The design and analysis of vaccine trials for COVID-19 for the purpose of estimating efficacy

After a preliminary explanation as to how I came to know Andy Grieve and some remarks about his career and mine and how they have intersected, I consider the design and analysis of trials of vaccines for COVID-19 for the purpose of estimating efficacy. Five large trials, run by the sponsors Pfizer/BioNTech, AstraZeneca/Oxford University, Moderna, Novavax and J&J Janssen are considered briefly. Frequentist approaches to analysis were used for four of the trials but Pfizer/BioNTech nominated a Bayesian approach. The design and analysis of this trial is considered in some detail, in particular as regards the choice of prior distribution. I conclude by drawing some general lessons.