Convergence Behavior of Optimal Cut-Off Points Derived from Receiver Operating Characteristics Curve Analysis: A Simulation Study

The area under the receiver operating characteristics curve is a popular measure of the overall discriminatory power of a continuous variable used to indicate the presence of an outcome of interest, such as disease or disease progression. In clinical practice, the use of cut-off points as benchmark values for further treatment planning is greatly appreciated, despite the loss of information that such a dichotomization implies. Optimal cut-off points are often derived from fixed sample size studies, and the aim of this study was to investigate the convergence behavior of optimal cut-off points with increasing sample size and to explore a heuristic and path-based algorithm for cut-off point determination that targets stagnating cut-off point values. To this end, the closest-to-(0,1) criterion in receiver operating characteristics curve analysis was used, and the heuristic and path-based algorithm aimed at cut-off points that deviated less than 1% from the cut-off point of the previous iteration. Such a heuristic determination stopped after only a few iterations, thereby implicating practicable sample sizes; however, the result was, at best, a rough estimate of an optimal cut-off point that was unbiased and positively and negatively biased for a prevalence of 0.5, smaller than 0.5, and larger than 0.5, respectively.