Estimating treatment means in a mixed-effect ANOVA model for bioequivalence studies

In order to establish bioequivalence between two formulations in a crossover trial, it is common to assume a mixed-effect analysis of variance (ANOVA) model and perform two one-sided tests. When the analysis is done on the untransformed data, the numerators of the test statistics are not, in general, treatment contrasts. Consequently, the standard errors of the numerators are difficult to compute. The usual practice is to approximate these with the standard errors of treatment contrasts (the "usual approximation"). This paper examines the goodness of this approximation. We present a few technical issues involved in analyzing the untransformed data with a mixed-effect ANOVA model, and state a parametric definition for the terminology "treatment means." The best linear unbiased estimator (BLUE) for the treatment means is derived, as well as its covariance matrix. Due to the presence of the intersubject variability, the variances and covariances of the BLUE of the treatment means are much larger than is commonly believed. A simulation study shows that these larger-than-expected variances/covariances may widen the usual approximate 90% confidence interval by as much as 10%.