Vaccine Efficacy Calculator

Vaccine efficacy is built from the ratio of the two groups' attack rates, so more cases among the vaccinated (holding group size fixed) pushes that ratio toward 1 -- meaning vaccination looks less protective -- and lowers VE. More cases among the unvaccinated has the opposite effect: it makes the unvaccinated group's baseline risk look worse by comparison, which mathematically raises the calculated efficacy of the vaccine even though nothing about the vaccinated group changed.

Vaccine efficacy is a relative measure -- the percentage reduction in risk compared to the unvaccinated group's own baseline -- while absolute risk reduction is the raw percentage-point gap between the two attack rates. A vaccine can post a high relative efficacy (say 90%) while still representing a small absolute risk reduction if the disease is rare to begin with, which is exactly why number needed to vaccinate is reported alongside both: it translates the absolute reduction into a concrete "how many people" figure.

A larger total vaccinated denominator, holding the case count fixed, lowers the vaccinated group's attack rate (fewer cases per person), which shrinks the ratio against the unvaccinated group's attack rate and therefore raises the calculated VE. This is a purely arithmetic relationship between group size and attack rate, not evidence that adding more vaccinated people to a study makes the vaccine itself more effective.

It depends heavily on how many cases occurred, not just group size -- a trial with very few total cases, even across large groups, tends to produce a wide confidence interval because the case counts driving the variance estimate are small, while a trial with more cases in both arms narrows the interval considerably around the point estimate for vaccine efficacy.