In a single-arm, two-stage, phase II cancer clinical trial for efficacy screening of cytotoxic agents, a common primary endpoint is a binary (yes/no) patient response to treatment. Usually, fixed decision boundaries are used in binomial tests to determine whether the study treatment is promising enough to be studied in a large-scale, randomized phase III trial. We may know in advance that the patient response distribution for a phase II clinical trial will be heterogeneous, making it advisable to stratify patients into subgroups, each with a different prognosis. In this case, fixed decision boundaries may be inappropriate. In this article, we propose two-stage tests based on the Neyman-Pearson lemma. The proposed test statistic is a linear combination of the observed number of responders in each stratum. The test allows adjustment of the decision boundaries to the observed numbers of patients in each stratum and permits sample sizes to be increased adaptively after the originally planned number of patients is observed at each of the two stages. Our numerical results show that the proposed test is more powerful than an existing test in many cases. Finally, we present an application to a Children's Oncology Group phase II clinical trial in patients who relapsed after initial treatment for neuroblastoma.
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