggest that graphical interpretations alone are insufficient for threshold selection.

The authors propose that diagnostic thresholds should be chosen based on expected utility maximization using a combination of ROC and indifference curves. This approach accounts for both test performance and clinical context. The optimal threshold is where the ROC curve's slope equals the product of prior odds and a sensitivity-to-specificity ratio. Indifference curves help visualize this optimal point. The study clarifies that popular threshold rules of thumb are limited in general applicability. The use of likelihood ratios as a canonical decision variable is supported by the analysis. The framework provides a principled method for threshold selection that goes beyond graphical interpretations. The authors suggest that this method can improve clinical decision-making by aligning thresholds with patient-specific factors.