Plausibility of claimed Covid-19 vaccine efficacies by age: a simulation study

Abstract

BACKGROUND: Multiple vaccines against Covid-19 have passed through phase-3 trials; however, concerns have been raised about alleged excessive similarity of efficacy across age groups for the Sputnik V vaccine. STUDY QUESTION: How likely are the observed efficacies for all age subgroups to fall within the range of by-age efficacies claimed for the AstraZeneca, Janssen, Moderna, Pfizer, and Sputnik V vaccines, assuming that there is no effect of age on efficacy? STUDY DESIGN: We performed a simulation study using R of 1000 and then 50,000 simulated trials for each vaccine, with random allocation to each arm but fixed enrolment numbers by age group. We used study-wide efficacy and infection rate for all age groups. We recorded the observed vaccine efficacies in each age group and summated how many simulations had all observed efficacies fall within the range of efficacies described in the relevant article. RESULTS: In the 1000-trial simulation for the AstraZeneca vaccine, in 23.8% of simulated trials, the observed efficacies of all age subgroups fell within the efficacy bounds for age subgroups in the published article. The J + J simulation showed 44.7%, Moderna 51.1%, Pfizer 30.5%, and 0.0% of the Sputnik simulated trials had all age subgroups fall within the limits of the efficacy estimates described by the published article. In 50,000 simulated trials of the Sputnik vaccine, 0.026% had all age subgroups fall within the limits of the efficacy estimates described by the published article, whereas 99.974% did not. CONCLUSIONS: The distribution of alleged vaccine efficacies of the Sputnik vaccine by age in the phase-III trial is very unlikely to occur in genuine experimental data, even if the number of patients recruited, vaccine efficacy, and overall infection rate are true and there is no underlying difference in vaccine efficacy by age.