Dr. Jacques Balayla (MDCM鈥�12, PGME鈥�20) developed a passion for mathematics after fleeing with his parents from the ongoing social, political and economic turbulence of his native Venezuela in 2002. Now a husband and father of five, mathematics still plays a large role in his life.
鈥淕rowing up in Venezuela鈥攁 country with a rich cultural history but marked by instability and constant change鈥攂rought uncertainty and fear about the future,鈥� recalls Balayla. Mathematics was the perfect calming antidote and outlet for this bright, budding physician, now faculty lecturer in obstetrics and gynecology at 黑料不打烊 University and clinical investigator at the Lady Davis Institute of the Jewish General Hospital.
鈥淚 was always fascinated by mathematics, the opposite of the uncertainty I鈥檇 experienced,鈥� he explains. 鈥淢athematics provides a universal foundation for truth and logic, and it doesn鈥檛 allow room for ambiguity. Finding refuge in a discipline so consistent and reliable helped me manage uncertainty elsewhere, and regain a sense of peace and control.鈥�
As a student, he enjoyed solving mathematical problems to develop his analytical skills鈥攁 passion he now channels into applying mathematical and geometric models to bring greater precision to clinical medicine and public health decision-making in Canada and beyond.
Using geometry to address screening test failings
In his new book, , Balayla introduces the 鈥減revalence threshold鈥� concept. This principle, derived from the geometric study of screening curves, can enhance interpretation of screening test results across many medical conditions, ultimately increasing the value and reliability of clinical assessments.
The prevalence threshold is particularly useful in providing a quantifiable framework to help clinicians, public health policymakers and patients better understand and contextualize the limitations and lack of certainty in medical screening tests鈥攆alse positives, false negatives and inconclusive results鈥攁nd better assess overall risk.
鈥淭he primary job of a clinician is to gather information to arrive at a diagnosis. What is not known is, how much information is required to be confident in our assessment? The prevalence threshold is a tipping point in that information-gathering process beyond which further information starts to yield diminishing returns. It can act as a benchmark in clinical decision-making,鈥� he explains.
The distressing and confusing limitations of prenatal screening were a catalyst for Balayla to develop the novel theory proposed in his book. 鈥淚 was surprised by the high number of false positive results,鈥� he says. 鈥淧atients who tested positive were doubly stressed. First because of a potential life-altering diagnosis, and second because they had to undergo diagnostic testing, which is invasive and carries risks of complications鈥攎ost often with a false flag in the end.鈥� Balayla notes that a profusion of false positives also leads to more diagnostic tests, like amniocentesis, which cost the healthcare system over $500 each.
Screening curves reveal true risk probabilities
Balayla turned to mathematics and differential geometry to gain an objective and fuller understanding of false positives and other ambiguities in screening tests. His book shows how the reliability, or predictive value, of a test is related to a condition鈥檚 prevalence. A positive result for a common disease like diabetes, for example, is much more likely to be real than for a rarer condition. 鈥淭his is a big problem because in prenatal screening for rare conditions, like Down鈥檚 Syndrome, the test is fantastically accurate at detecting the condition when it鈥檚 there, but the predictive value is very poor since there are many more false positives than real positives.鈥�
The screening curves and equations presented in Balayla鈥檚 book visually illustrate鈥攁nd mathematically calculate鈥攖he true probability that a positive screening result reflects a true positive. These tools could help clinicians become more adept at interpreting and conveying risk information in a personalized, precise way.
More objective, nuanced assessments of these risk probabilities could also help reduce unnecessary testing. 鈥淭here are add-ons to standard prenatal screening tests, which test for even rarer genetic conditions, where doing the diagnostic testing almost carries a higher risk of complications than the very low risk of the result being a real positive,鈥� he cautions. 鈥淭hat鈥檚 why I often advise patients who have no risk factors to forgo this complementary testing.鈥�
Personalizing decision-making for many medical conditions
While the theory was born out of prenatal care, its applications are far-reaching, as they apply equally to virtually any medical condition amenable to screening. The book describes a diagnostic algorithm derived from Bayesian theory, which uses decision theory concepts to calculate the overall probability that a patient truly has a given condition. This algorithm incorporates the prevalence threshold and screening or diagnostic test results in the context of other relevant information such as a patient鈥檚 family history, age, symptoms, and other risk factors.
Balayla proposes that healthcare professionals can apply these tools and concepts to personalize the use of screening and diagnostic tests in clinical decision-making for individual patients, and optimize their use at the population level. 鈥淔or instance, a cancer screening test could be adjusted to account for a patient鈥檚 family history, age and other characteristics, allowing for a more tailored approach to diagnosis and treatment. The prevalence threshold would then help identify the exact population that would require more emergent screening, and thereby reduce the rate of false positive results and unnecessary testing.鈥�
Adds Balayla, 鈥淚鈥檓 proud of this work because it showcases the power of mathematics to explain the world in a way that鈥檚 easier to grasp than traditional subjective methods. We鈥檙e now building a team at 黑料不打烊 to test the theory and ensure these innovations are grounded in evidence and applicable in practice to improve the human experience in health care.鈥