title: 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.
authors.affiliation: a Department of Applied and Computational Mathematics and Statistics , University of Notre Dame , Notre Dame , Indiana , USA.
authors.forename: Fang
authors.initials: F
authors.lastname: Liu
mesh_terms: D001499:Bayes Theorem; D016001:Confidence Intervals; D064420:Drug-Related Side Effects and Adverse Reactions; D006801:Humans; D015994:Incidence; D015233:Models, Statistical; D018401:Sample Size
keywords: Confidence level; maximum allowable adverse events; minimum required adverse events; the rule of three