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.

Evaluation of two assumptions: single straight line, and single normal distribution.

Using graphical and statistical approaches, Laszlo Endrenyi and Mayank Patel describe methods that answer two frequently asked questions: 'Can the data be characterized by a single straight line, or should a more complex model be invoked?' and 'Do the observations follow a single normal distribution, or is there evidence for deviations from this assumption, including the possibility of bimodality?" These methods complement those addressed in a recent Principles article by Dick Barlow.

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.

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.

Comparative efficiencies of randomized concentration- and dose-controlled clinical trials.

OBJECTIVE: To compare efficiencies of randomized dose- and concentration-controlled trials (RDCT and RCCT) for estimating the parameters of concentration-effect relationships. RATIONALE: In 1991 Sanathanan and Peck (Controlled Clin Trials 1991;12:780-94) suggested that estimation by RDCT is biased and much less efficient than analysis by RCCT. Their conclusion was based on a pharmacodynamic model that characterizes the effect of theophylline in subjects with asthma, in which the response was related linearly to a limited range of concentrations and independent of concentration otherwise. Therefore it was intended to explore whether the conclusion of Sanathanan and Peck applied to other pharmacodynamic models. RESULTS: The results of Sanathanan and Peck were confirmed for the restricted linear, baseline-plateau model: with large pharmacokinetic and no pharmacodynamic variability, RCCT was 3.1 times more efficient than RDCT. However, under the same conditions, the efficiency of RCCT exceeded that of RDCT only 1.5 and 1.2 times when response was related, without restrictions, to concentration and log concentration, respectively. Moreover, in the presence of even moderate pharmacodynamic variability, the ratio of RCCT/RDCT efficiencies did not exceed 1.30 and 1.08, respectively. The parameters estimated by RDCT with these two models were not biased. Finally, in the presence of interindividual variability of the median effective concentration (EC50), pharmacokinetic variability did not affect the observed variation of the parameters in the log-linear pharmacodynamic relationship. CONCLUSIONS: RCCT generally estimates pharmacodynamic parameters with an efficiency that is not much higher than, or even similar to, those yielded by RDCT. Therefore statistical benefits often do not call for the application of RCCT. However, sometimes its use should be seriously considered, particularly for drugs having small therapeutic indexes or when the baseline and plateau of the response occur near the therapeutic region of concentrations.

Genetic study of amobarbital elimination based on its kinetics in twins.

Following the intravenous administration of 125 mg amobarbital sodium in 7 pairs of dizygotic and 7 pairs of monozygotic twins, the time-course of plasma concentrations was observed. The number of detectable compartments varied from subject to subject but was consistently 1 or 2 or 3 within a given individual. The terminal slope of the semilogarithmic concentration-time plot (corresponding to biologic half-life of 22.8 hr) did not represent the elimination rate constant even in persons with apparently single-compartmental characteristics. The redistribution of amobarbital was rapid in comparison with its elimination. The rate of the latter (characterized by kel = 0.051 hr-1, plasma clearance = 37.7 ml/min) could be closely identified with the rate of metabolism. The twin data showed that genetic control was exerted on kinetic parameters characterizing the rate of amobarbital elimination and, therfore, the rate of its metabolism. Correlation analysis suggested that this control was independent of size factors, which were themselves substantially heritable. The genetic analysis of twin data included, in addition to intracelass correlations and Holzinger's H factors, newly developed lower (and upper) bounds of the broad-sense heritability. In pharmacogenetic studies, assessment of model-independent kinetic parameters, such as plasma clearance with or without adjustment for body weight, is recommended.

Amobarbital--a probe of hepatic drug oxidation in man.

Some aspects of the fate of amobarbital were investigated since this drug is being used as a probe to gauge drug oxidation in man. The mean ratio of orally available over intravenously injected amobarbital was established as 0.99 +/- 0.11 (SD), by comparing integrated concentration-time curves, indicating complete absorption and absence of a first-pass effect. One subject ingested 200 mg of amobarbital sodium, and amobarbital concentrations in serum were monitored for 5 days thereafter. Elimination of amobarbital under these conditions followed first-order kinetics. One subject ingested amobarbital 7 times over a period of 3 yr; plasma clearances (32.1 +/- 1.8 [SD]ml/min) exhibited remarkable constancy, while biologic half-lives (26.5 +/- 3.1 hr) and distribution volumes (73.6 +/- 8.0 L) showed some fluctuation. The distribution of parameters of amobarbital elimination was investigated in 36 unrelated subjects. Amobarbital half-lives (23.8 +/- 6.7 hr) appeared to be normally distributed, while the clearances (36.7 +/- 10.0 ml/min) might not follow a normal distribution.

A method for studying drug metabolism in populations: racial differences in amobarbital metabolism.

