A fixed design commits to a single sample size and one analysis at the end. Sequential and adaptive designs allow looks at the data during the study and let you stop early (for benefit, harm, or futility) or modify the design — saving participants, time, and money. The catch: every interim look at the data is another chance to cross the significance threshold by luck, so the error rate must be controlled explicitly. Peeking at accumulating data and stopping the first time p < 0.05 inflates the Type I error rate badly (to ~0.20+ with a few looks) — this is the core problem these methods solve.
If you test at α = 0.05 at each of K interim analyses and stop at the first significant result, the overall false-positive rate is far above 0.05 — roughly 0.08 for 2 looks, ~0.14 for 5, ~0.20 for 10. The fix is to spend your total α across the looks so the cumulative Type I error stays at 0.05.
Pre-plan a fixed number of interim analyses (e.g. after 25%, 50%, 75%, 100% of data) and use adjusted, more stringent boundaries at each look so the overall α is preserved. Common boundary families:
You can stop for: - Efficacy — the effect crosses the upper boundary. - Futility — the effect is so small that continuing is unlikely to ever reach significance (a non-binding or binding lower boundary / conditional power threshold). - Harm — safety boundary crossed.
Group-sequential designs require a modestly larger maximum sample size than a fixed design (to pay for the looks), but the expected sample size is usually smaller because many trials stop early.
Python support is thinner than for fixed designs; common options:
- statsmodels has limited sequential utilities; for full boundary computation,
most practitioners call R packages via rpy2 or a subprocess:
- R gsDesign — the standard for group-sequential boundaries and spending functions.
- R rpact — confirmatory adaptive and group-sequential designs.
- For custom rules, simulate the whole sequential procedure (generate data, apply
the boundaries look by look, repeat) to confirm the realized Type I error and to
estimate expected sample size and power. This mirrors the simulation approach in the
statistical-power skill and is the most flexible route.
Broader than group-sequential: the design itself can change at an interim based on accumulating data, within a pre-specified plan that still controls error. Main types:
Adaptive designs are powerful but easy to get wrong: any adaptation that uses the unblinded treatment effect can inflate Type I error and bias the final effect estimate unless the method explicitly corrects for it. Two non-negotiables: 1. Pre-specify the adaptation rule and the error-control method before the study. 2. Validate by simulation that the entire procedure preserves the Type I error rate and yields acceptable power and unbiased-enough estimates.