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Theorems on the prevalence threshold and the geometry of screening curvesa bayesian approach to clinical decision-making /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Theorems on the prevalence threshold and the geometry of screening curvesby Jacques Balayla.
Reminder of title:	a bayesian approach to clinical decision-making /
Author:	Balayla, Jacques.
Published:	Cham :Springer Nature Switzerland :2024.
Description:	xxi, 308 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Clinical medicineDecision making
Online resource:	https://doi.org/10.1007/978-3-031-71452-8
ISBN:	9783031714528$q(electronic bk.)

Theorems on the prevalence threshold and the geometry of screening curvesa bayesian approach to clinical decision-making /
Balayla, Jacques.

Theorems on the prevalence threshold and the geometry of screening curvesa bayesian approach to clinical decision-making /[electronic resource] :by Jacques Balayla. - Cham :Springer Nature Switzerland :2024. - xxi, 308 p. :ill. (some col.), digital ;24 cm.

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.

ISBN: 9783031714528$q(electronic bk.)

Standard No.: 10.1007/978-3-031-71452-8doiSubjects--Topical Terms:

985493
Clinical medicine
--Decision making

LC Class. No.: RC48

Dewey Class. No.: 616

Theorems on the prevalence threshold and the geometry of screening curvesa bayesian approach to clinical decision-making /
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505 0 $a 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.
520 $a 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.
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