The two main metabolites of amobarbital excreted in urine are 3'-hydroxyamobarbital (C-OH) and 1-(beta-D-glucopyranosyl) amobarbital (N-glu). When testing the metabolite ratio in small single samples of urine, it was found that the urine in a Caucasian population contained about one-third glucose conjugation and two-thirds hydroxylation product, while an Oriental population excreted both metabolites in equal proportion. Attempts to learn the causes for the different metabolite ratios led to an investigation of metabolite concentrations in urine. The sums of the average urinary concentration of C-OH was greater in Caucasians than in Orientals, no matter how the data were expressed; the reverse was true for the N-glu metabolite. C-OH data was scattered more widely among Orientals than Caucasians; this might indicate bimodality of the distribution curves. There also was a trend toward more N-glu metabolite in urine of females than of males. Measuring the metabolite/creatinine ratios narrowed the distribution range of the data, particularly after correction for sex difference in creatinine, but population differences were not changed. Expected relationships between metabolite content of urine, sampling times, and plasma half-life (t1/2) were established by calculation. A Caucasian female with no capacity for N-glucosidation was found during the first part of this population survey. An Oriental male with only trace capacity for amobarbital hydroxylation was found in the second part.

Mechanism and significance of carbohydrate intolerance in chronic alcoholism.

Intravenous glucose tolerance tests were carried out in 61 chronic alcoholic patients, divided into two groups, and in a third group consisting of healthy, nonalcoholic volunteers. Members of one experimental group were drinking alcohol throughout the study. The patients of the other experimental group received no alcohol and were in withdrawal from alcohol. The glucose tolerance tests were carried out on each patient on admission to the hospital and 1 wk later. During the test, blood was drawn at 10 min intervals for glucose, immunoreactive insulin, and glucagon determinations. The results indicated that there was transient carbohydrate intolerance in the great majority of both patient groups, and it became evident that the carbohydrate intolerance was the result of continuous alcohol consumption and was not part of the withdrawal syndrome. Significant decrease in insulin secretion was found in the early part of the glucose tolerance tests in the majority of the patients in both alcohol and withdrawal groups. Based on results of this study and evidence from the literature, it is suggested that chronic alcoholism is dabetogenic in susceptible individuals and that the transient carbohydrate intolerance found in our study represents and early step in the development of adult-onset diabetes eventually developing in a significant number of chronic alcoholics.

Plasma concentration-response relationships of two formulations of propranolol.

The time-course of beta blockade induced by two formulations of propranolol was compared to their plasma concentration-time curves. Graded infusions of isoproterenol were used to assess the degree of beta blockade at different times after oral administration of 80 mg of propranolol to 11 healthy volunteers. The time-course of drug effect was measured as the decline of the systolic pressor dose 20 (SPD 20) and the chronotropic dose 20 (CD 20). Variability of plasma propranolol concentration was small, varying within subjects from 27% to 36% and between subjects from 19% to 28% at the various sampling times. Pharmacodynamic effects showed a similar reproducibility: intra-individual variation was 15% to 28% for CD 20 and 17% to 32% for SPD 20; interindividual variation was 10% to 24% for CD 20 and 13% to 23% for SPD 20. Pooling of the data of all subjects indicated a parallel decline of drug concentration and effect. However, three of the 11 subjects showed drug effects declining at a faster rate than drug levels. This dissociation between serum concentrations and effects points out the clinical relevance of complementing kinetic studies of propranolol with pharmacodynamic studies. The good reproducibility within subjects and the small interindividual variation suggests that isoproterenol dose-response curves may be a useful tool for such studies.

The value of decompression for acute experimental spinal cord compression injury.

A clip compression method was used to produce acute spinal cord compression injury in rats. The force and duration of the spinal cord compression were independently varied, and functional recovery of the cord was assessed using the inclined plane technique. Mathematical modeling produced a curve defining the relationship between force, duration, and functional recovery for each week after injury. The study clearly showed the beneficial effect of decompression and that increasing either the force or duration of compression, or both, caused a reduction in recovery.

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.

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.

A method for the evaluation of individual bioequivalence.

A method is presented for the evaluation of individual bioequivalence. The approach is simple and effective. It considers two drugs to be inequivalent in individuals if their contrast shows larger variation than that observed within formulations, which are repeatedly administered to the subjects. The necessary information can be obtained in 3- or 4-period crossover trials, in which individuals receive not only both drug products but also the replicate application of at least one of them. In the implementation of the procedure, it is suggested that two drug products could be considered to show individual bioequivalence if the upper, one-sided confidence limit for the ratio of intraindividual variances estimated between and within formulations does not exceed a preset critical value, Fcr. For initial considerations, a confidence level of 90% and Fcr = 4.0 are recommended. The intraindividual variances between and within formulations can be estimated either by simple, direct calculations or by an analysis of variance (ANOVA). The structure of the latter is different from that of the ANOVA applied for the assessment of average bioequivalence. Another approach assessing individual bioequivalence from an estimated variance component is less favoured. Graphical, exploratory analysis of the multiperiod crossover trials is recommended and illustrated. The suggested procedures are demonstrated on an example evaluating the individual (and average) bioequivalence of olsalazine tablets and capsules.

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.

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.

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.

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.

Glucose intolerance in alcoholism.

Intravenous glucose tolerance tests were given to 31 nondiabetic alcoholics and 11 healthy nonalcoholic controls. In almost half of the alcoholics peak glucose concentration was higher and glucose elimination from the plasma was slower than in the controls.