Bayesian adaptive determination of the sample size required to assure acceptably low adverse event risk

An emerging concern with new therapeutic agents, especially treatments for type 2 diabetes, a prevalent condition that increases an individual's risk of heart attack or stroke, is the likelihood of adverse events, especially cardiovascular events, that the new agents may cause. These concerns have led to regulatory requirements for demonstrating that a new agent increases the risk of an adverse event relative to a control by no more than, say, 30% or 80% with high (e.g., 97.5%) confidence. We describe a Bayesian adaptive procedure for determining if the sample size for a development program needs to be increased and, if necessary, by how much, to provide the required assurance of limited risk. The decision is based on the predictive likelihood of a sufficiently high posterior probability that the relative risk is no more than a specified bound. Allowance can be made for between-center as well as within-center variability to accommodate large-scale developmental programs, and design alternatives (e.g., many small centers, few large centers) for obtaining additional data if needed can be explored. Binomial or Poisson likelihoods can be used, and center-level covariates can be accommodated. The predictive likelihoods are explored under various conditions to assess the statistical properties of the method.