Sample size for K 2×2 tables in equivalence studies using Cochran's statistic

This paper presents a new sample size formula for Cochran's test that uses additional information on stratum-specific success rates and requires fewer subjects for an equivalence study. Equivalence studies are common in clinical trials, where unlike superiority studies, the goal is to show whether a new drug therapy is as effective as a standard one. Stratification is typically used to adjust for differences among individual clinical trial centers with different success rates. The sample size is derived for a clinical trial design where two independent binomial proportions are compared within each stratum. Implementation of the sample size formula is described when the number of centers is large and the success rates of each individual center are not known exactly. The effect of variability of the success rates on the power of Cochran's test is shown through simulation. The variability of the success rates is measured by the intracluster correlation coefficient, which can be estimated by the ANOVA estimator of Donald and Donner. The simulation results show that the new sample size formula requires fewer subjects than sample size methods, which ignore stratification. The new method provides greater savings as the variability of success rates among centers increases.