A Bayesian method to estimate the optimal threshold of a longitudinal biomarker.

The objective of this study was to develop methods to estimate the optimal threshold of a longitudinal biomarker and its credible interval when the diagnostic test is based on a criterion that reflects a dynamic progression of that biomarker. Two methods are proposed: one parametric and one non-parametric. In both the cases, the Bayesian inference was used to derive the posterior distribution of the optimal threshold from which an estimate and a credible interval could be obtained. A numerical study shows that the bias of the parametric method is low and the coverage probability of the credible interval close to the nominal value, with a small coverage asymmetry in some cases. This is also true for the non-parametric method in case of large sample sizes. Both the methods were applied to estimate the optimal prostate-specific antigen nadir value to diagnose prostate cancer recurrence after a high-intensity focused ultrasound treatment. The parametric method can also be applied to non-longitudinal biomarkers.