Bayesian Historical Borrowing Calculator
Incorporates external or historical control data into a current trial's prior with explicit discounting, so a design can borrow strength while limiting the influence of data that may not be exchangeable with the current population. Reports the effective prior and its effective sample size, and compares the design with and without borrowing.
How it works
For a binary event rate the tool builds a Beta prior from historical data using one of three approaches: a power prior with a fixed discount factor, a commensurability-parameter variant, or a robust MAP (meta-analytic-predictive) prior that pools multiple historical studies and mixes in a vague component for robustness. It reports the resulting effective prior, its effective sample size, and prior-data conflict diagnostics.
When to use it
- You have relevant external or historical control data and want to formally, but conservatively, incorporate it.
- You want to quantify how much information (effective sample size) borrowing contributes, and how it changes the required sample size.
- You are comparing designs with and without borrowing to justify the approach.
Assumptions & limitations
- Borrowing is only valid to the extent the historical and current populations are exchangeable; borrowing from a dissimilar population can bias the estimate and inflate the type I error rate.
- The effective sample size is method- and prior-dependent — it summarizes the borrowed information under the chosen model, not a universal measure.
- Prior-data conflict diagnostics can flag disagreement but do not by themselves remove the bias that borrowing can introduce; a compatibility check is necessary but not sufficient.
- Sample-size savings from borrowing are conditional on the borrowed data being appropriate; under prior-data conflict the same borrowing can increase the sample size needed to control error and should be stress-tested by simulation.
For the full methodology, derivation, and worked examples, read the complete guide.