Theorems on the Prevalence Threshold and the Geometry of Screening Curves: A Bayesian Approach to Clinical Decision-Making - Softcover

Balayla, Jacques

Softcover

ISBN 10: 3031714547 ISBN 13: 9783031714542

Publisher: Springer, 2025

Synopsis

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.

About this title

About the Author

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.

From the Back Cover

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.

Edition details

• Publisher: Springer
• Publication date: 2025
• Language: English
• ISBN 10: 3031714547
• ISBN 13: 9783031714542
• Binding: Paperback
• Number of pages: 329