Sample size determination in stratified trials to establish the equivalence of two treatments.

When designing a trial to establish that a new treatment is as effective as a standard one, the conventional test procedure and sample size based on a null hypothesis of no difference between two treatments is inappropriate. Several authors have investigated test statistics and corresponding sample sizes based on the null hypothesis that the standard treatment is more effective than the new by at least some specific value for a single 2 x 2 table. This paper considers a trial that involves several 2 x 2 tables and presents an approximate formula for the sample size required to obtain a given power of a one-tailed score test for a null hypothesis of a specific common non-zero difference between two treatments across strata. I show that the sample size for a trial based on an unstratified test is always larger than that based on a stratified test when the design is balanced.