Finding the optimal cut-point for Gaussian and Gamma distributed biomarkers

Categorization is often needed for clinical decision making when dealing with diagnostic (prognostic) biomarkers and a binary outcome (true disease status). Four common methods used to dichotomize a continuous biomarker X are compared: the minimum P-value, the Youden index, the concordance probability and the point closest-to-(0,1) corner in the ROC plane. These methods are compared from a theoretical point of view under Normal or Gamma biomarker distributions, showing whether or not they lead to the identification of the same true cut-point. The performance of the corresponding non-parametric estimators is then compared by simulation. Two motivating examples are presented. In all simulation scenarios, the point closest-to-(0,1) corner in the ROC plane and concordance probability approaches outperformed the other methods. Both these methods showed good performance in the estimation of the optimal cut-point of a biomarker. However, when methods do not lead to the same optimal cut-point, scientists should focus on which one is truly what they want to estimate, and use it in practice. In addition, to improve communicability, the Youden index or the concordance probability associated to the estimated cut-point could be reported to summarize the associated classification accuracy. The use of the minimum P-value approach for cut-point finding is strongly not recommended because its objective function is computed under the null hypothesis of absence of association between the true disease status and X. This is in contrast with the presence of some discrimination potential of X that leads to the dichotomization issue