In group sequential designs, where several data looks are conducted for early stopping, we generally assume the vector of test statistics from the sequential analyses follows (at least approximately or asymptotially) a multivariate normal distribution. However, it is well-known that test statistics for which an asymptotic distribution is derived may suffer from poor small sample approximation. This might become even worse with an increasing number of data looks. The aim of this paper is to improve the small sample behaviour of group sequential designs while maintaining the same asymptotic properties as classical group sequential designs. This improvement is achieved through the application of a modified permutation test. In particular, this paper shows that the permutation distribution approximates the distribution of the test statistics not only under the null hypothesis but also under the alternative hypothesis, resulting in an asymptotically valid permutation test. An extensive simulation study shows that the proposed permutation test better controls the Type I error rate than its competitors in the case of small sample sizes.

翻译：在分组序贯设计中，为早期停止而对数据进行多次检验时，通常假设序贯分析的检验统计量向量（至少近似或渐近地）服从多元正态分布。然而，众所周知，基于渐近分布推导的检验统计量在小样本情况下可能表现不佳，且随着数据检验次数的增加，这一问题可能进一步恶化。本文旨在改进分组序贯设计的小样本表现，同时保持与传统分组序贯设计相同的渐近性质。这一改进通过应用修正的置换检验实现。特别地，本文证明置换分布不仅在原假设下，而且在备择假设下都能近似检验统计量的分布，从而得到渐近有效的置换检验。广泛的模拟研究表明，在小样本情况下，所提出的置换检验在控制第一类错误率方面优于其他竞争方法。