Secondary metrics for the assessment of bioequivalence.
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Area Under Curve↗
Biomedical subjects
L Endrenyi
Publications and source records attributed to L Endrenyi.
Some issues for the consideration of individual bioequivalence.
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Chemistry, Pharmaceutical↗
Variation of the peak concentration following single and repeated drug administrations in investigations of bioavailability and bioequivalence.
Contrasts were evaluated for the maximum blood or plasma concentration (C(max)) of drugs measured after repeated and single oral administrations. Variances of C(max) were calculated and also simulated for a single drug as well as the comparison of two formulations, i.e., for the analysis of investigations of both bioavailability and bioequivalence. The coefficient of variation (CV) of C(max) was higher in the steady state than after a single drug administration when the variability of the disposition rate constant (k) was substantially larger than that of the absorption rate constant (k(a)). In turn, the CV of C(max) was substantially lower following repeated than after single drug administration when the variability of k(a) dominated that of k. The latter condition often prevails in practice since the relative variation of absorption rates generally substantially exceeds that of clearance (the latter being proportional to k). The statistical insensitivity is superimposed on the low kinetic sensitivity exhibited by C(max) following repeated drug administrations. Consequently, bioequivalence trials conducted in the steady state generally permit a declaration of equivalence even between drug products that have very different absorption rates.
Biological Availability↗
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.
Analysis of Variance↗
Evaluation of orally administered highly variable drugs and drug formulations.
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Administration, Oral↗
Without extrapolation, Cmax/AUC is an effective metric in investigations of bioequivalence.
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Kinetics↗
Sensitive and specific determination of the equivalence of absorption rates.
PURPOSE: To develop a new method for the direct, sensitive evaluation of the equivalence of absorption rates in linear kinetic systems. METHODS: Concentrations are obtained before the earlier peak. Ratios of concentrations adjusted for the corresponding ratio of AUCs (area under the curve contrasting plasma concentration with time), or their logarithm, are extrapolated by linear regression to the time of drug administration. The intercept estimates the ratio of absorption rate constants (ka), or its logarithm. RESULTS: The intercept metric assesses the equivalence of absorption rates with very favourable characteristics. The metric reflects the ka-ratio specifically (i.e., not affected by other kinetic parameters), is approximately linear to it, exhibits high kinetic sensitivity and excellent statistical properties. With many observations, the intercept metric has near-ideal features, including high power for determining bioequivalence and the ability to detect a 25% difference between ka values. With only 3 or 4 measurements before the earlier peak, the performance of the metric depends on the preset regulatory conditions. Reasonably good power is noted if the bioequivalence limits determine a 50% difference between two metrics and, approximately, between two ka values. The intercept metric shows very high power with a wider bioequivalence range. The power declines only moderately with increasing intraindividual variation of ka. The equivalence of absorption rates is assessed with much higher power by the intercept metric than by Cmax. CONCLUSIONS: The excellent kinetic and statistical properties of the intercept metric enable the specific and sensitive determination of the equivalence of absorption rates.
Absorption↗
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.
Dose-Response Relationship, Drug↗
Pharmacokinetics of inhaled pyrene in rats.
Male Wistar rats were exposed to micronized aerosol concentrations of a 14C-labeled model polycyclic aromatic hydrocarbon (pyrene) at 200, 500, and 800 mg/m3 for a period of 95 min. Both the 14C label and free pyrene were monitored in the blood, urine, and feces. At the termination of the blood sampling, three of the six rats per dose group were killed and the distribution of [14C]pyrene to eight major tissues was analyzed. The analysis of blood concentration data using a one-compartment pharmacokinetic model revealed that the uptake and elimination kinetic parameters were dose dependent, for both total radioactivity (pyrene plus metabolites) and for pyrene per se, over the range of exposures used in this study. The ratio of the percent excreted via the urinary and fecal routes, collected over a 5-d period postexposure was about 1.0 at each exposure level.
Absorption↗
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.
Analysis of Variance↗
Percutaneous uptake, distribution, and excretion of pyrene in rats.
