Estimating protective vaccine efficacy from large trials with recruitment

Vaccine response is often random because of possible vaccine failures and variation in the immune systems of hosts. A concept of protective vaccine efficacy is defined as the mean vaccine ability to reduce individual susceptibilities to infection. The problem under study is how to measure this efficacy from data on a large vaccine trial in which participants are recruited over a period of time. First, lower and upper bounds are derived that apply for all types of protection induced by the vaccine. Then, the lower bound is shown to be a good estimator under certain conditions usually met in practice.