A crucial parameter in the design of a diagnostic test is the cutoff point, the threshold which separates a negative result from a positive one. Because the actions decided by the diagnostic test inevitably incur risk if administered where unneeded, and vice versa, quantitative Benefit-Risk (BR) analysis is used to determine the optimal cutoff point. This requires measurable benefit and risk and a function, e.g., linear or ratio, to combine the components.
We investigate strategies that optimize the BR results of diagnostics tests. When all four BR categories (Chuang-Stein et al. (1991)) corresponding to the possible diagnostic test outcomes are scaled in units of risk from an untreated disease, and assuming no penalty for correctly administering no treatment to a true-negative diagnosis, we find that both net (linear) BR and BR ratio can be expressed as interpretable functions of diagnostic parameters with respect to known benefit and risk measurements. The optimal cutoff point can then be obtained by receiving operation curve (ROC) analysis using either net BR or BR ratio. We examine the pros and cons of net BR vs BR ratio, and present a comparison of different diagnostic tests.