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ANOVA CV%

Figure 1 BE limits (left side) and extreme GMR values, which ensure BE (right side) as a function of within-subject variability (ANOVA CV), for the classic (0.80-1.25) limits (dashed lines) and three proposed procedures (solid lines): expanded BE limits beyond a switching variability CVo = 30% (24) (top)-, BE limits with levelling-off properties based on a sigmoid function (63) (middle)-, and scaled BE limits (equation 10) with a preset variability CVW0 = 25.4% and switching variability CV0 = 30% (35,64) (bottom). A two-period crossover study with 36 subjects was assumed for the calculation of extreme GMR values. Abbreviations-. BE, bioequivalence; GMR, geometric mean ratio; CV, coefficient of variation.

ANOVA CV%

Figure 1 BE limits (left side) and extreme GMR values, which ensure BE (right side) as a function of within-subject variability (ANOVA CV), for the classic (0.80-1.25) limits (dashed lines) and three proposed procedures (solid lines): expanded BE limits beyond a switching variability CVo = 30% (24) (top)-, BE limits with levelling-off properties based on a sigmoid function (63) (middle)-, and scaled BE limits (equation 10) with a preset variability CVW0 = 25.4% and switching variability CV0 = 30% (35,64) (bottom). A two-period crossover study with 36 subjects was assumed for the calculation of extreme GMR values. Abbreviations-. BE, bioequivalence; GMR, geometric mean ratio; CV, coefficient of variation.

Thus, the acceptance criterion can be expressed as

It has been also suggested that the regulatory criterion of ABE, in the case of HV drugs, could be scaled by a standard deviation, leading to an approach known as scaled average bioequivalence (ABEsc) (59,60). The acceptance criterion is then defined as

The scaling factor, erw, in the case of a two-period design is the residual standard deviation, <7Res, estimated from ANOVA, while for a replicate design the within-subject standard deviation of the R formulation, <7Wr, is used.

An approach using the noncentral t distribution to calculate the confidence limits for ABEsc has been suggested (60). An alternative procedure consisting of a numerical approximation based on the method of Hyslop et al. (61) has been also proposed for the statistical evaluation of ABEsc.

It is worth mentioning that the model for ABEsc (equation 7) can be readily converted to that of the scaled BE limits (equation 6). Indeed, when investigated, the two approaches yielded very similar results (60).

Various suggestions have been made for the most appropriate proportionality factor, k, for scaled BE limits (39,58,62). The value of k affects the slope of the BE limits and therefore the degree of expansion.

Simple scaled BE limits When variability is low, very small deviations of GMR from unity are permitted to declare BE. Consequently, scaled BE limits appear to be very strict for drugs with low variability and probably inappropriate even for the evaluation of drugs with narrow therapeutic range. At a specific value of the variability (erw = <70), depending on the value of the proportionality factor k, scaled BE limits become equal to the classic BELq.

As variability increases, scaled BE limits become very liberal, allowing GMR values higher than 1.25 (40). Therefore, a common drawback of the reported scaled BE limits (39,58,62) is their continuous increase with variability. This leads to very broad acceptance limits of BE. The GMR acceptance region has a nonconvex shape (40), similar to that for the Hauck and Anderson procedure as pointed out by Schuirmann (see Fig. 12 of Ref. 25), and gets wider and wider with increasing CV. Thus, BE studies with GMR deviating considerably from unity even at very high CVs could be accepted. Since large differences between the means can be accepted by scaled methods with substantial probabilities, an additional regulatory criterion was proposed to be imposed concomitantly with the CI test (53). This secondary criterion suggests that the estimated GMR should be constrained in the range 0.80 to 1.25. Nevertheless, even with the concomitant application of the above-mentioned additional criterion, the acceptance region still has a nonconvex shape, and BE studies with GMR values between 0.80 and 1.25 can be accepted, even at very high variability level.

Mixed model An interesting variant of the simple scaled procedure has been proposed (62). It involves the use of both the classic unsealed ABE (when drugs do not exhibit high variability) and the ABEsc for HV drugs (when a preset magnitude of the variability is exceeded) (62). The switching variability, <70, for the ABEsc was set to 0.20, and corresponds to a proportionality constant, k = In (1.25)/cr0 = 1-116. This mixed model (62) for ABEsc can be converted to a mixed approach of scaled BE limits, using the classic unsealed criterion up to CV 20% and scaled BE limits with a proportionality factor of 1.116, for CV over 20%. When the mixed model is used, the boundaries of the GMR acceptance region converge to a minimum value as CV values increase up to 20%, and then start to spread apart, for values of CV higher than 20% (see Fig. 2 of Ref. 40). Consequently, this approach is less "permissive" for drugs with moderate variability (CV ~ 20%) than for drugs with low or high variability. The nonmonotony of the extreme accepted GMR versus CV plots is an unfavorable property of the method, because it appears to "punish" drug products with moderate variability (40). Moreover, as the mixed model is a scaled procedure, it suffers also from the common drawback of the simple scaled BE limits mentioned previously, i.e., the continuous increase with variability leading to very broad acceptance BE limits. Again, the GMR acceptance region has a nonconvex shape and an additional (3rd) point estimate constraint criterion, e.g., 0.80 < GMR < 1.25 may be needed. Nevertheless, BE studies with GMR deviating from unity can be accepted even at very high CVs.

Finally, if one uses a different value for k, e.g., k = 0.760 (39,62) for the mixed model, the switching variability, <70, is 0.294 (corresponding to a CV = 30%), and a stricter BE criterion is constructed.

