Bayesian trial design

Conventional trial statistics ask how surprising the data would be if the treatment did nothing, and report that surprise as a p-value. Bayesian statistics ask the question patients actually have: given everything known before the trial and everything seen in it, how likely is it that the treatment helps, and by how much? The answer is a posterior probability distribution, summarised as a probability of benefit and a credible interval, and it can be updated after every patient, which is why Bayesian methods sit underneath most adaptive designs: response-adaptive randomisation, model-based dose finding such as the continual reassessment method and the Bayesian optimal interval design, graduation rules in I-SPY 2, and hierarchical models that let small baskets in a basket trial borrow strength from each other.

The controversial ingredient is the prior, the belief before the trial. A non-informative prior lets the data speak and gives answers close to the conventional ones. An informative prior built from earlier trials or adult data can shrink a trial dramatically, which is how paediatric extrapolation and rare-disease trials are made feasible, and how external control arms are blended with a small randomised control (dynamic borrowing). A sceptical prior deliberately doubts large effects so that a small trial cannot overclaim. Regulators require the prior to be justified and fixed in advance and usually ask to see how the design behaves under a range of priors, and they still check the frequentist false-positive rate of the whole procedure by simulation.

In the corpus the Bayesian influence is most visible in dose finding and in externally controlled approvals. NMTRC003 compared 105 children on eflornithine with a propensity-matched external control drawn from an earlier cooperative-group trial, the kind of comparison Bayesian borrowing formalises, and the FDA approved the drug while acknowledging the design. Where a Bayesian design is used, the honest report gives the prior, the posterior probability of benefit and the credible interval, not just a statement that a threshold was crossed.