Or, perhaps, they never came in contact with someone who already had the virus.

Someone once said "you can prove anything with statistics"

Vaccine efficacy is the percentage reduction of disease in a vaccinated group of people compared to an unvaccinated group, using the most favorable conditions. Vaccine efficacy was designed and calculated by Greenwood and Yule in 1915 for the cholera and typhoid vaccines. It is best measured using double-blind, randomized, clinical controlled trials, such that it is studied under “best case scenarios.” Vaccine effectiveness differs from vaccine efficacy in that vaccine effectiveness shows how well a vaccine works when they are always used and in a bigger population whereas vaccine efficacy shows how well a vaccine works in certain, often controlled, conditions. Vaccine efficacy studies are used to measure several possible outcomes such as disease attack rates, hospitalizations, medical visits, and costs.

Vaccine efficacy formula

The outcome data (vaccine efficacy) generally are expressed as a proportionate reduction in disease attack rate (AR) between the unvaccinated (ARU) and vaccinated (ARV), or can be calculated from the relative risk (RR) of disease among the vaccinated group.

The basic formula is written as:

where RR is the relative risk of developing the disease for vaccinated people compared to unvaccinated people.

Testing for efficacy

Vaccine efficacy differs from vaccine effectiveness in the same way that an explanatory clinical trial differs from an intention to treat trial: vaccine efficacy shows how effective the vaccine could be given ideal circumstances and 100% vaccine uptake; vaccine effectiveness measures how well a vaccine performs when it is used in routine circumstances in the community. What makes the vaccine efficacy applicable is that it shows the disease attack rates as well as a tracking of vaccination status. Vaccine effectiveness is more easily tracked than the vaccine efficacy considering the difference in environment;[vague] however, the vaccine efficacy is more expensive and difficult to conduct. Because the trial is based on people who are taking the vaccination and those not vaccinated, there is a risk for disease, and optimal treatment is needed for those who become infected.

The advantages of a vaccine efficacy have control for all biases that would be found with randomization, as well as prospective, active monitoring for disease attack rates, and careful tracking of vaccination status for a study population there is normally a subset as well, laboratory confirmation of the infectious outcome of interest and a sampling of vaccine immunogenicity. The major disadvantages of vaccine efficacy trials are the complexity and expense of performing them, especially for relatively uncommon infectious outcomes of diseases for which the sample size required is driven up to achieve clinically useful statistical power.

Or, perhaps, they never came in contact with someone who already had the virus.

Someone once said "you can prove anything with statistics"