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Biom J. 2010 Jun;52(3):333-47. doi: 10.1002/bimj.200900242.

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

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  • 1Universit√© de Lyon, France. <>


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.

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