A Bayesian Sample Size Estimation Procedure Based on a B-Splines Semiparametric Elicitation Method

Sample size estimation is a fundamental element of a clinical trial, and a binomial experiment is the most common situation faced in clinical trial design. A Bayesian method to determine sample size is an alternative solution to a frequentist design, especially for studies conducted on small sample sizes. The Bayesian approach uses the available knowledge, which is translated into a prior distribution, instead of a point estimate, to perform the final inference. This procedure takes the uncertainty in data prediction entirely into account. When objective data, historical information, and literature data are not available, it may be indispensable to use expert opinion to derive the prior distribution by performing an elicitation process. Expert elicitation is the process of translating expert opinion into a prior probability distribution. We investigated the estimation of a binomial sample size providing a generalized version of the average length, coverage criteria, and worst outcome criterion. The original method was proposed by Joseph and is defined in a parametric framework based on a Beta-Binomial model. We propose a more flexible approach for binary data sample size estimation in this theoretical setting by considering parametric approaches (Beta priors) and semiparametric priors based on B-splines.