Group sequential t-test for clinical trials with small sample sizes across stages

Interim analyses are often applied in clinical trials for various reasons. To assess the effect of a clinical treatment, the group sequential t-test with a fixed number of interim analyses is frequently used in clinical trials. The existing critical values used in group sequential t-tests are obtained from normal approximations of t-statistics. In practice, however, normal approximation is not accurate when some sample sizes of treatment arms in some stages are small. In this paper, instead of using normal approximation, we directly obtain the critical values via a Monte Carlo method. We list some critical values for certain sample sizes and number of interim analyses, and provide some SAS code for general situations. We also consider the sample size calculation and run some simulations to check the accuracy of our critical values. The simulation results show that our critical values yield type I error probabilities that are very close to the nominal significance level, whereas the existing critical values based on normal approximation are not accurate when some sample sizes are small across stages.