Application of the Bayesian Multiplier to quantitative analysis of tests in medical practice: a methodological study with modeling of clinical situations

Abstract

Introduction. In modern clinical practice, the interpretation of diagnostic data is often based on the physician's subjective experience, which determines variability of decisions and increases the likelihood of diagnostic errors. The imperatives of evidence-based medicine necessitate the implementation of standardized mathematical approaches to improve the accuracy of clinical judgments. The Bayesian Multiplier Factor (BMF) is one of the tools frequently used for decision-making based on a probabilistic approach. Aim: To systematize the methodology for BMF application in clinical practice; to demonstrate calculation algorithms using model examples and substantiate the potential of the tool for objectifying diagnostic test assesment. Material and methods. Six clinical scenarios were analyzed, covering genetic diagnostics, prenatal screening, therapy, and infectious pathology. Mathematically, BMF was defined as the likelihood ratio, calculated using sensitivity (Se) and specificity (Sp): for a positive test result, BMF – = Se / (1-Sp), for a negative test result, BMF + = (1-Se)/ Sp. The strength of evidence was interpreted using the verified Jeffreys scale. The posterior probability of pathology was calculated using Bayes' theorem, using the prior risk as the baseline propensity. Results. A wide range of BMF values was recorded: from 0.101 (ruling out celiac disease) to 950 (verifying malaria). With a prior risk of Down syndrome of 0.5% and a BMF of 21.25, the posterior probability was 9.6%. For familial hypercholesterolemia, with a baseline risk of 40% and a BMF of 90, the resulting risk reached 97.8%. A negative test for celiac disease (BMF of 0.10) reduced the probability of pathology from 20% to 2.1%. The birth of a healthy boy to a hemophilia carrier (BMF of 0.5) reduced the risk from 50% to 33.3%. Conclusion. The application of BMF ensures a transition from intuitive judgment to the quantitative assessment of diagnostic information. BMF values > 1 support a diagnosis, while BMF values < 1 support it. The effectiveness of the tool is modulated by prior probability: the diagnostic value of a test varies depending on the underlying risk. Implementation of the algorithm minimizes cognitive biases; online calculators or the Fagan nomogram are recommended for clinical use.