Combined scaled criterion To improve the performance of the above-mentioned scaled procedures, a novel approach has been proposed, consisting of a combined criterion for evaluating BE (40). Scaled BE limits containing an effective constraint have been developed. The proposed BE limits scale with intrasubject variability but incorporate also a GMR-dependent criterion, which makes them less permissive as GMR values depart from unity (40,57).

### Scaled BE Limits with Leveling-off Properties

A new rationale for the design of scaled BE limits has been developed (63) to improve the too restrictive behavior of the classic BE limits when truly bioequivalent HV drugs are compared, and concomitantly to avoid the drawbacks of the simple scaled or mixed methods, discussed previously. To this end, the BE limits developed scale with intrasubject variability but only until a "plateau" value and combine the classic (0.80-1.25) and expanded (0.75-1.33) BE limits into a single criterion (Fig. 1). To combine the above-mentioned desired properties into a single criterion, the upper BE limit is expressed as a function of intrasubject variability, which levels off at a predefined plateau value. Accordingly, this function has three controlling parameters, which are

1. the minimum (or starting) value of the upper BE limit,

2. the maximum (or plateau) value of the upper BE limit, and

3. the "rate" of the gradual change of the upper BE limit value as a function of variability.

The new scaled limits become more permissive than the classic unsealed BE limits as variability increases, and thus they require fewer subjects to prove BE. Nevertheless, the GMR acceptance region has a convex shape (Fig. 1), which is similar to that of the classic unsealed 0.80 to 1.25 limits (29,40). Undoubtedly, this is not only a desired property but also a unique characteristic for a scaled method. This finding is a consequence of the new structure of the BE limits with leveling-off properties.

One of the major advantages of the new scaled limits is their gradual expansion with variability until a plateau value. The gradual expansion of the BE limits is by far preferable than the use of expanded criteria only beyond an arbitrarily chosen, critical switching variability value (Fig. 1), as the discontinuity of the BE limits may lead to preferential treatment of drugs presenting only minor differences in variability. The gradual expansion from a strict to a permissive BE limit, apart from avoiding the discontinuity around a switching variability, makes the new BE limits also suitable for use at low CV levels. In fact, when variability is low, BE limits with leveling-off properties exhibit similar percentage of accepted BE studies as the classic BE limits (63). Therefore, these BE limits would be implemented in practice, e.g., in the case of Cmax ratio, in lieu of a wider acceptance interval (23). It is also worthy to mention that leveling-off BE limits present a quite flexible structure, and therefore a variety of starting and plateau values for the upper BE limit can be considered. The flexibility, continuity, and leveling-off properties of these scaled BE limits in conjunction with their performance in simulation studies (63) make them suitable for the assessment of BE studies, without the need of a secondary criterion of constrained GMR value and irrespective of the level of variability encountered.

Current Thinking Within the FDA for the Evaluation of Highly Variable Drugs and Drug Products

For drugs with an expected within-subject variability of >30%, a BE study with three-period, R-replicated, crossover design has been proposed (34,35,64). The minimum number of subjects that would be acceptable is 24. The BE assessment comprises two parts: an ABEsc evaluation and a point estimate constraint. The BE criterion for both AUC and Cmax is defined as where 6 = (In A)2/°wo' with A = 1.25 and <7W0 = 0.25 (the preset standard variability).

A 95% upper confidence bound for (/iT — /iR)2/er2WR must be <9, or equivalently, a 95% upper confidence bound for — /UR)2- da2WR must be <0. Additionally, the point estimate for GMR of T/R must fall within (0.80, 1.25). In the original scale, the proposed BE limits are

According to this criterion, the value of the k factor chosen is k = In (1.25)/0.25 = 0.892, presenting an intermediate value between the too liberal approach of k = 1.116 (62) and the stricter one, k = 0.760 (39,62). However, the choice of this value (or equivalently the choice of <7Wo = 0.25) presents the demerit of an inherent discontinuity of the BE limits when applied for drugs with CV > 30% (i.e., with Owr > 0.294), (Fig. 1). The cause of this attribute is that the preset standard variability value (<7W0 = 0.25) is not the same as the switching variability value (<70 = 0.294). A relevant comment has been also made recently (65). Consequently, if the estimated within-subject CV of the R formulation is just above the changeover point of 30%, the BE limits will be much wider (i.e., > 1.30) than just below (i.e., 1.25).

Moreover, the proposed procedure suffers from the same drawbacks as all the mixed models of the scaled methods: The boundaries of the GMR acceptance region converge to a minimum at the switching variability value and then start to spread apart for higher values of CV, presenting a nonconvex shape (Fig. 1). Consequently, an additional point estimate constraint criterion on GMR is needed.

The EMEA Approach for the Evaluation of Highly Variable Drugs

EMEA in the Note for Guidance on the Investigation of Bioavailability and Bioequivalence (24) states that the 90% CI for AUC and Cmax ratios should lie within an acceptance interval of 0.80 to 1.25. However, "in certain cases a wider interval may be acceptable" for Cmax (Fig. 1), provided that there are no safety or efficacy concerns. Some points of this statement were furthermore clarified in a Questions & Answers document (33) as follows: The possibility offered by the guideline to widen the acceptance range

"should be considered exceptional and limited to a small widening (0.75-1.33)." Furthermore, this possibility is restricted to those products for which at least one of the following applies: Safety and efficacy should be clinically justified [i.e., using adequate pharmacokinetic/pharmacodynamic (PK/PD) or clinical data], or should refer to a defined HV drug (i.e., an R product with intrasubject variability greater than 30%). Recently, EMEA has addressed more intensively the issue of HV drugs. In this context, the Committee for Medicinal Products for Human use (CHMP) has also released a concept paper for an addendum, focusing on scaled procedures for the evaluation of BE of HV drugs (66) and a recommendation document on the need for revision of the note for guidance (67).

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