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When estimating the prevalence of an event, a common approach is to use Wald-based confidence intervals. However, when the event is rare, it is best to use score-based or other non-Wald methods. While problems with Wald-based methods are well-known among statisticians, these problems and alternative methods may be less well-known in practice.
This analysis examines the performance of confidence intervals computed under a variety of Wald and non-Wald-based methods by simulation when events are rare. When events are rare, Wald-based 95% confidence intervals presented coverage probabilities substantially below 95%; score-based 95% confidence intervals presented coverage probabilities closer to 95% and exact and adjusted Wald 95% confidence intervals presented coverage probabilities above 95%. Score and exact intervals may be wider than unadjusted Wald-based intervals when the event is rare.
Statistical practice may be improved by increasing awareness of the limitations of common statistical methods when analyzing rare events and in increasing support in computing intervals based on non-Wald alternatives.
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