Professor Endrenyi’s Legacy: An Evaluation of the Regulatory Requirement “Fixed Effects, Rather Than Random Effects, Should Be Used for All Terms”

Purpose: In the latest revision of the guideline for evaluation of bioequivalence (BE), European regulators introduced the requirement for using subjects as fixed factors in the underlying statistical models, even in replicate and semi-replicate studies. The implication was that estimates of within-subject variability were derived with a linear model rather than with a mixed model based on restricted maximum likelihood (REML). While REML-based methods are generally thought to give rise to less biased estimates of variance components, there have been no studies that compared the quality of REML-based estimates and estimates derived via linear models. Methods: A publication by Endrenyi and Tothfalusi from 1999 described simulations in a fashion that is useful for testing the European Medicines Agency’s (EMA) requirement.  This study defines 7 scenarios within which 10,000 individual 2-sequence, 2-treatment, 4-period trials are simulated and makes a comparison of the quality of estimates. Results: It is concluded that estimates based on REML are closer to the true values than estimates based on linear models, but significant differences are only shown in two of the seven scenarios tested.  REML-based estimators have less variability. Both types of estimates appear negatively biased and will therefore decrease the width of the acceptance range.