Limits for the Scaled Average Bioequivalence of Highly Variable Drugs and Drug Products Laszlo Tothfalusi 1 and Laszlo Endrenyi 2,3 Received September 4, 2002; accepted January 22, 2003 Purpose. To provide a rational procedure for establishing regulatory bioequivalence (BE) limits that can be applied in determinations of scaled average BE for highly-variable (HV) drugs and drug products. Methods. Two-period crossover BE investigations with either 24 or 36 subjects were simulated with assumptions of a coefficient of varia- tion of 10, 20, 30, or 40%. The decline in the fraction of accepted studies was recorded as the ratio of geometric means (GMR) for the two formulations was raised from 1.00 to 1.45. Acceptance of BE was evaluated by scaled average BE, assuming various BE limits, and, for comparison, by unscaled average BE. A procedure for calculating exact confidence limits in two-period studies is presented, and an approximate method, based on the linearization of the regulatory model, is applied. Results. A mixed model is proposed for average BE. Accordingly, at low variabilities, the BE limit is constant, ±BEL o , generally log(1.25). Beyond a logarithmic, limiting, “switching” variability ( o ), in the region of HV drugs, the approach of scaled average BE is applied with limits of ±(BEL o / o ). It is demonstrated that the performance of the mixed model corresponds to these expectations. The effect of  o and of the resulting BE limits is also demonstrated. Scaled average BE, with all reasonable limits for HV drugs, requires fewer subjects than an unscaled average BE. In two-period studies, the exact and approximate methods calculating confidence limits yield very com- parable inferences. Conclusions. Scaled average BE can be effectively applied, with the recommended limits, for determining the BE of HV drugs and drug products. The limiting, “switching” variability ( o ) will have to be established by regulatory authorities. KEY WORDS: highly-variable drugs; bioequivalence; scaled average bioequivalence; mixed model for average bioequivalence; regulatory limits; crossover designs. INTRODUCTION The problems of establishing bioequivalence (BE) for highly variable (HV) drugs and drug products are well known. It can be very difficult for these to satisfy the usual regulatory requirement that the 90% confidence interval around the estimated ratio of geometric means (GMR) of the two formulations be between 0.80 and 1.25. The approach is often referred to as the determination of average BE. The frustrating problem of determining BE for HV drugs has been considered in recent years, but mainly in the context of individual BE. It was suggested in various studies (e.g.,1– 6), culminating in a guidance published by the Food and Drug Administration (7), that a criterion recommended for indi- vidual BE could be normalized (or “scaled”) by an estimated variance. It was thought that scaled individual BE would re- lieve the difficulties involving HV drugs. The evaluation of both unscaled and scaled individual BE requires replicate- design investigations that involve not two but three or, more typically, four study periods. However, several investigations have found that, in prac- tice, individual BE has unfavorable properties, and numerous objections have been raised to its implementation (e.g., 8–13). An alternative approach has also been proposed, namely, that scaling be applied not to individual but to average BE (3,14). It was suggested that scaled average BE has more favorable characteristics (i.e., with given risks, requiring fewer subjects) than scaled individual BE. Moreover, scaled average BE could be determined by both two- and four-period investiga- tions. It was also noted (14) that the approach of scaled av- erage BE is equivalent to expanding the BE limits as the variability increases, an approach that had been suggested by Boddy et al. (15). The present communication focuses on the application of scaled average BE for HV drugs and drug products. The main purpose is to outline the procedures and alternatives for set- ting BE limits for the analysis of HV drugs and thereby to lay the groundwork for regulatory considerations. Attention was recently called to the need for establishing such preset limits (16). A secondary goal of the present study is to summarize the calculations that are required for the evaluation of scaled average BE. METHODS A summary of the notations used is provided in the Ap- pendix. A Mixed Model of Average BE: Unscaled and Scaled Schall and Willams (4) recommended a mixed model for individual BE. According to this, a constant-referenced (i.e., in effect, unscaled) criterion is applied when the (within- subject reference) variability does not exceed a critical level ( o ), and a “reference-scaled” criterion (i.e., one scaled by the within-subject reference variability) is used with higher than the critical variability, i.e., for HV drugs (4–6). The scheme has been implemented in an FDA guidance (7). The approach can also be applied to a judicious mixture of unscaled and scaled average BE. Thus, the usual criterion of unscaled average BE prevails provided that drugs do not have unusual properties, for instance, if they do not exhibit high variability. Accordingly, under these conditions it is usu- ally expected that the ratio of the geometric means (GMR) of the test (T) and reference (R) formulations should be be- tween BE limits, the magnitudes of which are set by regula- tory agencies. The multiplicative BE limit is often set at the value of 1.25: 0.80  GMR  1.25 (1) Here and later, such statements of regulatory expectations do not merely indicate the relationship between a regulatory model and BE limits but imply that the indicated measure is, together with its (usually 90%) confidence limits, within the BE limits. 1 Department of Pharmacodynamics, Semmelweis University, 1089 Budapest, Hungary. 2 Department of Pharmacology, University of Toronto, Toronto, On- tario M5S 1A8, Canada. 3 To whom correspondence should be addressed. (e-mail: l.endrenyi@ utoronto.ca) Pharmaceutical Research, Vol. 20, No. 3, March 2003 (© 2003) Research Paper 382 0724-8741/03/0300-0382/0 © 2003 Plenum Publishing Corporation