Theorems on the Prevalence Threshold and the Geometry of Screening Curves : A Bayesian Approach to Clinical Decision-Making / by Jacques Balayla.

Format:

Book

Author/Creator:

Balayla, Jacques.

Language:

English

Subjects (All):

Gynecology.

Diagnosis.

Internal medicine.

Internal Medicine.

Local Subjects:

Gynecology.

Diagnosis.

Internal Medicine.

Physical Description:

1 online resource (315 pages)

Edition:

1st ed. 2024.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Springer, 2024.

Summary:

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.

Contents:

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.

ISBN:

9783031714528

3031714520