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

Area of Science:

• Biostatistics
• Medical Diagnostics
• Biomarker Research

Background:

• Diagnostic tests often rely on biomarkers that change dynamically over time.
• Estimating optimal thresholds for longitudinal biomarkers with credible intervals is crucial for accurate diagnosis and monitoring.

Purpose of the Study:

• To develop and evaluate parametric and non-parametric Bayesian methods for estimating optimal longitudinal biomarker thresholds and their credible intervals.
• To apply these methods to the specific case of prostate-specific antigen (PSA) nadir for prostate cancer recurrence detection.

Main Methods:

• Development of a parametric Bayesian inference method for longitudinal biomarker threshold estimation.
• Development of a non-parametric Bayesian inference method for longitudinal biomarker threshold estimation.
• Bayesian inference used to derive posterior distributions for threshold estimates and credible intervals.

Main Results:

• The parametric method demonstrated low bias and good credible interval coverage, with minor asymmetry in some scenarios.
• The non-parametric method also showed favorable performance, particularly with larger sample sizes.
• Both methods were successfully applied to estimate the optimal PSA nadir for diagnosing prostate cancer recurrence post-treatment.

Conclusions:

• The proposed parametric and non-parametric Bayesian methods provide reliable tools for estimating optimal thresholds and credible intervals for longitudinal biomarkers.
• These methods are applicable to dynamic diagnostic criteria and have demonstrated utility in clinical settings, such as prostate cancer recurrence monitoring.
• The parametric approach is also adaptable for non-longitudinal biomarkers.