Adaptive and Bayesian designs
Can a trial change its plan on the way and still be fair?
Bayesian means updating a belief with each patient, as in module 1.
Power is the chance a trial finds a real effect (module 3). A false positive (a false win) calls a useless drug a success. The target is 2.5% (the one-sided 0.025 line from module 2). The default bar 0.90 gives about 10% false wins. A bar of 0.975 ("97.5% sure") gives about 2.5%, but only with no prior opinion and one look at the data.
1. The rule
After the trial, compute the chance the drug beats placebo. Call it a success if that chance is above the bar.
2. The trial
1,500 simulated trials where the drug does nothing (orange) and 1,500 where it works (teal).
Trials right of the dashed line call the drug a success.
Truth versus what the trial sees
The true response rates are hidden from the trial. Patients arrive one by one. The better a treatment looks so far, the likelier the next patient gets it. This is response-adaptive randomization: more patients go to the treatment doing better.
Benefit: more patients get the better treatment (watch "On the drug"). Pitfall: early luck can fool it (try "Start over with new luck"), and it can need more patients for the same power.
Hidden truth
What the trial sees
filled = improved outline = did not. An arm is the group on one treatment.
The price of a lower bar
Each bar gives one false-positive rate and one power.
Each point on the curve is one bar. False positives run across, power runs up, and the grey diagonal is a coin flip instead of a trial.
Red dashed line: your bar.
Borrowing from history
Last year's trial had 30 improvements in 100 placebo patients. Can we reuse it, so today's trial needs fewer placebo patients?
How much to borrow
Today 30 placebo patients enroll. Their results are drawn at random from the true rate. Made-up example.
Average error of the estimate. Lower is better.
Predict, then check
Cards 1, 3 and 4 use numbers from the sequential cost-based design in Sokolova, Sokolov and Polson (2026), which this lab does not simulate.
Real trial 1: AWARD-5, picking a dose on the fly
Seven doses of dulaglutide (0.25 to 3.0 mg) and placebo and an approved drug started together. Step through what happened.
The drug was approved in 2014.
Real trial 2: lecanemab Study 201
Alzheimer's drug, 5 doses plus placebo. Planned split versus final split.
Phase 2 (the smaller first trial) estimated 33% slower decline at 18 months on CDR-SB, a score of memory and daily living. Phase 3 (the big trial) found 27% on the same score.
At 12 months it missed its own pre-set success bar on a different score (ADCOMS): a 0.64 chance of at least 25% slower decline, versus 0.80 needed. It still went on to a positive phase 3.
Sources: Swanson 2021, van Dyck 2023.
Regulator's corner
The FDA's draft guidance on Bayesian methods (January 2026) describes a success rule like ours as:
"the posterior probability that the true treatment effect size exceeds some threshold"
Posterior probability = the chance after the trial. Effect size = the gap between the groups.
FDA draft guidance on Bayesian methods, section IV.A. The Bayesian guidance is still a draft. Adaptive plans: FDA guidance (2019).
Takeaway
- Before the trial, simulate a Bayesian rule to count its false positives and its power.
- Borrowing history helps when it matches today and hurts when it does not.
- A trial may adapt, if the rules are written before the first patient.