Bayesian Single-Arm Sample Size Calculator
Determines the sample size for a single-arm Bayesian trial in which success is declared when the posterior probability that the response rate exceeds a target passes a decision threshold. Operating characteristics are estimated by Monte Carlo simulation.
How it works
For a binary endpoint the tool uses a Beta–Binomial conjugate model: a Beta prior on the response rate is updated by the observed responses, and the trial succeeds if the posterior probability that the rate exceeds the reference exceeds the decision threshold. Simulation across many hypothetical datasets yields the probability of declaring success under the null and alternative, from which the required sample size is chosen. A continuous endpoint option is also available.
When to use it
- You are designing a single-arm (e.g., Phase II) study with a binary primary endpoint and a target response rate.
- You want a decision rule expressed as a posterior probability rather than a p-value.
- You want simulated operating characteristics (probability of success under null and alternative scenarios) to justify the sample size.
Assumptions & limitations
- The decision threshold is a posterior probability, not a frequentist type I error rate; the simulated probability of declaring success under the null is what characterizes error behavior and should be reported.
- Results depend on the prior; a more informative prior changes both the required sample size and the operating characteristics, so prior sensitivity should be examined.
- Single-arm designs have no concurrent control, so conclusions rest on the appropriateness of the reference/target rate.
- Operating characteristics are simulation estimates for the planned design — they describe expected behavior across trials, not a guarantee for one realized trial.
For the full methodology, derivation, and worked examples, read the complete guide.