Two-stage winner designs for non-inferiority trials with pre-specified non-inferiority margin.

*(English)*Zbl 1357.62269Summary: In drug development, a two-stage winner design [K. K. G. Lan et al., in: Random walk, sequential analysis and related topics. A Festschrift in honor of Yuan-Shih Chow. Papers presented at the international conference, Shanghai, China, July 18–19, 2004. Hackensack, NJ: World Scientific. 28–43 (2006; Zbl 1158.62050); Z. Shun et al., “Interim treatment selection using the normal approximation approach in clinical trials”, Stat. Med. 27, No. 4, 597–618 (2008; doi:10.1002/sim.2990)] can be cost-effective when the best treatment is to be determined from multiple experimental treatments in superiority trials. However, the statistical methods assessing non-inferiority in a two-stage winner design have not yet been studied, for which the complexity arises in determining the critical value when parameter space is not a single point under the null hypothesis. Because the maximum error may not occur at the vertex of the null space, it is unclear if naive use of critical values and distributional results from the test for superiority remains correct. In this paper, we provided rigorous justifications to determine the critical value for testing non-inferiority hypothesis, with a pre-specified non-inferiority margin, in a two-stage winner design with two experimental treatments and an active control. We studied the distribution of the test statistics, critical values, sample size and power calculations using the exact distribution of the test statistics as well as using normal approximations. Theoretical justifications and extensive numerical assessments were conducted to calculate the design parameters and evaluate the performance of our methods.

##### MSC:

62L10 | Sequential statistical analysis |

62L05 | Sequential statistical design |

62P10 | Applications of statistics to biology and medical sciences; meta analysis |

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\textit{P.-W. Wang} et al., J. Stat. Plann. Inference 183, 44--61 (2017; Zbl 1357.62269)

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