04104nam a22005175i 4500 978-3-031-71452-8 DE-He213 20251030113306.0 cr nn 008mamaa 241110s2024 sz | s |||| 0|eng d 9783031714528 978-3-031-71452-8 10.1007/978-3-031-71452-8 doi RG1-991 MJT bicssc MED033000 bisacsh MKC thema Balayla, Jacques. author. aut http://id.loc.gov/vocabulary/relators/aut 87291 Theorems on the Prevalence Threshold and the Geometry of Screening Curves [electronic resource] : A Bayesian Approach to Clinical Decision-Making / by Jacques Balayla. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XXI, 308 p. 64 illus., 50 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda 1. Introductory remarks on screening -- 2. Clinical judgement and decision-making -- 3. Bayes' theorem -- 4. Odds, probability and likelihood ratios -- 5. Prevalence threshold, screening curves and screening probability square plane S -- 6. Sequential Bayesian updating -- 7. Orthogonal Bayesian updating, parallel testing and asymptotic convergence -- 8. Theorems on the geometric definition of the positive likelihood ratio K -- 9. The screening paradox and dynamic systems -- 10. Performance metrics of binary classifiers -- 11. Applications in Bayesian epistemology and artificial intelligence (AI) -- 12. What constitutes a sufficiently adequate binary classification system? -- 13. Gaussian distribution, confidence intervals, binomial (Wald) proportion, wilson score interval and delta theorem -- 14. Prevalence Threshold and Public Health -- 15. Shannon's entropy, Kullback-Leibler divergence, and mutual information in diagnostic systems -- 16. Estimating pretest probabilities -- 17. Case studies - clinical examples -- 18. Limitations and future directions. In Theorems on the Prevalence Threshold and the Geometry of Screening Curves, the author explores the mathematical underpinnings of screening and diagnostic testing, offering a unique and novel perspective which employs classical differential geometry and Bayesian theory to elucidate critical aspects of clinical decision-making. Taking the reader on a mathematical journey which bridges these seemingly unrelated worlds, the author presents a quantifiable framework on clinical judgement by introducing the “prevalence threshold” – a novel statistical parameter derived from Bayesian principles by means of the study of the geometry of screening curves. As the prevalence threshold demarcates the pretest probability level beyond which additional information ceases to significantly enhance the yield and reliability of a clinical assessment, it may serve as a benchmark for confidence in clinical decision-making. Given the theorems herein described, readers will find comprehensive analyses and insightful explorations of how these geometric concepts apply to real-world diagnostic scenarios, allowing the clinician to navigate clinical care more effectively at both the individual and public health levels. Gynecology . 64086 Diagnosis. 64942 Internal medicine. Gynecology. 64086 Diagnosis. 64942 Internal Medicine. SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031714511 Printed edition: 9783031714535 Printed edition: 9783031714542 https://doi.org/10.1007/978-3-031-71452-8 ZDB-2-SME ZDB-2-SXM 64845 64845