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A group sequential design evaluates accumulating data at several planned interim analyses instead of committing to one final test. At each analysis, a prespecified rule can stop for efficacy, stop for futility, or continue collecting observations. The design specifies both the timing of analyses and the sequential stopping boundaries.

Repeated inspection changes the probability of rejecting a Null hypothesis. Even two independent tests, each at significance level $0.05$, reject at least once with probability $1-0.95^2=0.0975$ under their common Null hypothesis. Tests on accumulating observations are dependent, so their rejection boundaries require their actual joint distribution rather than that independence calculation. An Alpha-spending function distributes the permitted type I error over information fractions; it does not make unchanged fixed-sample critical values valid at every analysis.

For a simple valid construction with $K$ planned analyses, choose separate rejection events whose null probabilities are each at most $\alpha /K$. The union bound makes the probability of any rejection at most $\alpha$, whatever their dependence. More efficient boundaries exploit the dependence between successive test statistics. A Futility boundary removes rejection paths, and a Conditional error principle can justify a later design adaptation while preserving the original error guarantee. The possibility of early stopping also affects point estimation and confidence intervals; fixed-sample formulas do not automatically retain their usual interpretation after selection.

An interim analysis examines data before a study reaches its planned maximum Sample size.

A group sequential design can reduce the expected sample size by stopping at an interim analysis once efficacy or futility is sufficiently clear. It does not generally reduce the prespecified maximum sample size: repeated opportunities to reject inflate the Type I error, so valid sequential stopping boundaries usually require a modest increase in maximum information relative to a fixed-sample design with the same power. The benefit is a smaller expected sample size under alternatives that often cross an early boundary, and sometimes under the null through early futility stopping.

A Two-stage clinical trial design permits early stopping after an interim analysis for futility or efficacy and otherwise continues to a prespecified final decision boundary.