Exact tests using binary data in adaptive two or multi-stage designs

Abstract

When establishing an effective treatment with binary data in a two-stage design, one-sided tests for a proportion p are employed. Researchers use the parameter configuration at the boundary of the null hypothesis space to determine a rejection region and an optimal design. However, it is unclear whether the (maximum) Type I error rate is achieved at the boundary especially when the sample size in stage 2 varies. In this paper, we first prove that this is true for a large family of tests in adaptive two-stage designs by showing that any test in the family has a nondecreasing power in p and then derive optimal designs. Second, similar results are established for m-stage designs with m > 2. Supplementary materials for this article are available online.

Optimal single-arm two-stage designs with consideration of dependency on efficacy and safety

“…As mentioned in Section 2., the hypotheses (9) are appropriate for establishing an effective and safe treatment when p 1 is large. The construction for their optimal two-stage designs is mathematically equivalent to Case A of Yin et al 5 , where they focused on the single parameter p r. The rejection region for (9) has a form offor some nonnegative integers a 1 , b 1 and c 1.…”

“…They showed numerically that the maximum type I and II error rates of the design are controlled by the given α and β, respectively. Yin et al 5 proposed adaptive two-stage designs, which strictly control the maximum type I and II error rates and have a nonincreasing sample size as in Shan et al 4 . The above papers considered the binary outcomes of a treatment response which are defined by Response Evaluation Criteria in Solid Tumors (RECIST).…”