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An analytical study of the critical values of response rate in single-arm phase II clinical trial designs

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A single-arm phase II clinical trial is usually conducted for finding an appropriate dose-level and testing toxicity for an experimental cancer therapy in comparison to some historical controls, and is usually the most doable trial type due to the feasibility under limited budget, patient pool and medical conditions that can be met. We considered the standard setting of a single-arm two-stage phase II clinical trial, and investigated the patterns of critical values and sample sizes at both two stages of minimax and optimal designs under different design parameters, i.e., under different response rates of control and treatment, significant level of the test, and statistical power. We provided analytic derivations to the patterns we are interested under large sample approximation, and investigated them under finite ans small sample via a numerical study by considering extensively possible design parameters over a fine grid. We finally concluded that the critical values at different stages of the test are related to the sample sizes at different stages in a similar way for both optimal and minimax designs, but they also reveal some differences and reflected the nature of these two types of design. 


single-arm two-stage trial, optimal design, minimax design, critical value, response rate