## Background

The realization of the importance of product formulation for the speed of onset, intensity, and duration of drug response occurred in the early 1960s. At that time, various scattered reports in the literature (1-5) indicated that formulation changes result in marked differences in maximum observed plasma concentration (Cmax) and area under the concentration-time curve (AUC), and the term "bioavailability" was coined to describe the fraction of dose reaching the general circulation. A few years later, dramatic bioavailability problems were observed with formulations of phenytoin in Australia and New Zealand in 1968 (6,7) and digoxin in the United Kingdom and the United States in 1971 (8,9). Consequently, comparative bioavailability studies were introduced in the United States regulatory setting (10,11) and the term bioavailability was officially introduced by the Food and Drug Administration (FDA) (12) and defined as follows: "Bioavailability means the rate and extent to which an active drug ingredient or therapeutic moiety is absorbed from a drug product and becomes available at the site of drug action." Since the late 1970s, a test (T) formulation that meets statistical criteria for the measures of relative bioavailability is termed "bioequivalent" to, and therapeutically interchangeable with, the reference (R) formulation. For more details on the regulatory history of generic drug development the reader is referred to relevant publications (13-15).

According to the bioavailability definition given above and because of the (most frequently) linear relationship between AUC and the fraction, F, of dose reaching the systemic circulation, AUC is used as a measure of the amount of drug reaching the general circulation.

By expressing the parameters of equation (1) in terms of the T and R formulations, assuming that the drug clearance is the same after administration of the two products, i.e., CLt = CLr, and assuming that the two formulations contain the same dose, i.e., (dose)T = (dose)R, one can easily derive from equation (1) that the ratio of bioavailability coefficients ft/fr is equal to the ratio of AUCs.

Equation (2) comprises the pharmacokinetic (PK) basis for the routine use of AUC in bioequivalence (BE) studies as a robust measure of the amount of drug reaching the general circulation.

The rate of appearance in the general circulation is the second component in the definition of bioavailability. Since most frequently the rate is a time-dependent parameter, comparisons of rates are based on Cmax values, because they are supposed to reflect adequately the input rate constant of the drug. Simulations have shown that Cmax is not only insensitive to changes in the rate of input, but it is also dependent on amount of drug reaching the general circulation, i.e., it is a hybrid parameter (16). Several other absorption rate metrics like Cmax/AUC (17), partial area (18,19), and the intercept of In (c/t) versus time curve (20) with more favorable kinetic sensitivity properties have been proposed in literature. However, Cmax continues to be the unique measure for rate comparisons in the regulatory setting, since it is considered meaningful from a clinical point of view. Today, AUC and Cmax are viewed as clinically relevant measures of total and peak exposure, respectively (21).

In the early stages of recognition of BE, physicians by general consensus recommended that a difference of 20% between the two formulations would have no clinical significance for many drugs. This recommendation was interpreted as an allowable difference of 20% in the means of PK variables, namely, AUC and Cmax, measured after administration of the T and R formulations. However, this definition is a statement for the difference of relative bioavailability of the total production (or population) of the two formulations. Since the assessment of BE relies on a sample of the formulations administered to a limited number of human subjects, regulatory agencies developed methodologies for the assessment of BE based on statistical criteria.

AVERAGE BIOEQUIVALENCE: THE CLASSIC APPROACH

Classically, the assessment of BE relies on the concept of average bioequivalence (ABE)

(22). Determination of the ABE of two drug products (T vs. R) is based on the comparison of the means of logarithmically transformed PK parameters, such as AUC and Cmax. BE is accepted if the difference of the log means and for the T and the R formulations, respectively) falls between specific predefined values for the upper and lower BE limits

(23). The current approach of ABE is based on constant BE limits (BEL0) at a level set by the regulatory agencies (22,24), and usually BEL0 = In (1.25). Thus, the criterion applied for the determination of ABE is

In practice, the true population means (¡j,t and are estimated by the calculated sample averages of the logarithmic parameters of the two formulations (mT and mR). In this context, ABE is declared if the calculated 90% confidence interval (CI) for the difference of the log means lies within the preset BE limits (23). Assuming the classic two-treatment, two-period, crossover BE study design, with equal numbers of subjects in each sequence, the upper and lower limits of the 90% CI are calculated according to equation (4).

where Diff is the difference of T and R means, i.e., Diff = mT — mR; t the student's statistic; s2 the residual variance, calculated by the residual mean square error of ANOVA (reflecting within-subject variance); and N the number of subjects. The usual statistical approach for the evaluation of ABE consists of two one-sided t procedures (25) to determine if the PK measures of the T and R products are comparable. This definition of ABE ensures the consumer safety, since the probability of an erroneous acceptance of BE does not exceed the preset level of significance (22).

