STATISTICS IN MEDICINE Statist. Med. 2000; 19:2867–2878 Properties of the estimated variance component for subject-by-formulation interaction in studies of individual bioequivalence Laszlo Endrenyi 1;*;† , Nathan Taback 1 and Laszlo Tothfalusi 2 1 University of Toronto; Department of Pharmacology; Toronto; Ontario; Canada 2 Semmelweis Medical University; Department of Pharmacodynamics; Budapest; Hungary SUMMARY Characteristics of the variance component for the subject-by-formulation interaction ( 2 D ), estimated in sim- ulated studies of individual bioequivalence and in three- and four-period cross-over trials reported by the FDA, were compared.  2 D was estimated by (i) restricted maximum likelihood (REML) and (ii) the method of moments (MM). Variation of the variance component, estimated by both procedures (s 2 D ) and for both the simulated and FDA data, increased with rising intra-individual variation. Consequently, a constant level of s 2 D (such as 0.0225 suggested by the FDA) may not be regarded as a basis for demonstrating substantial interactions. Features of the FDA and simulated parameters were similar. The results suggested that the FDA data were compatible with assuming D =0:05 or perhaps 0.00. Therefore, there is no foundation for concerns about public health. Both simulations and calculations demonstrated that s 2 D estimated by MM was unbiased and its variance was proportional to  4 WF when  2 D = 0. Copyright ? 2000 John Wiley & Sons, Ltd. 1. INTRODUCTION A study by Anderson and Hauck [1] initiated great interest in principles and procedures for the evaluation of individual bioequivalence. The Food and Drug Administration (FDA) of the United States has found the underlying rationales intriguing, and established a powerful Working Group in order to consider the background and develop methods for the determination of individual bioequivalence. As a result of its deliberations, an interim draft guidance, dated October 1997, was issued [2]. Some of the motivation for the deep interest of the FDA was based on a set of three- and four-period, two-formulation cross-over studies on its les. They appeared to suggest the presence of large subject-by-formulation interaction for a substantial proportion of the estimated parameters. This could be a source of concern since the observation could suggest that various subjects would respond dierently to the substitution of one formulation by another. The condition could be * Correspondence to: Laszlo Endrenyi, Department of Pharmacology, University of Toronto, Medical Sciences Building, 1 King’s College Circle, Toronto, Ontario M5S 1A8, Canada. † E-mail: l.endrenyi@utoronto.ca Copyright ? 2000 John Wiley & Sons, Ltd.