Two-Stage Experimental Designs: Early Stopping with a Negative Result

We propose two‐stage experimental designs which allow for early termination if the first‐stage results are not promising. These group sequential designs have boundaries for the first‐stage test statistic which are equivalent to critical values for conditional power, calculated under a plausible but optimistic alternative, given the initial data. The procedures preserve power for reasonable critical values, even if the nominal second‐stage significance levels are unadjusted. We provide designs which adjust the first‐stage parameters to achieve specified size and power exactly. The choice of design parameters minimizing expected sample size under Hő are derived and are shown to be intuitively unappealing, suggesting that choosing a design based on minimizing expected sample size under Hő may be unreasonable.