Cut-Point Finding Methods For Continuous Biomarkers In The Presence Of Binary And Censored Failure Time Outcome

Statisticians are continuously challenged to face out several methodological issues when dealing with novel biomarkers, one of which is the definition of optimal cut-points to classify subjects testing positive from those testing negative. Our aim is to review widely used cut-point finding methods in the presence of binary outcome [1], to extend them to the case of censored failure time outcome [2], and to evaluate methods’ performance through simulations. In the presence of binary outcome, methods based on the receiver operating characteristic (ROC) curve such as: i) the Youden index, i.e. the maximum difference between sensitivity (SE) and 1- specificity (SP) at c of the biomarker X, ii) the concordance probability, i.e. the maximum of the product of SE and SP at c, iii) the c corresponding to the point closest-to-(0,1) corner in the ROC plane, and iv) the c minimizing the P-value of the chi-square test statistic on the absence of association between the resulting dichotomized X and the binary outcome, are commonly and indistinctly used. Extension of these methods to the censored failure time outcome scenario is of interest to identify whether there will be the development, or not, of a disease condition up to some time horizon τ of clinical interest in disease free subjects at the biomarker assessment. This is not straightforward since we need to resort to estimators of the SE and SP accounting for censoring [3]. We compared the performance of these methods under a Gaussian distribution of X, a condition ensuring that estimators point theoretically to the same optimal true cut-point. For all methods the relative bias of the estimated cut-point is small on all levels of classification accuracy of X both in the case of binary and censored failure time outcome. Results on mean square error show that the point closest-to-(0,1) corner and concordance probability methods have better performance than the minimum P-value and Youden index approaches. The performance of all methods improves with increasing biomarker classification accuracy. We showed that methods for defining a cut-point of a continuous biomarker can be extended to censored data [2]. The use of the minimum P-value approach is not recommended as shown from the simulation results. This is due to the objective function that is computed under the null hypothesis of absence of association between the true disease status and X, in contrast with the presence of some discrimination potential that leads to the dichotomization issue [1]. The point closest-to-(0,1) corner approach has the best performance. However, given the lack of clinical meaning of its objective function, the calculation of the Youden index or concordance probability associated to the cut-point identified through the closest-to-(0,1) corner approach could be used to ease interpretability of the classification accuracy of the biomarker.