Bayes Theorem Governs the Reliability of Covid Testing
The ongoing global pandemic that refuses to subside despite immense vaccination rates has made COVID testing very important. The linked article talks about the importance of Bayes’ Theorem in understanding the accuracies of lateral flow tests (LFTs), and applies the formula to check the rate of false positives and negatives in COVID testing. This is a very direct application of Bayes’ Theorem, and, in fact, is very similar to a disease-modeling problem on one of our Homeworks. The main concern with LFTs is that they are less sensitive than typical COVID tests but are more precise. Given that LFTs have a high accuracy, we note that if a person gets a positive result, the chance of having COVID cannot be estimated only from the false positivity rate; this is where Bayes theorem comes in and we prove this from simple substitutions in the formula.
The real interesting part is that this phenomenon is not only true in theory, but also in actual cases. A study found out that 60% of women who get annual mammograms have at least one false positive, which is an alarming large number for a test of this importance. Another study about prostrate cancer found that 70% of all screenings were false positives. In fact, the application also extends to courts of law, when we have the probability of a person being guilty and have to make decisions based off of it. There have been cases where people were falsely accused because the right considerations were not made. According to an old study linked in the article, even doctors have misunderstood Bayesian reasoning. This article tackles multiple fields, not just COVID tests, where the knowledge of Bayes’ Theorem is so important, and a lack of understanding of this concept can lead to wrong decision-making. It was interesting to see that a simple formula we learn in class has such clear and direct real-world impacts.
“The Obscure Maths Theorem That Governs the Reliability of Covid Testing.” The Guardian, Guardian News and Media, 18 Apr. 2021, https://www.theguardian.com/world/2021/apr/18/obscure-maths-bayes-theorem-reliability-covid-lateral-flow-tests-probability.
Breast Cancer Study: https://pubmed.ncbi.nlm.nih.gov/26756737/
Prostrate Cancer Study: https://pubmed.ncbi.nlm.nih.gov/1371559/