Estimating product bioequivalence for highly variable veterinary drugs.

The occurrence of drugs and drug formulations associated with large intrasubject pharmacokinetic (PK) variability has been well described in humans and is likewise encountered in veterinary medicine. The scaled average bioequivalence (SABE) approach adopted by CDER of the FDA for the determination of bioequivalence (BE) of highly variable drugs (HVD) needs to be considered when applied to veterinary dosage forms. However, because of some of the unique challenges that are encountered within the framework of veterinary medicine, variations of CDER's approach are presented. The present manuscript discusses HVD and highly variable veterinary drugs (HVVD) from the perspective of possible alternative approaches to support the assessment of product BE in veterinary medicine. Limitations in the use of 3- and 4-way crossover study designs are enumerated. In addition to a need for a statistical analysis of HVVD when using a parallel study design, the use of the secondary criteria (test-to-reference ratio), definition of σ(0) , and average BE with expanding limits are raised. A number of the details need to be finalized, from the selection of a regulatory constant to the determination of 'highly variable' in a veterinary drug product. Academicians, industrial scientists, and regulators should continue this discussion and resolve these details.

Scaling or wider bioequivalence limits for highly variable drugs and for the special case of C(max).

OBJECTIVE: To illustrate that bioequivalence (BE) can be effectively evaluated for highly variable (HV) drugs and drug products and for the special case of C(max) by using average BE. To demonstrate that either scaling or wider regulatory limits need not result in large observed ratios of the geometric means (GMR) of the 2 drug products. METHODS: Two- and 4-period crossover BE investigations with 24 subjects were simulated. Variabilities of 15, 25 or 35% were assumed in special studies of C(max) and 40% in the general investigations of HV drugs. Acceptance of BE was analyzed in each study by various procedures and regulatory criteria. Under each condition, the percentage of simulated investigations accepting BE was recorded as the simulated GMR was gradually raised from 1.00. RESULTS: Scaled average BE for HV drugs (in both 2- and 4-period studies) and expanding limits for C(max) increased substantially, as expected, the proportion of investigations accepting BE. An additional secondary regulatory criterion constrained the simulated GMR to 1.25 and limited the possibility of large deviations between the mean metrics of the 2 formulations. Acceptance of BE by the composite regulatory expectation never exceeded the acceptances by the separate component criteria. CONCLUSIONS: The sample size required for the evaluation of BE for HV drugs and drug products can be substantially reduced by applying the approach of scaled average BE. The same conclusion is reached from the determination of BE for the C(max) metric by expanding the regulatory limits to 0.75 - 1.33 or even to 0.70 - 1.43. Concerns for observations of high GMR values can be eased by imposing constraints with a secondary regulatory criterion.

Evaluation of the bioequivalence of highly-variable drugs and drug products.

PURPOSE: To establish procedures for the effective evaluation of bioequivalence (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 geometric means (GMR) of the two formulations was evaluated for various 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 properties 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 affected by these parameters. CONCLUSIONS: Scaled ABE and expanding BEL evaluate BE effectively for HVD/P in both 2- and 4-period investigations. However, additional, useful information can be obtained from 4-period studies.

Evaluation of some properties of individual bioequivalence (IBE) from replicate-design studies.

BACKGROUND: One of the claimed benefits of the individual bioequivalence (IBE) approach has been that the aggregate regulatory model rewards a test formulation when it has a within-subject variation smaller than the reference product. Hauck et al. [1996] demonstrated that, in the absence of random variations, this property of IBE was due to the tradeoff between the difference of the means and the deviation between the intrasubject variances of the two formulations. The tradeoff was a consequence of the aggregate regulatory model. However, calculations of Endrenyi and Hao [1998] showed that, in the presence of random variations, not only rewards but also penalties can arise due to chance alone. METHODS: A data set of 55 investigations made public by the FDA in 1999 and containing replicate crossover designs was analyzed. Two parameters, AUC and Cmax, were determined in each investigation. RESULTS: The analyses of the FDA data indicate that: rewards and penalties occur at similar frequencies, large rewards and penalties are recorded quite often, and the aggregate IBE model is rather insensitive to the difference between the estimated means and is compatible with the frequent occurrence of large deviations. CONCLUSION: Rewards and penalties, apparently arising from random variations, can affect regulatory decisions on the acceptance of IBE and can lead to incorrect conclusions.

