  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.
