Capstone: write and defend a Bayesian protocol
Design one trial in nine steps, then print a one-page summary you can defend.
The trial has two arms, drug and placebo, and a yes or no outcome. A false win calls a useless drug a success. Power is the chance to win when the drug works (module 3). The target for false wins is 2.5%.
1Question and endpoint
Pick what you ask. Each patient is a yes (improved) or a no.
How to say exactly what you are estimating: the estimand, in module 6. We assume about 30% of placebo patients improve (made-up).
One clear question and a yes or no outcome keep every later step simple.
2The prior
A prior is what you believe before the trial. Pick one, and see what it is worth in patients.
Beta(a, b) = as if you had already seen a − 1 responders and b − 1 non-responders (module 1). So an arm is "worth" a + b − 2 patients. Historical: 30 of 100 placebo patients in an earlier trial, placebo arm only.
A prior is worth a number of patients, and you must be able to defend that number.
3When the new data disagree with history
History says 30% on placebo. Today's trial enrolls 40 placebo patients. Drag the result.
Full borrowing: trust history as 100 patients. Robust mixture: 80% history, 20% flat, and the data decide which one fits.
The robust mixture lets go of history when the new data clearly disagree. Full borrowing does not.
4The success rule
The trial wins if the chance that the drug beats placebo by more than a points is above c. Write it as Pr(drug − placebo > a | data) > c.
A trial result to try
The curve is the chance for each true gap (drug minus placebo), using your prior from step 2 or 3. The dashed line is a.
The rule has two dials, and both go in the protocol before the first patient.
5Simulation report
Simulate 2,000 trials in each row where the drug does nothing (placebo 20%, 30%, 40%), and 2,000 where it works. If a is above 0, also simulate rows where the drug beats placebo by exactly a: the edge of the claim.
Pass the test in the worst row, not the friendliest one.
6Sensitivity analyses
Rerun everything under the other priors, with your a, c and trial size.
If the answer flips with the prior, the protocol must say why yours is the right one.
7Interim looks and the DMC
A DMC (Data Monitoring Committee, a small independent group of experts) and its independent analysis team see interim results by treatment. The sponsor’s trial team stays blinded. Pick the futility rule.
Predictive probability of winning is defined in module 7. The simulation in step 5 has no futility stop, so a real protocol must simulate it too.
Write who looks, when, and what they may do before the trial starts.
8Talking to the FDA
Pick where you bring this design.
The CID program takes 1 to 2 proposals a quarter. Who talks to whom, and when: module 13. FDA CID meeting program.
Agree the success rule and the simulations with the FDA before you run the trial.
9. The one-page protocol summary
Regulator's corner
Both documents are drafts. The FDA Bayesian draft (January 2026) says:
"It is always critical for Bayesian analyses to have a prespecified prior"
Section IV.B. FDA draft guidance on Bayesian methods. Simulation reports: ICH E20 draft, section 5.2, ICH E20.
Takeaway
- Write the prior, the success rule and the simulations before the first patient.
- Test the rule where history is wrong, not only where it is right.
- Raise c until the worst null row is at or below 2.5%.