Recommendations for the use of Taylor series confidence intervals for estimates of vaccine efficacy.

A simple formula for calculating confidence intervals by means of a Taylor series variance approximation has been recommended for gauging the precision of estimates of vaccine efficacy. To evaluate the performance of Taylor series 95% confidence intervals for vaccine efficacy, we conducted a simulation study for commonly expected values of vaccine efficacy, risk of disease in the unvaccinated population, and sample sizes of the vaccinated and unvaccinated groups. In the first simulation, the sample size in the vaccinated group was 500 or 1000, whereas that in the unvaccinated group ranged from 10 to 1000. The confidence intervals were accurate when the sample size in the unvaccinated group was >/=50 and the risk of disease was 0.3-0.9. In contrast, the intervals were too narrow when all three of the following situations occurred: the number of unvaccinated was small (10 or 20), the true vaccine efficacy was relatively low (60% or 80%), and the risk of disease was 0.5-0.9. Furthermore, when the true vaccine efficacy was high (90% or 95%) and the disease risk in the unvaccinated was low (0.1 and 0.2), the confidence intervals were too broad, especially when the unvaccinated sample size was <50. Additional simulations with a sample size in the vaccinated group of 200 gave broad intervals for 95% vaccine efficacy (for all values of disease risk) and for 90% vaccine efficacy when the disease risk was </=0.3.