A simple Bayesian approach to quantifying confidence level of adverse event incidence proportion in small samples

ABSTRACT

In both clinical development and post-marketing of a new therapy or a new treatment, incidence of an adverse event (AE) is always a concern. When sample sizes are small, large sample-based inferential approaches on an AE incidence proportion in a certain time period no longer apply. In this brief discussion, we introduce a simple Bayesian framework to quantify, in small sample studies and the rare AE case, (1) the confidence level that the incidence proportion of a particular AE p is over or below a threshold, (2) the lower or upper bounds on p with a certain level of confidence, and (3) the minimum required number of patients with an AE before we can be certain that p surpasses a specific threshold, or the maximum allowable number of patients with an AE after which we can no longer be certain that p is below a certain threshold, given a certain confidence level. The method is easy to understand and implement; the interpretation of the results is intuitive. This article also demonstrates the usefulness of simple Bayesian concepts when it comes to answering practical questions.

KEYWORDS:

• Confidence level
• maximum allowable adverse events
• minimum required adverse events
• the rule of three

Acknowledgment

We wish to thank an anonymous referee and the associate editor for their useful comments and suggestions that have greatly improved the presentation and quality of the article.