Reasonable two-stage adaptive designs for single-arm phase II clinical trials

In cancer phase II trials, determining the sample size of a single-arm two-stage design remains a challenge. To overcome this problem, Simon's two-stage design was extended to an adaptive design: at the interim analysis, the total sample size can be set to either of the two preplanned values. However, without any restriction on design construction, an optimal or suboptimal design derived may have counter-intuitive or unreasonable design features, which make the chosen design less persuasive and inefficient. Thus, we thoroughly examined how the expected, total, and maximum sample sizes of the optimal or suboptimal designs are affected by excluding the counter-intuitive or unreasonable designs. We adopted the four optimality criteria: minimizing the expected sample size at the null hypothesis (O1), minimizing the maximum expected sample size over the hypotheses (O2), and minimizing the maximum sample sizes with additional adaption of either of the former two (O3 or O4, respectively). We found that focusing on reasonable design may drastically reduce the maximum sample size when the first optimality criterion is applied. Under the other optimality criteria, although the impact on optimality brought by our proposed strategy may be slight, exclusion of unreasonable design is still useful to reduce the candidate designs, which will considerably reduce the computational time for design search and can facilitate the design choice among optimal and suboptimal designs. We further discuss the utility of our proposal in an example of a real clinical trial and conclude the paper with general recommendations.