Establishing equivalence of two treatments and sample size requirements in matched-pairs design

Statistical methods for testing the null hypothesis of a nonzero difference between two treatments and the sample size determination for matched-pairs studies are investigated. A Wald-type test proposed by Lu and Bean (1995, Statistics in Medicine 14, 1831-1839) is anticonservative, i.e., its false positive error rate is greater than specified. Score method and normal deviate based on a restricted maximum likelihood estimation are presented. These two test statistics are shown to be algebraically equal. Their actual type I error probabilities are satisfactorily close to a nominal level. Numerical examinations demonstrate that the sample size formulas using these alternative methods are reasonable while that by Lu and Bean is not. The efficiency of matching in equivalence studies is positively related to intercorrelation or the kappa coefficient of agreements. We recommend the score or ML methods to establish equivalence of two treatments for individually matched samples.