Application of Bézier Curves for Calculating Likelihood Ratios for Plasma Amyloid-β Biomarkers for Alzheimer's Disease

Introduction: Alzheimer's disease, being the most frequent cause of dementia in elderly people, still is difficult to diagnose and to predict its occurrence. The clinical application of biomarkers for diagnosis of Alzheimer's disease has been restricted so far to the analysis of proteins in the cerebrospinal fluid like amyloid β(1−42) and p-tau. However, in a recently published nature letter it has been shown that the high-performance measurement of amyloid-β in plasma alone could provide a method well suited for a broad clinical application. The study uses ROC analysis to evaluate the clinical significance of the method but it does not provide likelihood ratios (LR) of the measured results. Methods: In this article, a newly developed method is used to calculate LRs for any measurement result of a study by approximation of the ROC curves using Bézier curves. Such LRs provide an estimation of the clinical significance of any particular test result by applying Bayes' theorem: Pretest odds for disease multiplied by the LR of the test result give the posttest odds. Results: The application of the Bézier curve approximation to the data of the plasma amyloid-β study is demonstrated. To generalize the calculation of LRs for all test results, a relation between the test results and the points on the Bézier curve with their LRs is established. Discussion: The application of Bézier curves in ROC analysis allows calculating LRs for all individual test results when measuring amyloid-β biomarkers for Alzheimer's disease.