Bayesian Sample Size Methods
Bayesian interim-analysis calculator for a binary endpoint. Computes the posterior probability that the response probability exceeds a prespecified null value, using a Beta prior and the observed interim number of responses. Runs entirely in your browser.
This calculator uses the conjugate Beta-Binomial model for a binary endpoint. If the interim data contain x responses among n patients and the prior distribution is Beta(α, β), the posterior distribution is Beta(α + x, β + n − x).
Here, Ip0(·) is the regularized incomplete beta function. The calculator evaluates the beta tail probability directly, without Monte Carlo simulation or an external statistical server.
A trial is classified here as meeting the specified Bayesian interim success criterion when P(p > p0 | data) ≥ η, where η is the user-specified posterior probability threshold. If the posterior probability is below the threshold, the calculator reports that the specified success criterion has not been reached.
This is a posterior-probability approach: it evaluates the probability of the hypothesis given the data already observed at the interim analysis. It should not be confused with Bayesian predictive probability of success, which additionally integrates over possible future observations. The FDA's Bayesian guidance distinguishes these two interim approaches.
A published illustration considers 12 responses among 20 patients, a uniform Beta(1,1) prior, and a null response probability of 0.50. The resulting posterior probability is approximately 0.81.
The calculator reproduces this value to numerical precision. With a success threshold of 0.95, this particular interim result therefore does not meet the specified Bayesian success criterion.
Saville, B.R., Connor, J.T., Ayers, G.D., & Alvarez, J. (2014). The utility of Bayesian predictive probabilities for interim monitoring of clinical trials. Clinical Trials, 11(4), 485–494.
The paper gives the worked binary-endpoint illustration of 12 responses among 20 patients under a uniform prior, with P(p > 0.50 | data) = 0.81. Published article
U.S. Food and Drug Administration. (2010). Guidance for the Use of Bayesian Statistics in Medical Device Clinical Trials.
The FDA guidance describes posterior-probability approaches at interim analyses and distinguishes them from predictive-distribution approaches. FDA guidance
Statsols /. Bayesian Clinical Trial Design Software. Bayesian module as supporting Bayesian testing and predictive-power methods for clinical trial design and interim assessment.