Solution

ID: 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.

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