Groups of 12 male Wistar rats, of about 400 g body weight, were dosed with 2, 6, or 15 mg/kg of 14C-labeled pyrene, dissolved in acetone, applied to 4 cm2 of a shaved area of the mid back. Three animals in each dose group were killed at 1, 2, 4, and 6 d post-dosing, and their principal organs were removed and analyzed for pyrene and [14C]pyrene equivalents. Urine and feces, as well as the area of skin to which the dose was applied, were also analyzed for [14C]pyrene equivalents. The rate of uptake from the skin was rapid (t1/2 0.5-0.8 d) relative to rate processes for the other organs, and about 50% of the applied dose was excreted over the 6 d of the study. The significant decrease in the fraction of the dose excreted and in the normalized amounts distributed to the various organs and tissues, as the dose increased for all chemical species measured, was strongly suggestive of nonlinear kinetics, as has been observed in previous studies. Levels of pyrene were highest in the liver, kidneys, and fat. Levels of metabolites were also high in the lung. It was evident that the dermal route of uptake was not insignificant for this model polycyclic aromatic hydrocarbon and may represent a significant exposure route for exposed humans.
Adipose Tissue↗
Variation of Cmax and Cmax/AUC in investigations of bioequivalence.
In order to enable the setting of regulatory criteria for the equivalence of absorption rates on a sound scientific basis, the variation of Cmax/AUC and Cmax was evaluated. Under most conditions, the variation of Cmax/AUC was 10-25% higher than that of AUC independently of the variability of the extent of absorption. By contrast, the variation of Cmax was 50-60% higher than that of AUC and was strongly dependent on the variability of the extent of absorption. Therefore, it is recommended that for establishing the equivalence of absorption rates, the 90% confidence limits for the percentage ratio of the Cmax/AUC values of two drug products should be (based on their logarithmic averages or medians) between 75 and 133%. Regulatory decisions based on Cmax, while not favored, should expect that the 90% confidence limits for the percentage ratio of the Cmax values of two drug products be (based on their logarithmic averages or medians) between 70 and 143%. These recommendations parallel and are contingent upon the internationally harmonized criterion for the equivalence of extents of absorption which requires that the 90% confidence limits for the percentage ratio of two AUC values (based on their logarithmic averages or medians) be between 80 and 125%.
Absorption↗
A computationally efficient approach for the design of population pharmacokinetic studies.
A computationally efficient procedure was devised for designing experiments in which population pharmacokinetic parameters are estimated. The method, referred to as the large-sample approach, evaluates the variances of parameter estimates for a population pharmacostatistical model. The procedure utilizes the NONMEM program and requires a single simulation that assumes many, say 1000, subjects. The approach reduced CPU time by about a factor of 50 when compared with the evaluation of the same variances by the direct simulation of experiments. The large-sample and simulation approaches yielded generally similar values for the variances of parameter estimates. The variances calculated by the large-sample approach were, in the case of a simple model, close to the expected variances. The proposed method identified correctly the imprecise parameter estimates but somewhat underestimated their variances.
Computer Simulation↗
Vasodepressor reaction induced by inferior vena caval occlusion and isoproterenol.
UNLABELLED: Testing for the susceptibility for vasodepressor reaction in humans involves the combination of restriction of venous return by passive upright tilting and the administration of isoproterenol. To explore the basis of the vasodepressor test in humans, the present experiment examined whether a reduced cardiac volume coupled with adrenergic stimulation causes a vasodepressor reaction in rats. Vasodepressor reaction was defined as paradoxical heart rate slowing in conjunction with hypotension during inferior vena caval occlusion. Inferior vena caval occlusion was performed for 60 s and the maximum changes in R-R were measured during seven states as follows. (A) Under control conditions inferior vena caval occlusion alone accelerated the rate in 32 of 32 rats (delta R-R, -13.9 +/- 1.7 ms, p less than 0.001). (B) When inferior vena caval occlusion was performed during an infusion of isoproterenol (0.5-1.0 micrograms.min-1), a vasodepressor reaction was observed in all rats as the heart rate slowed (delta R-R, +138.1 +/- 14.8 ms, p less than 0.001). The vasodepressor reaction was further examined during isoproterenol and inferior vena caval occlusion under five additional states. (C) After atropine the vasodepressor reaction was unchanged (delta R-R, +132.7 +/- 24.8 ms, p less than 0.001). (D) After bilateral vagotomy the paradoxical slowing was eliminated. (E) After intrapericardial lidocaine the paradoxic slowing was eliminated. (F) After bilateral stellectomy nonsignificant slowing was still present, but this was markedly reduced when compared with B (p less than 0.001). (G) Following chronic chemical sympathetic denervation with 6-hydroxydopamine the paradoxic bradycardia was eliminated. CONCLUSIONS: (1) Reduced cardiac volume combined with adrenergic stimulation can stimulate a vasodepressor reaction; (2) the vasodepressor reaction requires signalling by the afferent but not efferent vagal fibers; (3) the bradycardia is mainly due to withdrawal of sympathetic efferent tone.
