False Positives & Negatives for COVID-19 tests | Using Bayes' Theorem to Estimate Probabilities

Suppose you test positive or negative for SARS-Cov-2, the coronavirus that causes COVID-19. What are the chances you actually have the disease? In this video we're going to look at Bayes' Theorem from mathematics to help us compute the conditional probabilities. COVID-19 tests are actually in two categories, genetic tests and antibody tests, and both of these have different levels of sensitivity and specificity - i.e how accurate they are. While Genetic tests have extremely low false positive rates, some antibody tests do have higher false positive rates and, given the low prevalence in the general population, Bayes' theorem demonstrates how problematic this can actually be. Disclaimer: I'm not a medical doctor or epidemilogist, just a math prof, and so these toy examples are meant to illustrate the ideas of Bayes' theorem, not make actual concrete predictions based on a specific test. Intro to Bayes' Theorem Video: https://www.youtube.com/watch?v=XQoLVl31ZfQ&vl=en Some references: FDA (genetic test have nearly 100% specificity):https://www.fda.gov/media/136151/download Genetic Test False negatives: https://www.medscape.com/viewarticle/930650 Abbott Test study showing 15% false negatives: https://www.npr.org/sections/health-shots/2020/04/21/838794281/study-raises-questions-about-false-negatives-from-quick-covid-19-test Antibody test sensitivity and specificities: https://www.centerforhealthsecurity.org/resources/COVID-19/serology/Serology-based-tests-for-COVID-19.html Antibody tests false positive due to cross-reactivity with other coronavirus antibodies: https://www.aruplab.com/news/4-21-2020/How-Accurate-Are-COVID-19-Tests Course Playlists: ►CALCULUS I: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m ► CALCULUS II: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n ►CALCULUS III -Multivariable Calculus: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd ►DISCRETE MATH: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS ►LINEAR ALGEBRA: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6 *************************************************** ► Want to learn math effectively? Check out my "Learning Math" Series: https://www.youtube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw ►Want some cool math? Check out my "Cool Math" Series: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpiho **************************************************** ►Follow me on Twitter: http://twitter.com/treforbazett ***************************************************** This video was created by Dr. Trefor Bazett. I'm an Assistant Teaching Professor at the University of Victoria. BECOME A MEMBER: ►Join: https://www.youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/join MATH BOOKS & MERCH I LOVE: ► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett