Bayes’ Theorem and its application to COVID-19 Testing
Source: https://www.varsity.co.uk/science/21149
Bayes’ Theorem is a critical part of our course relating to information cascades. It allows us to determine the probabilities of events that are dependent on each other occurring, given known information about some of the events. This article implements Bayes’ Theorem to a topic that has dominated our society for over a year: COVID-19 tests.
The article makes assumptions about the sensitivity and specificity rates of a certain COVID-19 test and uses those assumptions to determine the probability of someone with a positive test result having the virus. The shocking result in this experiment: only 16% of those who test positive have COVID-19. The operating assumptions were that 1% of a population was infected, and the test had a 95% specificity and sensitivity. 16% seems like a completely unrealistic figure, but the fact is that false positives make up the majority of positive tests. Now, if the same person tests positive twice, the probability that they are infected, using Bayes’ Theorem, jumps to over 78%. These figures start to put nationwide COVID-19 protocols into perspective. The first thing that happens when someone tests positive is testing them again. The natural reaction would be that it is a simple verification of the results, but knowing that the majority of positive tests are false, testing again is absolutely necessary for accuracy in the results.
The most interesting piece of the article is how the basic assumptions drastically change the mathematical results of the experiment. One of the key pieces in determining the likelihood of infection was the prior probability of infection. In the 16% example, the person in question has no symptoms of COVID-19, so their likelihood of infection was 1%, equal to that of the total population. However, if symptoms were noted as well, such as a cough, fever, or lack of smell, that 1% increases to a significantly higher figure, which in turn increases the probability of infection. Other factors could be considered as well, such as proximity to others who tested positive and lifestyle habits. These groups of people who test positive can be treated as subgroups of a larger population network, one in which degrees of separation is crucial in determining the likelihood of infection for a tight group of nodes. As you can see, this is all incredibly relevant to both our current discussions in class and those from the outset of the semester.