The disproportionate impact of pre-test probability estimation errors: an analysis across different pre-test probability contexts
-
Matheus Bento de Souza
und
José Nunes de Alencar
Abstract
Objectives
Diagnostic reasoning in clinical medicine is permeated by uncertainty. This study aims to analyze how errors in the estimation of pre-test probability affect the application of Bayesian inference in diagnostic reasoning.
Methods
We examined the propagation of pre-test probability misestimation through Bayes’ Theorem, focusing on its interaction with different likelihood ratios and pre-test probabilities. The analysis explored the mathematical consequences of prior misestimation on post-test probability estimation.
Results
We demonstrate that misestimation of prior probabilities has a nonlinear impact on posterior probabilities, with errors propagating differently depending on the likelihood ratio of the diagnostic test and the real pre-test probability. Misestimated priors can produce substantial distortions in posterior probabilities, leading to misplaced confidence in diagnostic test results.
Conclusions
Accurate estimation of pre-test probability is essential for the validity of Bayesian diagnostic reasoning. Objective and evidence-based approaches to pre-test probability estimation are necessary to minimize diagnostic errors and to enhance the reliability of clinical decision-making.
-
Research ethics: Not applicable.
-
Informed consent: Not applicable.
-
Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.
-
Use of Large Language Models, AI and Machine Learning Tools: None declared.
-
Conflict of interest: The authors state no conflict of interest.
-
Research funding: None declared.
-
Data availability: Not applicable.
References
1. Cahan, A. Diagnosis is driven by probabilistic reasoning: counter-point. Diagnosis 2016;3:99–101. https://doi.org/10.1515/dx-2016-0019.Suche in Google Scholar PubMed
2. Newman, TB, Kohn, MA. Evidence-based diagnosis. Cambridge: Cambridge University Press; 2009.10.1017/CBO9780511759512Suche in Google Scholar
3. Simel, DL, Rennie, D. The rational clinical examination: evidence-based clinical diagnosis. New York: McGraw Hill Professional; 2008.Suche in Google Scholar
4. Loscalzo, J, Fauci, AS, Kasper, DL, Hauser, S, Longo, D, Jameson, JL. Harrison’s principles of internal medicine, Twenty-First ed. New York: McGraw Hill Professional; 2022, 1 & 2.Suche in Google Scholar
5. Rzepiński, T. Subjectivity of pre-test probability value: controversies over the use of Bayes’ theorem in medical diagnosis. Theor Med Bioethics 2023;44:301–24.10.1007/s11017-023-09614-6Suche in Google Scholar PubMed PubMed Central
6. Hajek, A, Hitchcock, C. The oxford handbook of probability and philosophy. Oxford: Oxford University Press; 2017.10.1093/oxfordhb/9780199607617.001.0001Suche in Google Scholar
7. Uy, EJB. Key concepts in clinical epidemiology: estimating pre-test probability. J Clin Epidemiol 2022;144:198–202. https://doi.org/10.1016/j.jclinepi.2021.10.022.Suche in Google Scholar PubMed
8. Phelps, MA, Levitt, MA. Pretest probability estimates: a pitfall to the clinical utility of evidence-based medicine? Acad Emerg Med 2004;11:692–4. https://doi.org/10.1111/j.1553-2712.2004.tb02416.x.Suche in Google Scholar
9. Morgan, DJ, Pineles, L, Owczarzak, J, Magder, L, Scherer, L, Brown, JP, et al.. Accuracy of practitioner estimates of probability of diagnosis before and after testing. JAMA Intern Med 2021;181:747–55. https://doi.org/10.1001/jamainternmed.2021.0269.Suche in Google Scholar PubMed PubMed Central
10. Noguchi, Y, Matsui, K, Imura, H, Kiyota, M, Fukui, T. Quantitative evaluation of the diagnostic thinking process in medical students. J Gen Intern Med 2002;17:848–53. https://doi.org/10.1046/j.1525-1497.2002.20139.x.Suche in Google Scholar PubMed PubMed Central