Properties of the estimated variance component for subject-by-formulation interaction in studies of individual bioequivalence.

Characteristics of the variance component for the subject-by-formulation interaction (sigma(2)(D)), estimated in simulated studies of individual bioequivalence and in three- and four-period cross-over trials reported by the FDA, were compared. sigma(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 sigma(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 sigma(4)(WF) when sigma(2)(D)=0.

Evaluation of the genetic component of variability in CYP3A4 activity: a repeated drug administration method.

The CYP3A4 enzyme contributes to the disposition of more than 60 therapeutically important drugs and displays marked person-to-person variability of the catalytic function. However, the extent of genetic contribution to variability in CYP3A4 activity remains elusive. Recently, we showed that a comparison of between- (SDb2) and within-person (SDW2) variances provides an estimate of the genetic component of variability in drug disposition. The aim of the present analysis was to assess the genetic control of CYP3A4 activity in vivo. A computerized literature search was conducted covering 1966 to September 1999 to identify studies reporting repeated administration of CYP3A4 substrates. The genetic contribution (rGC) to disposition of each CYP3A4 substrate was obtained by the formula (SDb2-SDW2)/SDb2. The rGC values approaching 1.0, point to overwhelming genetic control, whereas those close to zero suggest that environmental factors dominate. A total of 16 studies with 10 different CYP3A4 substrates were identified (n = 161 subjects). The rGC for hepatic CYP3A4 activity as measured by midazolam plasma clearance or the erythromycin breath test was 0.96 (0.92-0.98) (95% Cl) and 0.89 (0.65-0.98), respectively (P < 0.05). The point estimates of rGC for composite (hepatic + intestinal) CYP3A4 activity measured after oral administration of cyclosporine, ethinylestradiol, ethylmorphine, nifedipine and nitrendipine, ranged from 0.66-0.98 (median: 0.83) (P < 0.05). Cyclosporine data suggested a higher genetic control of CYP3A4 at night than during the day. These data indicate that further molecular genetic investigations are warranted to identify genetic variants at CYP3A4 or elsewhere in the genome which contribute to regulation of CYP3A4 activity.

Sensitivity of empirical metrics of rate of absorption in bioequivalence studies.

PURPOSE: The sensitivity and effectiveness of indirect metrics proposed for the assessment of comparative absorption rates in bioequivalence studies [Cmax, Tmax, partial AUC (AUCp), feathered slope (SLf), intercept metric (I)] were originally tested by assuming first-order absorption. The present study re-evaluates their sensitivity performances using the more realistic inverse Gaussian (IG) model characterizing the input process for oral drug administration. METHODS: Simulations were performed for both the first-order or exponential model (EX) which is determined by only one parameter, the mean absorption time (MAT = 1/k(a)), and the IG model, which additionally contains a shape parameter, the relative dispersion of absorption time distribution (CV2A). Kinetic sensitivities (KS) of the indirect metrics were evaluated from bioequivalence trials (error free data) generated with various ratios of the true parameters (MAT and CV2A) of the two formulations. RESULTS: The behavior of the metrics was similar with respect to changes in MAT ratios with both models: KS was low with Cmax, moderate with SLf and AUCp, and high with I and Tmax following correction for apparent lag time (Tlag). Changes of the shape parameter CV2A, however, were not detectable by Cmax, Tmax, SLf, and AUCp. Changes in both MAT and CV2A were well reflected by I with CV2A - ratio > 1. I exhibited approximately full KS also with CV2A - ratio < 1 when a correction was first applied for the apparent lag time. CONCLUSIONS: The time profile of absorption rates is insufficiently characterized by only one parameter (MAT). Indirect metrics which are sensitive enough to detect changes in the scale and shape of the input profile could be useful for bioequivalence testing. Among the tested measures, I is particularly promising when a correction is applied for Tlag.

Subject-by-formulation interaction in determinations of individual bioequivalence: bias and prevalence.