During the past three decades or so, significant contributions to the theoretical and practical aspects of BE have been made by professional associations such as the American Pharmaceutical Association, American Association of Pharmaceutical Scientists and regulatory bodies, e.g., FDA and European Medicines Evaluation Agency (EMEA). Also, international symposia (26-28) have contributed to the evolution of BE studies and methodology. During the last decade significant advances on scientific issues relating to BE assessment have been made in three areas: in the assessment of the BE of highly variable (HV) drugs and drug products (28), in identifying situations where BE could or should be based on the plasma levels of metabolites (28), and in identifying situations where an in vivo BE study could be waived (29).

HIGHLY VARIABLE DRUGS AND DRUG PRODUCTS The Problem in Establishing Bioequivalence

A drug or drug product is usually characterized as HV if the within-subject coefficient of variation (CV) of its PK responses is >30% (30-35). It is worth mentioning that the CV is related to the residual variance s2 in the log scale, calculated by ANOVA, with the formula: s2 = In (CV2 + 1). For HV drugs, the 0.80 to 1.25 BE limits seem to be too restrictive, leading to high producer risks (30-32,36,37).

As can be seen from equation (4), the width of the 90% CI is proportional to the within-subject variability and inversely proportional to the number of subjects participating in the study. Consequently, as within-subject variability increases, a higher rejection rate of BE for truly equivalent drug products is observed. Therefore, for truly equivalent products, it becomes too difficult to establish BE unless a large number of subjects are recruited to achieve adequate statistical power.

The need for unusually large numbers of healthy volunteers for the assessment of BE of HV drugs can raise ethical and practical issues. The exposure of large numbers of healthy volunteers to a drug even if it is deemed to be "safe," to satisfy a traditional preset criterion, must be seriously considered (38). In addition, the increase in the cost of the investigations of HV drugs—with usually wide therapeutic indices (35,38)—may result in difficulties in the development of new or generic drug products.

In the case where the upper limit of the 90% CI (equation 4) falls exactly on the upper preset BE limit, Diff becomes equal to Diffmax, which is the maximum acceptable difference between means (25,39). Diffmax, and therefore the maximum acceptable geometric mean ratio (GMRmax) [GMRmax = exp(Diffmax)], for a given number of subjects, is related not only to the estimated intrasubject variance but also to the value of the preset upper BE limit.

The major feature of the definition of classic unsealed ABE relies on the fact that two constant "borderline" values (0.80 and 1.25) are assigned for BE limits. Under this condition, extreme geometric mean ratio (GMR) values, which ensure BE, converge at unity as intrasubject variability increases (25,40). In other words, when upper and lower BE limits are fixed, the demonstration of BE requires that the means of two products must be as close as possible as variability increases. Although setting constant the BE limits is conceptually fundamental, the 0.80 to 1.25 limits appear very "strict" in the case of HV drugs. To overcome the difficulties encountered in the assessment of the bioavailability of HV drugs with the currently used BE limits, several approaches have been proposed.

Approaches for the Evaluation of Bioequivalence

### Multiple-Dose Studies

To reduce within-subject variability, multiple-dose steady-state studies have been considered (24,41). It has been shown that the observed variation of PK parameters is often lower at steady state than after single dosing (41-43). The reduced variation of Cmax at steady state is probably due to its lower kinetic sensitivity in reflecting absorption rate

(22.44). Nevertheless, under certain conditions, Cmax was found to exhibit higher variation at steady state than after a single administration, and therefore multiple-dose designs were not considered to be the solution for the assessment of BE of HV drugs

(43.45). Currently, the FDA approach recommends applicants to conduct single-dose studies rather than multiple-dose studies because "single-dose studies are generally more sensitive in assessing release of the drug substance from the drug product into the systemic circulation" (22).

