Mean-Minimum Exact Confidence Intervals

Confidence interval estimation for vaccine efficacy against COVID-19

This article focuses on the construction of a confidence interval for vaccine efficacy against contagious coronavirus disease-2019 (COVID-19) in a fixed number of events design. Five different approaches are presented, and their performance is investigated in terms of the two-sided coverage probability, non-coverage probability at the lower tail, and expected confidence interval width. Furthermore, the effect of under-sensitivity of diagnosis tests on vaccine efficacy estimation was evaluated. Except for the exact conditional method, the non-coverage probability of the remaining methods may exceed the nominal significance level, e.g., 5%, even for a large number of total confirmed COVID-19 cases. The narrower confidence interval width from the Bayesian, approximate Poisson, and mid-P methods are on the cost of increased instability of coverage probability. When the sensitivity of diagnosis test in the vaccine group is lower than that in the placebo group, the reported vaccine efficacy tends to be overly optimistic. The exact conditional method is preferable to other methods in COVID-19 vaccine efficacy trials when the total number of cases reaches 60; otherwise, mid-p method can be used to obtain a narrower interval width.

Ensemble confidence intervals for binomial proportions

We propose two measures of performance for a confidence interval for a binomial proportion p: the root mean squared error and the mean absolute deviation. We also devise a confidence interval for p based on the actual coverage function that combines several existing approximate confidence intervals. This "Ensemble" confidence interval has improved statistical properties over the constituent confidence intervals. Software in an R package, which can be used in devising and assessing these confidence intervals, is available on CRAN.