Bayes’ Rule in COVID-19 Breakthroughs
In July 2021, the amount of Covid-19 cases increased exponentially due to the rise in the Delta variant. The Delta variant is highly transmissible in comparison to other variants due to the high replication rate. Moreover, the Delta variant can even impact those who are unvaccinated. For example, a case has shown that in Massachusetts three-fourths of the people who were infected by the Delta variant were vaccinated. But, none of the people who were vaccinated died. Thus, the article encourages that people should continue getting vaccinated as soon as possible to reduce the risk of getting the Delta variant along with other symptoms. In conjunction with vaccines, universal masking is proven as an effective way to eliminate the high risk of getting the Delta variant. The vaccine cannot be relied on just on its own. With the rise in more people getting vaccinated, it does increase the possibility of there being more breakthrough infections. The CDC uses Bayes’ theorem to calculate the probability of there being a breakthrough. Given that 60% of the population is fully vaccinated and the vaccination has an 80% effectiveness rate, then the probability of there being breakthroughs is a quarter. However, if 70% of the population is fully vaccinated (10% increase) then the probability of there being a breakthrough is now one-third. Thus, with a higher vaccination rate comes a higher probability of there being a breakthrough. However, the CDC does discuss implications with these estimates as some areas, such as nursing homes, can result in a disproportionate number of breakthroughs since the effectiveness of the vaccine would decrease.
This article connects with the application of the Bayes’ rule from the lecture and our problem sets. In Bayes’ rule, we use this formula to conclude which decision is best given the information we got. From there, we can also get the reverse conditional probability from the given conditional probabilities. The lecture used marbles as an example given that if a person draws a blue or red marble then what is the probability that it is majority red or majority blue marbles. And, one of the problems given to us applies the concepts of probability to also calculate the erroneous diagnosis produced by the BCF-detection test. Connecting these ideas of probability to deduce the best response from the lecture, here the CDC is also using Bayes’ rule and the probability rules to find the probability of there being a breakthrough where vaccinated people get Covid-19 given the number of people fully vaccinated. Here, the CDC uses Bayes’ rule to assess the potential risks associated with also getting vaccinated. Despite the Bayes’ rule giving the following probability that a higher vaccination percentage results in also a higher breakthrough infection number, the CDC still concludes being vaccinated is still the best option.
Source: Nedelman, Michael. “Five Takeaways on the Science Behind CDC’s Latest Mask Guidance.” CNN, Cable News Network, 31 July 2021, https://www.cnn.com/2021/07/31/health/covid-breakthrough-cdc-masks-five-takeaways/index.html.