### Replicate Designs

For single-dose studies, replicate designs that reduce the total number of subjects required have been also proposed (22,24,32,41) for the assessment of BE for HV drugs. Roughly, about half as many volunteers are needed in a four-period study than in a two-period investigation to attain the same statistical power.

However, replicate designs (as multiple-dose studies) lead to increased duration of exposure to the drug and, moreover, potential practical problems may arise, e.g., increased incidence of subject withdrawals. In addition, in certain cases, e.g., for drugs with long half-lives, replicated designs are difficult to apply.

Consideration of Only the Point Estimate of the Mean Test/Reference Ratio

Another approach for the assessment of BE of HV products has been based on the point estimate of the mean T/R ratio. In this context, a relaxed requirement is adopted by the regulatory authority in Canada in the case of Cmax. This PK parameter is a single-measure estimate and often shows higher variation than AUC. Therefore, Health Canada requires that only the point estimate of the GMR for Cmax, and not its 90% CI, fall between the BE limits of 0.80 to 1.25 (46).

### Individual Bioequivalence

Individual BE (23,47-52), a procedure relying on the concept of switchability between drug formulations, has been also proposed for the evaluation of HV drugs. According to this concept, the T-R difference is compared with the R-R difference within subjects using repeated measures. The individual BE criterion comprises the ratio of the sum of the contrast of the squared means of the two formulations, the contrast of their within-subject variances and the subject by formulation variance over the within-subject variance of the R formulation. While individual BE represents an attractive approach, several problems have limited its application in practice (38,51).

Widening of Acceptance Limits to Prefixed Constant Values

Widening the BE acceptance limits to prefixed constant values (0.70-1.43 or 0.75-1.33) (24,31,53) has been proposed, especially for PK parameters showing increased variation,

### Ciuax.

Expanded 0.75 to 1.33 or 0.70. to 1.43 BE limits for drugs meeting a "high variability criterion" Several questions may arise, indicative of the difficulties of the application of this approach: What is the high variability criterion? An intrasubject variability value, estimated from ANOVA? For example, when CV > 30% (33,34)? A problem may arise about the classification of drugs presenting borderline variability values (54). It was estimated that about 20% of the evaluated HV drugs constitute borderline cases (34). Nevertheless, the use of an extended region of acceptance reduces the producer risk at high CV values, but at the same time, large differences between the means are allowed (55) for drug products with moderate residual variability. This constitutes a potential problem of switchability for multisource formulations, each declared bioequivalent to the same R product (39,56). Consequently, an additional point estimate constraint criterion on GMR, e.g., 0.80 < GMR < 1.25, may be needed.

Widening of BE limits only beyond a limiting, "switching" variability value (mixed model) It has been suggested to use either the classic 0.80 to 1.25, or the more "liberal" (e.g., 0.75-1.33 or 0.70-1.43) BE limits only beyond a switching variability value (24,53). However, apart from the fact that in this case two criteria are required, applying an arbitrarily chosen switching variability value can lead to unfair treatment of different formulations of the same drug evaluated in separate BE studies and presenting only minor differences in variability (57). For example, assuming a switching variability of CV = 30%, it seems rather unfair that a drug with broad therapeutic index and CV = 29.9% has to be evaluated using the classic 0.80 to 1.25 BE range, which allows a maximum accepted value of GMR, GMRmax = 1.08, while the same drug could be evaluated in a different BE study with CV = 30%, using the expanded 0.70 to 1.43 range, which allows a GMRmax = 1.24 (see Fig. 6B of Ref. 57). The major cause of this attribute is the inherent discontinuity when these two BE criteria are concomitantly applied (Fig. 1). Consequently, a question arises: How do we deal with BE studies with borderline variability values, i.e., BE trials presenting variability values very close to the switching variability?

### Scaled Procedures

A method for expanding the limits for HV drugs, based on an estimate of intrasubject variation, was proposed: The BE limits are scaled according to a fixed multiple, of within-subject standard deviation, erw, on the log scale (58).

where k is a multiplying factor.

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