Bayes’ Theorem in a Pandemic World
Bayes’ Theorem is one of the fundamental rules in statistics, helping compute the probability of various events and using these calculated probabilities to reason about decision-making. With the COVID-19 pandemic almost fully behind us, we can take the lessons we have learned about how COVID spreads and determine best-course actions for future pandemics. One of the most important aspects that helped stop the spread of COVID at its peak were COVID tests. Ranging from antigen to PCR tests, different tests were available and the speed of their results often correlated with their accuracy.
Bayes’ Theorem helps us analyze and create models of decision-making with new information and data, and using this theorem we can see the reliability and accuracy of positives in COVID tests. More often than not, many people said they think they had COVID, but possibly asymptomatically, especially at the beginning of the pandemic. But for simplicity sake, we will analyze using Bayes’ Theorem the probabilities that a given person who tested positive for COVID actually has it.
Let’s say that someone with COVID tests positive for COVID at a rate of 98%.
P(TEST+|COVID+) = 0.98
Let’s say that someone who does not have COVID tests negative for COVID at a rate of 96%.
P(TEST-|COVID-) = 0.96
Now, we want to find the probability that a given person who tested positive for COVID actually has the virus, or P(COVID+|TEST+).
Therefore, by Bayes’ Theorem, we know that
P(COVID+|TEST+) = P(COVID+)P(TEST+|COVID+) / (P(COVID+)P(TEST+|COVID+) + P(COVID-)P(TEST+|COVID-) )
Let’s say that the probability of getting COVID is 0.1% if you double mask. Then,
P(COVID+|TEST+) = (0.001*0.98)/(0.001*0.98+0.999*0.04) = 2.39%
This matches with the fact that PCR tests are about 97-98% accurate. It is also possible to analyze and see how likely it is to get COVID based on certain probabilities, such as how effective single vs double masking is or surgical masks compared to KN95 masks. We see from here that Bayes’ Theorem has many applications and will continue to be useful for judging how useful certain decisions are amidst uncertainty, which this pandemic definitely was the epitome of.