Sequential equivalence testing and repeated confidence intervals, with applications to normal and binary responses

We propose group sequential tests of the equivalence of two treatments based on ideas related to repeated confidence intervals. These tests adapt readily to unpredictable group sizes, to the possibility of continuing even though a boundary has been crossed, and to nonnormal observations. In comparing two binomial distributions, the required sample size depends strongly on the average success probability and an adaptive choice of group size is needed to produce an efficient test meeting specified error probability constraints. A special case is the experiment where interim analyses are performed, not for the purpose of early termination but simply to adjust the sample size so that nominal error rates will be guaranteed, despite the presence of a nuisance parameter.