Theorems on the Prevalence Threshold and the Geometry of Screening Curves

Dr. Jacques Balayla MD, MPH is a board-certified Obstetrician-Gynecologist. He obtained his medical degree from McGill University in 2012, where he went on to complete subspecialty training in Obstetrics and Gynaecology.  He is now a faculty lecturer and Osler fellow in the department of Obstetrics and Gynecology at McGill University and is a clinical investigator at the Lady Davis Institute (LDI) of the Jewish General Hospital in Montreal, Canada. During his training, Dr. Balayla obtained a certification in Human Genetics with distinction at Harvard University. Likewise, he graduated from the Clinician-Investigator Program (CIP) from the Royal College of Physicians and Surgeons of Canada with honours and obtained a Master of Public Health (MPH) degree with honours at the University of Montreal's School of Public Health (ESPUM).  Dr. Balayla has been active in clinical research for over 14 years and has been the recipient of numerous honours and recognitions for his work. Most notably, the Pregnancy Foundation, and the Society for Maternal-Fetal Medicine awarded Dr. Balayla the prestigious ``Quilligan Scholar" title, for his promise as a future leader in Obstetrics and Perinatology. Dr. Balayla has also been recognized by the Quebec Medical Association (QMA) as the ``Emerging Medical Professional of the Year" as well as by his Alma Matter, where he received the ``McGill Alumni Global (MAG) - Young Alumni Award" for having made extraordinary contributions to McGill University, fellow alumni and Society.

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.