Evaluation of the Bioequivalence of Highly-Variable Drugs and Drug Products Laszlo Tothfalusi, 1 Laszlo Endrenyi, 2,4 Kamal K. Midha, 3 Maureen J. Rawson, 3 and John W. Hubbard 3 Received December 14, 2000; accepted March 7, 2001 Purpose. To establish procedures for the effective evaluation of bio- equivalence (BE) for highly-variable drugs and drug products (HVD/P). Methods. 2- and 4-period crossover BE studies with 24 subjects were simulated which generally assumed within-subject coefficients of variation of 40%. The relationship between the fraction of studies in which BE was accepted (the statistical power) and the ratio of geo- metric means (GMR) of the two formulations was evaluated for vari- ous methods of analysis. These included, primarily, scaled average BE (ABE), the corresponding approach of expanding BE limits (BEL), and, for comparison, unscaled ABE and scaled individual BE (IBE). Results. Scaled ABE and expanding BEL showed very similar prop- erties in both 2- and 4-period studies. They had steeper power curves than scaled IBE. Unscaled ABE had very low statistical power. The acceptance of BE by unscaled and scaled ABE and expanding BEL was almost independent of subject-by-formulation interaction and the ratio of within-subject variations of the two formulations. By contrast, the conclusions reached by scaled IBE were strongly af- fected by these parameters. Conclusions. Scaled ABE and expanding BEL evaluate BE effec- tively for HVD/P in both 2- and 4-period investigations. However, additional, useful information can be obtained from 4-period studies. KEY WORDS: highly-variable drugs; bioequivalence; scaled regula- tory criterion; regulatory limits; 2- and 4-period crossover design; simulated clinical trials. INTRODUCTION The determination of the bioequivalence (BE) of two drug formulations has proved to be a difficult problem for highly-variable drugs and drug products (HVD/P) which are characterized by large within-subject variation. Customarily, two-way crossover studies have been conducted. The loga- rithmic means of the two kinetic responses (e.g., of AUCs, the areas under the concentration vs. time curves) have been evaluated together with the 90% confidence intervals (CI) of their difference. Bioequivalence of the formulations is de- clared if the CI is within preset regulatory limits. Typically, the limits have been set at ±log (1.25), with the corresponding untransformed bioequivalence limits (BEL) being between 0.80 and 1.25 for the ratio of the geometric means (GMR) of the two kinetic responses. When the within-subject variation is large then the esti- mated CI is wide, and it is very difficult to remain within preset BE limits. An obvious remedy is to increase the num- ber of subjects participating in a study and thereby to narrow the CI. However, a BE study becomes, as a result, very ex- pensive and cumbersome. To alleviate this difficulty, other approaches were pro- posed. Blume et al. (1) recommended that some kinetic pa- rameters could have smaller variations if BE studies were conducted in the steady state instead of following single-dose administrations. A workshop discussing highly-variable drugs and drug products considered procedures for determining their BE (2). The approach for widening the BEL for this category drugs and drug products was particularly favored. Boddy et al. (3) quantitatively formalized the method. Ac- cording to their procedure, the BEL expands in proportion to the estimated intrasubject coefficient of variation of the ref- erence formulation. Recent proposals related to the determination of indi- vidual and population BE offered a parallel approach to the regulatory criterion by scaling it with the intraindividual vari- ance of the reference product (4–6). This variance can be evaluated in replicate-design investigations which are con- ducted over 3 or 4 study periods (5–7). The same experimental design can be applied also to the determination of average bioequivalence (i.e., of the equiva- lence of the two mean responses) again by using reference scaling (8). It can be, however, reasonably expected that the procedure of scaling can be applied to the evaluation of av- erage BE also from the results of 2-period crossover studies. Therefore, the principal purpose of the present study is to compare the effectivenesses of 2- and 4-period investiga- tions performed for the determination of average BE. The secondary goals include a contrast of the procedures of scal- ing and of extending the BEL, and a comparison of some characteristics of average and individual BE. METHODS The regulatory approaches to be discussed below will consider several regulatory models and criteria. Using either observed or simulated data, the parameters of a given model are estimated and substituted into the model expression. Con- fidence limits around the estimated magnitude of the model are then calculated. Therefore each of the regulatory criteria to be discussed will imply that the appropriate confidence limit(s) of the model should be within preset bioequivalence limit(s). Unscaled Average Bioequivalence The usual procedure for determining the bioequivalence of two formulations was evaluated for comparison with the other approaches. Accordingly, the average logarithmic ki- netic responses of the test and reference products ( T and  R , respectively) are contrasted. Bioequivalence is declared if the 90% confidence limits around their logarithmically calculated difference are within preset BE limits (BEL): -BEL  T -  R  BEL (1) 1 Semmelweis University of Budapest, Department of Pharmacody- namics, 1089 Budapest, Hungary. 2 University of Toronto, Department of Pharmacology, Toronto, On- tario M5S 1A8, Canada. 3 PharmaLytics Inc., Saskatoon Saskatchewan, S7N 5C9, Canada. 4 To whom correspondence should be addressed. (e-mail: l.endrenyi@ utoronto.ca) Pharmaceutical Research, Vol. 18, No. 6, 2001 Research Paper 728 0724-8741/01/0600-0728$19.50/0 © 2001 Plenum Publishing Corporation