PURPOSE: 1. To determine properties of the estimated variance component for the subject-by-formulation interaction (sigma D2) in investigations of individual bioequivalence (IBE), and 2, to evaluate the prevalence of interactions in replicate-design studies published by FDA. METHODS: Four-period crossover studies evaluating IBE were simulated repeatedly. Generally, the true bioequivalence of the two formulations, including sigma D2 = 0, was assumed. sigma D2 was then estimated in a linear mixed-effect model by restricted maximum likelihood (REML). The same method was applied for estimating sigma D2 for the data sets of FDA. RESULTS: 1. sigma D estimated by REML was positively biased. The bias and dispersion of the estimated sigma D increased approximately linearly with the estimated within-subject standard deviation for the reference formulation (sigma WR). Only a small proportion of the estimated sigma D exceeded the estimated sigma WR. 2. Distributions of the estimated sigma D were evaluated. At sigma WR = 0.30, a level of estimated sigma D = 0.15 was exceeded, by random chance, with a probability of about 25%. 3. Importantly, the behaviour of the sigma D2 values estimated from the FDA data sets was similar to that exhibited by the simulated estimates of sigma D2 which were generated under the conditions of true bioequivalence. CONCLUSIONS: 1. sigma D estimated by REML is biased; the bias increases proportionately with the estimated sigma WR. Consequently, exceeding a fixed level of sigma D (e.g., 0.15) does not indicate substantial interaction. 2. The data sets of FDA are compatible with the hypothesis of sigma D2 = 0. Consequently, they do not demonstrate the prevalence of subject-by-formulation interaction. Therefore, it could be sufficient and reasonable to evaluate bioequivalence from 2-period crossover studies.

Individual bioequivalence--has its time come?

A forthcoming draft Guidance of the Food and Drug Administration is expected to replace the current framework for the assessment of bioequivalence, based on the comparison of average kinetic responses, with a very different approach, the evaluation of individual bioequivalence. It emphasizes the estimation of intraindividual variances of the contrasted drug products as well as of the subject-formulation interaction, and requires the conduct of 4- (or 3-) period crossover bioequivalence trials. In order to facilitate the discussion of the draft Guidance and of the new approach, the underlying rationale, principles and procedures are described. Following this, various open questions are raised. It is suggested that their resolution should be carefully and widely discussed, and that more research and experience is needed before the possible implementation of the new approach.

Hypothesis: comparisons of inter- and intra-individual variations can substitute for twin studies in drug research.

Twin studies are useful devices to determine the heritability of persistent but variable characteristics that tend to differ among individuals. Drug responses are not persistent affairs; they are temporary characteristics. One therefore may ask whether twin studies are necessary to assess the genetic element in pharmacological responsiveness. To measure the genetic component contributing to their variability, it seems logical to investigate the response variation by repeated drug administration to given individuals, and to compare the variability of the responses within and between individuals. We attempt here to describe a theoretical background of this venture, and to show some results of the exercise. Potential sources of error or uncertainty are discussed.

Asymmetry of the mean-variability tradeoff raises questions about the model in investigations of individual bioequivalence.

Tradeoff between changes of intraindividual variations of 2 drug formulations and of the difference between their means is a characteristic of a procedure suggested for the determination of individual bioequivalence [Schall and Luus 1993] and to be proposed by the Food and Drug Administration for adoption. Hauck et al. [1996] investigated properties of the tradeoff. Their procedure was applied and extended in the present study. The tradeoff was shown to be asymmetric. Notably, a small change in intrasubject variations can elicit, under various conditions, a comparatively large change in the allowable difference between means which can still be compatible with the declaration of bioequivalence. For instance, when the intraindividual coefficients of variations are 40% and 38% for the reference and test formulations, respectively, the allowable difference between means may increase, as a benefit, by 12.3%. A penalty by 11.2% is elicited if the intrasubject variations of the reference and test products are 40 and 42%, respectively. In addition, 4-period crossover trials were simulated. Ratios of estimated variances of the 2 formulations followed an F-distribution. Distributions of changes in allowable deviations between means were calculated from the tradeoff relationships; generally substantial changes were noted with high probabilities. For example, with an intraindividual variation of 30% there is an estimated 37% probability that a benefit of 10% increase, or larger, is gained by chance in the allowable difference between means, and an additional 36% probability that a penalty of a 10%, or larger, decrease in the allowable difference is suffered. With an intrasubject variation of 40%, the estimated probabilities are 42% and an additional 42% for a 10% expansion and contraction, respectively, of the allowable difference between means. Consequently, the strong asymmetry of the tradeoff could result in very large probabilities for benefits and penalties. Therefore, the investigated model assessing individual bioequivalence does not appear to be suitable for implementation.

Metrics comparing simulated early concentration profiles for the determination of bioequivalence.

