A Bayesian Estimator of Sample Size

We consider a Bayesian estimator of sample size (BESS) and an application to oncology dose optimization clinical trials. BESS is built upon balancing a trio of Sample size, Evidence from observed data, and Confidence in posterior inference. It uses a simple logic of "given the evidence from data, a specific sample size can achieve a degree of confidence in the posterior inference." The key distinction between BESS and standard sample size estimation (SSE) is that SSE, typically based on Frequentist inference, specifies the true parameters values in its calculation while BESS assumes a possible outcome from the observed data. As a result, the calibration of the sample size is not based on Type I or Type II error rates, but on posterior probabilities. We argue that BESS leads to a more interpretable statement for investigators, and can easily accommodates prior information as well as sample size re-estimation. We explore its performance in comparison to SSE and demonstrate its usage through a case study of oncology optimization trial. BESS can be applied to general hypothesis tests. R functions are available at https://ccte.uchicago.edu/bess.