An algorithm for the design of group sequential triangular tests for single‐arm clinical trials with a binary endpoint

Abstract

Consider the problem of testing H(0):p ≤ p(0) vs H(1):p > p(0), where p could, for example, represent the response rate to a new drug. The group sequential TT is an efficient alternative to a single-stage test as it can provide a substantial reduction in the expected number of test subjects. Whitehead provides formulas for determining stopping boundaries for this test. Existing research shows that test designs based on these formulas (WTTs) may not meet Type I error and/or power specifications, or may be over-powered at the expense of requiring more test subjects than are necessary. We present a search algorithm, with program available from the author, which provides an alternative approach to triangular test design. The primary advantage of the algorithm is that it generates test designs that consistently meet error specifications. In tests on nearly 1000 example combinations of n (group size), p(0), p(1), α, and β the algorithm-determined triangular test (ATT) design met specified Type I error and power constraints in every case considered, whereas WTT designs met constraints in only 10 cases. Actual Type I error and power values for the ATTs tend to be close to specified values, leading to test designs with favorable average sample number performance. For cases where the WTT designs did meet Type I error and power constraints, the corresponding ATT designs also had the advantage of providing, on average, a modest reduction in average sample numbers calculated at p(0), p(1), and (p(0) + p(1))/2.