PURPOSE: To compare the effectiveness of various metrics which evaluate bioequivalence in the early phase of concentration-time profiles. METHODS: Two-period crossover trials were simulated with increasing assumed ratio of the true absorption rate constants of the two formulations, and with various kinetic models. Kinetic sensitivities (KS) and standard errors (SE) of the various metrics were recorded and the percentage of trials accepting bioequivalence (the statistical power) was evaluated. The principal metrics included the partial AUC(AUCP), the intercept obtained by linear extrapolation of the ratios of the lower over higher concentrations (C) measured for the two formulations (I L/H), and the ratios of intercepts extrapolated from logarithmic C/ time values of the two products (MLOG). For comparison, also properties of CMAX and an ideally evaluated measure (Id) were determined. RESULTS: MLOG showed generally the highest statistical power and KS, and also the largest SE, closely followed by I L/H. Partial AUC exhibited lower power and KS, but also smaller SE than the intercept procedures. The three methods had much higher power, KS and SE than CMAX. These comparisons were maintained over various kinetic conditions and experimental designs. The effective evaluation of bioequivalence in the early phase of studies is assured with 3 (or more) measurements until the population average peak of the reference formulation. CONCLUSIONS: The three principal methods assess bioequivalence very effectively in the early phase of a concentration-time profile. MLOG had the highest statistical power, closely followed by I L/H and then by partial AUC.

The duration of measuring partial AUCs for the assessment of bioequivalence.

PURPOSE: To determine favourable sampling conditions for assessing bioequivalence by the comparison of partial AUCs in the early phase of concentration-time profiles. METHODS: Two-period crossover trials were simulated. They assumed a wide range of the ratios of absorption rate constants of the test (T) and reference (R) formulations (kaT/kaR). Averages and standard deviations of the corresponding ratios of simulated partial AUCs (AUCpT/AUCpR) were determined together with the statistical power of assessing bioequivalence, i.e., the percentage of simulated trials in which bioequivalence was declared. RESULTS: The power for stating bioequivalence was high when AUCp was recorded until the earlier rather than the later of two peaks in each subject. Similarly, power was comparatively high when AUCp was measured until the time of the reference peak instead of multiples of this time. Power was high also when AUCp was determined until the fixed true, population mean time of the reference formulation instead of multiples of this time. The pattern for the kinetic sensitivity parallelled that found for the power, while the standard deviations changed generally in the opposite direction. CONCLUSIONS: The effectiveness (power) of evaluating bioequivalence in the early phase of concentration-time profiles by partial AUCs generally decreases when the duration for measuring the metric is extended. Among the investigated designs, determination of partial AUCs until the earlier of two peaks in each subject is the most powerful.

Model-independent estimation of lag times with first-order absorption and disposition.

The effectiveness of five model-independent procedures for the estimation of lag times (Tlag) was evaluated. Two new methods utilize early concentrations which are weighted by a term exponential in time. They estimate Tlag by weighted linear regression. One of these approaches evaluates also the time when maximum concentration is reached (Tmax). In addition, three older, empirically used procedures are considered. Two methods apply either the first two or three quantifiable concentrations and estimate the lag time by linear regression. Finally, the last unquantifiable concentration is often used as a measure of lag time. Simulations demonstrated that this procedure had large bias and generally high standard deviation. In contrast, the new methods showed small variation and negligible bias. The procedures applying linear regression had intermediate characteristics. Lag times were evaluated effectively by an average of two observations between Tlag and Tmax.

Truncated AUC evaluates effectively the bioequivalence of drugs with long half-lives.

Crossover trials were simulated in order to evaluate whether shortening the duration of bioequivalence trials for drugs with long half-lives would adversely affect the statistical properties of estimated AUC ratios. The trials were simulated under a wide range of assumed kinetic and experimental conditions. The duration of the simulated experiments was gradually shortened and ratios of truncated AUCs were evaluated. In addition, simulations by Martinez and Jackson [1991] were substantially extended. It was demonstrated that the variation of truncated AUCs did not rise, and their bias was negligible when investigations were limited to 2 (and under many conditions to 1) half-lives following drug administration. With large variability of clearance, high limit of quantitation, and/or 2-compartmental models, the observed variation actually often increased when the duration of a study was extended. It was concluded that the assessment of bioequivalence for long half-life drugs would not be adversely affected by limiting the duration of an investigation and, consequently, by using truncated AUCs.