Confidence Intervals of COVID-19 Vaccine Efficacy Rates

This tutorial uses publicly available data from drug makers and the Food and Drug Administration to guide learners to estimate the confidence intervals of COVID-19 vaccine efficacy rates with a Bayesian framework. Under the classical approach, there is no probability associated with a parameter, and the meaning of confidence intervals can be misconstrued by inexperienced students. With Bayesian statistics, one can find the posterior probability distribution of an unknown parameter, and state the probability of vaccine efficacy rate, which makes the communication of uncertainty more flexible. We use a hypothetical example and a real baseball example to guide readers to learn the beta-binomial model before analyzing the clinical trial data. This note is designed to be accessible for lower-level college students with elementary statistics and elementary algebra skills.