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

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.

1. Kass R.E., Raftery A.E. Bayes Factors. Journal of the American Statistical Association. 1995;90(430):773–795. DOI: 10.1080/01621459.1995.10476572

2. Westbury C.F. Bayes' Rule for Clinicians: An Introduction. Front. Psychology. 2010;1:192. DOI: 10.3389/fpsyg.2010.00192

3. Sackett D.L., Strauss S.E., Richardson W.S., et al. Evidence-Based Medicine: How to Practice and Teach EBM (Book with CD-ROM). 2nd ed. Churchill Livingstone; 2000:261. ISBN: 9780443062407.

4. Haynes R.B., Sackett D.L., Guyatt G.H., Tugwell P. Clinical Epidemiology: How to Do Clinical Practice Research. 3rd ed. Lippincott Williams & Wilkins; 2006:496, ISBN: 0781745241

5. Bossuyt P.M., Reitsma J.B., Bruns D.E., et all. STARD Group. STARD 2015: an updated list of essential items for reporting diagnostic accuracy studies. BMJ. 2015;351:h5527. DOI: 10.1136/bmj.h5527

6. Jeffreys H. The Theory of Probability. 3rd ed. Oxford: Oxford University Press; 1998:470. ISBN:10-0198503687

7. Fagan T.J. Letter: Nomogram for Bayes's theorem. N. Engl. J. Med. 1975;293(5):257. DOI: 10.1056/NEJM197507312930513

8. Morris J.K., Wald N.J., Watt H.C. Fetal loss in Down syndrome pregnancies. Prenat. Diagn. 1999;19(2):142–145. DOI: 10.1002/(SICI)1097-0223(199902)19:2<142::AID-PD486>3.0.CO;2-7

9. Nordestgaard B.G., Chapman M.J., Humphries S.E., et al.; European Atherosclerosis Society Consensus Panel. Familial hypercholesterolaemia is underdiagnosed and undertreated in the general population: guidance for clinicians to prevent coronary heart disease: consensus statement of the European Atherosclerosis Society. Eur. Heart J. 2013;34(45):3478-90a. Erratum in: Eur. Heart J. 2020;41(47):4517. DOI: 10.1093/eurheartj/ehaa166. DOI: 10.1093/eurheartj/eht273

10. World Health Organization. WHO Malaria Microscopy Guidelines. Geneva: WHO; 2022. URL: https://www.who.int/activities/diagnostic-testing-for-malaria (06.07.2026).

11. Reardon W. Emery and Rimoin's Principles and Practice of Medical Genetics. J. Med. Genet. 2002;39(6):454. DOI: 10.1136/jmg.39.6.454-a

12. European Association for Study of Liver. EASL Clinical Practice Guidelines: Wilson's disease. J. Hepatol. 2012;56(3):671–685. DOI: 10.1016/j.jhep.2011.11.007

13. Husby S., Koletzko S., Korponay-Szabó I., et al. European Society Paediatric Gastroenterology, Hepatology and Nutrition Guidelines for Diagnosing Coeliac Disease 2020. J. Pediatr. Gastroenterol. Nutr. 2020;70(1):141–156. DOI: 10.1097/MPG.0000000000002497 EDN: FTUBXF

14. Zhou X.H., Obuchowski N.A., McClish D.K. Statistical Methods in Diagnostic Medicine. 2nd ed. Wiley; 2011:592. ISBN: 978-0-470-18314-4. DOI: 10.1002/9780470906514 EDN: WPXBVH

15. Ly A., Stefan A., van Doorn J., et al. The Bayesian Methodology of Sir Harold Jeffreys as a Practical Alternative to the P Value Hypothesis Test. Comput. Brain Behav. 3. 2020;3(2):153–161. DOI: 10.1007/s42113-019-00070-x EDN: QMFKBM

16. Sutton R.T., Pincock D., Baumgart D.C., et al. An overview of clinical decision support systems: benefits, risks, and strategies for success. NPJ Digit Med. 2020 Feb 6;3:17. DOI: 10.1038/s41746-020-0221-y EDN: RNFXIL

17. Kobrinskii B.A., Blagosklonov N.A. Artificial Intelligence System for Diagnosing Rare Diseases: Design Principles and Clinical Validation Results. Siberian Journal of Clinical and Experimental Medicine. 2025;40(2):218–225 (In Russ.) DOI: 10.29001/2073-8552-2025-2706 EDN: WZTSAO

18. Pepe M.S. The Statistical Evaluation of Medical Tests for Classification and Prediction. Oxford University Press; 2003:302. ISBN: 9780198565826

19. Bayarri M.J., Berger J.O., Forte A., García-Donato G. Criteria for Bayesian model choice with application to variable selection. The Annals of Statistics. 2012;40(3):1550–1577. DOI: 10.1214/12-AOS1013