Animals↗
The effects of sympathetic denervation on spontaneous ventricular defibrillation in the rat.
Ventricular tachycardia or ventricular fibrillation was electrically induced in 38 normal rats (group 1) and 24 sympathetically denervated rats (6-hydroxydopamine) (group 2). The time for spontaneous reversion to sinus rhythm was measured during (1) control, (2) isoproterenol, and (3) the combination of isoproterenol and phenylephrine. The time for spontaneous reversion was the same in both groups in the three states. The reversion time was prolonged threefold by isoproterenol, and restored to control values when phenylephrine was added to the infusion of isoproterenol. The tachycardia duration and the refractory period were inversely related: log10 (tachycardia duration) = 3.466-0.091 (refractory period). Ventricular tachycardia/fibrillation induction was examined as follows: (i) Ventricular tachycardia/fibrillation was induced in 100% of normal rats (group 1), but only 42% of the denervated rats (group 2, p less than 0.001); (ii) during isoproterenol, ventricular tachycardia/fibrillation was induced in 100% of rats of both groups; and (iii) when phenylephrine was added to isoproterenol, ventricular tachycardia/fibrillation was induced in 100% of group 1 rats versus 82% of group 2 rats, (p = NS). These observations suggest (1) the induction of ventricular tachycardia/fibrillation is highly dependent on intact sympathetic innervation, and (2) exogenous adrenergic agonists modulate the duration of ventricular fibrillation through their effects on ventricular refractory period, independent of sympathetic innervation.
Animals↗
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.
Research Design↗
Pharmacokinetics and bioavailability of pyrene in the rat.
Groups of 6 male Wistar rats, of about 400 g body weight, were dosed with 14C-labeled pyrene, dissolved in an Emulphor/water solvent vehicle, at 5 different dose levels by the intravenous or oral routes. Appropriate mathematical models were fitted to blood concentration-time data for [14C]pyrene and pyrene per se and dose-trend analyses were carried out. Areas under these curves were used to assess the bioavailability of the orally administered doses. Tissue concentrations, measured at the termination of the blood sampling period, gave a quantitative measure of the distribution of the administered dose. Attempts to repeat these studies with similar doses of tritium-labeled benzo[a]pyrene were frustrated by the lack of meaningful blood-level data. Dose trends for the derived pharmacokinetic parameters for pyrene revealed that the kinetics were nonlinear and strongly suggestive of enterohepatic recycling. Biliary excretion, measured in a separate experiment, gave support to this hypothesis. The bioavailability of the orally administered doses was between 50 and 60%. Over a 6-d period postdosing, some 45 and 40% of the administered dose was excreted via the urine and feces, respectively, irrespective of the route of administration. Distribution to the tissues of the 14C-label was highest in the perirenal fat, intermediate in the liver, kidneys, and lungs, and lowest in the heart, testes, spleen, and brain.
Administration, Oral↗
A new, sensitive graphical method for detecting deviations from the normal distribution of drug responses: the NTV plot.
1. A new graphical method was developed for the detection of deviations from the normal distribution. The approach took advantage of the similarity of graphical features of a graded dose-response relationship and a cumulative normal distribution. 2. The behaviour of the new normal test variable (NTV) plot was evaluated, in comparison with that of the probit plot and probability density functions (the generalization of histograms), for various assumed distributions. These included skewed distributions and composites of normal distributions with a variety of separations, ratios of peak sizes and widths. 3. The NTV approach generally detected deviations from the normal distribution more sensitively than the probit plot. 4. The NTV and probit plots may be able to identify biomadality by complementary approaches. 5. The characteristics of the three graphical representations were illustrated by a simulated sample from a composite of normal distributions and by an example of sparteine metabolism in 142 Cuna Amerindians.
Dose-Response Relationship, Drug↗