Past exam of the mathematics course of the University of Cambridge / 2013 / iii / Paper 32 / 3 / a / i / Solution

A group sequential design can stop early when the treatment is insufficiently promising, reducing expected recruitment, patient exposure and cost when the effect is poor. It also allows a planned decision before maximum enrollment.

A disadvantage is that the analysis is selected by the interim results: estimation and uncertainty must account for stopping, and power and operational planning depend on the stopping rule. The following parts quantify the resulting conditional estimation bias. If a design also allows repeated efficacy tests, its rejection boundaries must control overall Type I error. In the present futility-only design, stopping without rejection need not inflate the error rate of a single prespecified final test; it can make that test conservative. Earlier decisions are valuable, but the ordinary fixed-sample analysis is not automatically appropriate after selection.