Low incidence rate of COVID-19 undermines confidence in estimation of the vaccine efficacy

Knowing the true effect size of clinical interventions in randomised clinical trials is key to informing the public health policies. Vaccine efficacy is defined in terms of the ratio of two risks, however only approximate methods are available for the variance of the 'risk ratio'. In this article, we show using a probabilistic model that uncertainty in the efficacy rate could be underestimated when the disease risk is low. Factoring in the baseline rate of the disease we estimate broader confidence intervals for the efficacy rates of the vaccines recently developed for COVID-19. We propose a new method for calculating the sample size in case-control studies where the efficacy is of interest. We further discuss the deleterious effects of classification bias which is particularly relevant at low disease prevalence.