Response-Adaptive Randomization (RAR) Calculator
Designs a trial whose allocation ratio shifts toward better-performing arms as outcome data accumulate, and estimates the resulting operating characteristics by simulation. This is response-adaptive randomization — allocation responds to efficacy data — as opposed to covariate-adaptive randomization (e.g. minimization), which balances baseline covariates rather than responding to outcomes.
How it works
You choose an allocation rule — DBCD (doubly-adaptive biased coin, which adapts toward the Rosenberger-optimal target), clipped Thompson sampling, or a plug-in Neyman allocation based on accumulating parameter estimates — for a binary, continuous, or time-to-event endpoint with two or more arms. A burn-in period of equal allocation and a minimum-allocation floor limit how extreme the ratio can become. Monte Carlo simulation estimates power, the type I error rate, expected outcomes, and the distribution of per-arm sample sizes.
When to use it
- You want to allocate more participants to arms that appear more effective as the trial proceeds, typically in exploratory or multi-arm settings.
- Outcomes are observed quickly enough relative to enrollment for adaptation to be informative.
- You want to compare an adaptive allocation against equal randomization on power and expected outcomes.
Assumptions & limitations
- Response-adaptive allocation does not by itself control the frequentist type I error; under temporal drift in the outcome, the error rate can inflate substantially unless the adaptation is pre-specified and the analysis accounts for it — verify by simulation.
- Adaptation assumes outcomes accrue fast enough to inform allocation; with delayed outcomes the benefit shrinks.
- Naive treatment-effect estimates can be biased under adaptive allocation and time trends; the minimum-allocation floor and burn-in mitigate but do not eliminate these risks.
- Reported operating characteristics are simulation estimates for the modeled scenario, not guarantees for a realized trial; ethical/allocation benefits depend on the effect actually being present.
For the full methodology, derivation, and worked examples, read the complete guide.