11. Cahan, A, Gilon, D, Manor, O, Paltiel, O. Probabilistic reasoning and clinical decision-making: do doctors overestimate diagnostic probabilities? QJM 2003;96:763–9. https://doi.org/10.1093/qjmed/hcg122.Suche in Google Scholar PubMed
12. Srinivasan, P, Westover, MB, Bianchi, MT. Propagation of uncertainty in Bayesian diagnostic test interpretation. South Med J 2012;105:452–9. https://doi.org/10.1097/smj.0b013e3182621a2c.Suche in Google Scholar
13. Grimes, DA, Schulz, KF. Refining clinical diagnosis with likelihood ratios. Lancet 2005;365:1500–5.10.1016/S0140-6736(05)66422-7Suche in Google Scholar PubMed
14. de Alencar Neto, JN, Santos-Neto, L. The post hoc pitfall: rethinking sensitivity and specificity in clinical practice. J Gen Intern Med 2024;39:1506–10. https://doi.org/10.1007/s11606-024-08692-z.Suche in Google Scholar PubMed PubMed Central
15. Lewis, D. A subjectivist’s guide to objective chance. In: Harper, WL, Stalnaker, R, Pearce, G, editors. Ifs: conditionals, belief, decision, chance, and time. Dordrecht: Springer Netherlands; 1980:267–97 pp.Suche in Google Scholar
16. Jeffrey, R. Subjective probability: the real thing. Cambridge: Cambridge University Press; 2004.10.1017/CBO9780511816161Suche in Google Scholar
17. Titelbaum, MG. Fundamentals of Bayesian epistemology 1: introducing credences. Oxford: Oxford University Press; 2022.10.1093/oso/9780198707608.001.0001Suche in Google Scholar
18. Titelbaum, MG. Fundamentals of Bayesian epistemology 2: arguments, challenges, alternatives. Oxford: Oxford University Press; 2022.10.1093/oso/9780192863140.001.0001Suche in Google Scholar
19. de Alencar, JN, da Costa, GG, de Souza, VBP, Barbara, FN, Gonzaga, Y, Migowski, A. Evaluating clinical utility in diagnostic tests: likelihood ratios confidence intervals and proposal of a simple index. J Evidence Based Med 2024;17:477–9. https://doi.org/10.1111/jebm.12641.Suche in Google Scholar PubMed
20. Gigerenzer, G, Gaissmaier, W, Kurz-Milcke, E, Schwartz, LM, Woloshin, S. Helping doctors and patients make sense of health statistics. Psychol Sci Publ Interest 2007;8:53–96. https://doi.org/10.1111/j.1539-6053.2008.00033.x.Suche in Google Scholar PubMed
21. Steib, N, Büchter, T, Eichler, A, Binder, K, Krauss, S, Böcherer-Linder, K, et al.. How to teach Bayesian reasoning: an empirical study comparing four different probability training courses. Learn InStruct 2025;95:102032. https://doi.org/10.1016/j.learninstruc.2024.102032.Suche in Google Scholar
22. Welch, HG, Schwartz, L, Woloshin, S. Overdiagnosed: making people sick in the pursuit of health. Boston: Beacon Press; 2011.Suche in Google Scholar
23. Chu, K, Brown, AFT. Likelihood ratios increase diagnostic certainty in pulmonary embolism. Emerg Med Australas 2005;17:322–9. https://doi.org/10.1111/j.1742-6723.2005.00754.x.Suche in Google Scholar PubMed
24. Genders, TSS, Steyerberg, EW, Hunink, MGM, Nieman, K, Galema, TW, Mollet, NR, et al.. Prediction model to estimate presence of coronary artery disease: retrospective pooled analysis of existing cohorts. BMJ 2012;344:e3485. https://doi.org/10.1136/bmj.e3485. [cited 2025 Aug 4];Available from: https://www.bmj.com/content/344/bmj.e3485.Suche in Google Scholar PubMed PubMed Central
25. Kozlov, SG, Chernova, OV, Shitov, VN, Matveeva, MA, Alekseeva, IA, Saidova, MA. The diagnostic accuracy of exercise treadmill testing and stress echocardiography for the detection of obstructive coronary artery disease in patients aged ≥70 years. Kardiologiia 2019;59:23–30. https://doi.org/10.18087/cardio.2019.10.n438.Suche in Google Scholar PubMed
26. O’Sullivan, ED, Schofield, SJ. Cognitive bias in clinical medicine. J R Coll Physicians Edinburgh 2018;48:225–32.10.4997/jrcpe.2018.306Suche in Google Scholar
27. Raz, M, Pouryahya, P. Decision making in emergency medicine: biases, errors and solutions. Singapore: Springer Nature; 2021.10.1007/978-981-16-0143-9Suche in Google Scholar
© 2025 Walter de Gruyter GmbH, Berlin/Boston
