Abstract
BackgroundThe article aims to compare the efficiency of minimax, optimal and admissible criteria in Simon’s and Fleming’s two-stage design.MethodsThree parameter settings (p1-p0 = 0.25–0.05, 0.30–0.10, 0.50–0.30) are designed to compare the maximum sample size, the critical values and the expected sample size for minimax, optimal and admissible designs. Type I & II error constraints (α, β) vary across (0.10, 0.10), (0.05, 0.20) and (0.05, 0.10), respectively.ResultsIn both Simon’s and Fleming’s two-stage designs, the maximum sample size of admissible design is smaller than optimal design but larger than minimax design. Meanwhile, the expected samples size of admissible design is smaller than minimax design but larger than optimal design. Mostly, the maximum sample size and expected sample size in Fleming’s designs are considerably smaller than that of Simon’s designs.ConclusionsWhenever (p0, p1) is pre-specified, it is better to explore in the range of probability q, based on relative importance between maximum sample size and expected sample size, and determine which design to choose. When q is unknown, optimal design may be more favorable for drugs with limited efficacy. Contrarily, minimax design is recommended if treatment demonstrates impressive efficacy.
Highlights
The article aims to compare the efficiency of minimax, optimal and admissible criteria in Simon’s and Fleming’s two-stage design
In planning a phase II trial, we usually find ourselves in a dilemma when we must consider choosing one of the two designs by comparing the expected sample size and maximum sample size
Jung et al [13] firstly proposed to apply admissible design to Simon’s two-stage design. We extend such admissible design to Fleming’s two-stage design, too
Summary
Consider a single-arm design with tumor response rate as the primary endpoint, where a binary outcome is defined as either “response” or “no response”. The probability of early termination (PET) at the end of first stage (under null hypothesis) is PET S1 1⁄4 Bðr; n1; p0Þ where suffix S is used to represent the result of Simon’s design. Fleming’s design ensures sample sizes no larger than the single-stage design, a limitation is that calculated critical values for accepting and rejecting the null hypothesis are based on pre-fixed sample sizes at stage 1 (n1) and stage 2 (n2), which may be undesirable for investigating and planning optimal designs. Mander and Thompson extended Simon’s optimal and minimax criteria in Fleming’s two-stage design [10]. Such design will benefit from stopping early for either futility or efficacy, while preserve its simplicity and the small sample size. We extend such admissible design to Fleming’s two-stage design, too
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