03790nam a22004335i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001200153072001600165072002300181072001500204100007900219245017500298250001800473264006900491300006500560336002600625337002600651338003600677347002400713505107300737520122201810650001803032650001503050650002303065650001603088650001503104650002303119710003403142773002603176776003603202776003603238776003603274856004603310978-3-031-71452-8DE-He21320251030113306.0cr nn 008mamaa241110s2024    sz |    s    |||| 0|eng d  a97830317145287 a10.1007/978-3-031-71452-82doi 4aRG1-991 7aMJT2bicssc 7aMED0330002bisacsh 7aMKC2thema1 aBalayla, Jacques.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aTheorems on the Prevalence Threshold and the Geometry of Screening Curvesh[electronic resource] :bA Bayesian Approach to Clinical Decision-Making /cby Jacques Balayla.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aXXI, 308 p. 64 illus., 50 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda0 a1. 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.  aIn 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. 0aGynecology . 0aDiagnosis. 0aInternal medicine.14aGynecology.24aDiagnosis.24aInternal Medicine.2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303171451108iPrinted edition:z978303171453508iPrinted edition:z978303171454240uhttps://doi.org/10.1007/978-3-031-71452-8