Estimating with confidence the risk of rare adverse events, including those with observed rates of zero☆

Abstract

Omission of a confidence interval (CI) associated with the risk of a serious complication can lead to inaccurate interpretation of risk data. The calculation of a CI for a risk or a single proportion typically uses the familiar Gaussian (normal) approximation. However, when the risk is small, "exact" methods or other special techniques should be used to avoid overshooting (risks that include values outside of [0,1]) and zero width interval degeneration. Computer programs and simple equations are available to construct CIs reasonably accurately. In the special case in which the complication has not occurred, the risk estimated with 95% confidence is no worse than 3/n, where n is the number of trials.