https://www.dovepress.com/application-of-bayesian-decision-making-to-laboratory-testing-for-lyme-peer-reviewed-article-IJGM  Michael J Cook, Basant K Puri

Independent Researcher, Highcliffe, Department of Medicine, Hammersmith Hospital, Imperial College London, London, UK

Abstract: In this study, Bayes’ theorem was used to determine the probability of a patient having Lyme disease (LD), given a positive test result obtained using commercial test kits in clinically diagnosed patients. In addition, an algorithm was developed to extend the theorem to the two-tier test methodology. Using a disease prevalence of 5%–75% in samples sent for testing by clinicians, evaluated with a C6 peptide enzyme-linked immunosorbent assay (ELISA), the probability of infection given a positive test ranged from 26.4% when the disease was present in 5% of referrals to 95.3% when disease was present in 75%. When applied in the case of a C6 ELISA followed by a Western blot, the algorithm developed for the two-tier test demonstrated an improvement with the probability of disease given a positive test ranging between 67.2% and 96.6%. Using an algorithm to determine false-positive results, the C6 ELISA generated 73.6% false positives with 5% prevalence and 4.7% false positives with 75% prevalence. Corresponding data for a group of test kits used to diagnose HIV generated false-positive rates from 5.4% down to 0.1% indicating that the LD tests produce up to 46 times more false positives. False-negative test results can also influence patient treatment and outcomes. The probability of a false-negative test for LD with a single test for early-stage disease was high at 66.8%, increasing to 74.9% for two-tier testing. With the least sensitive HIV test used in the two-stage test, the false-negative rate was 1.3%, indicating that the LD test generates ~60 times as many false-negative results. For late-stage LD, the two-tier test generated 16.7% false negatives compared with 0.095% false negatives generated by a two-step HIV test, which is over a 170-fold difference. Using clinically representative LD test sensitivities, the two-tier test generated over 500 times more false-negative results than two-stage HIV testing.