Evaluation of Different Indirect Measures of Rate of Drug Absorption in Comparative Pharmacokinetic Studies

Evaluation of Different Indirect Measures of Rate of Drug Absorption in Comparative Pharmacokinetic Studies L. F. LACEY',0. N. KEENE~, C. DUQUESNOY~, AND A. BYE' Received November 30, 1992, from the 'Department of Clinical Pharmacokineticsand the $Department of Medical Statistics, Glaxo Group Research Ltd., Greenford Rd, Greenford, Middlesex, UB6 OHE, U.K., and the §Unit of Clinical Pharmacology, Laboratoires Accepted for publication May 13, 1993'. Glaxo, Paris 75116, France.

Abstract 0 As indirect measures of rate of drug absorption (metrics), maximum plasma concentration (C-) is confounded by extent of drug absorption and the time to reach C ,, (t-) is a discrete variable, dependent on blood sampling frequency. Building on the work of Endrenyi et al., we have compared different metrics, including &,/area under the curve of concentration versus time from time zero to infinity (AUC,), partial AUC from zero to fmx (AUC,), and C,,.t,, with simulated experiments. Importantly, the performance of these metrics was assessed with the results of actual pharmacokinetic studies involving Giaxo drugs. The results of the simulated and real experiments were consistent and produced the following is a more powerful metric than unambiguousfindings: ( I ) &,/AUC, &, in establishing bioequivaience when the formulations are truly bioequivaient;(2)&,IAUC, is more sensitive than C ,, at detecting differences in rate of absorption when they exist; and (3)the treatment ratios for AUC,, AUC,/AUC,, and &-& are very imprecisely estimated and are of no practical value as measures of rate of absorption. Of the metricsexamined, C-IAUC, is the most sensitive and powerfulindirect measureof rate of drug absorption in comparative pharmacokinetic studies involving immediate-reiease dosage forms and should be used instead of &, in bioequivalence testing.

Maximum plasma concentration of drug (C,,) and time to reach ,C (t,) are the indirect measures of rate of drug absorption (metrics) currently used in comparative pharmacokinetic studies. These are observational parameters that are easily obtained. However, they have serious shortcomings as indirect measures of rate of drug absorption. ,,C is confounded by extent of absorption1and tm, is a discrete variable, dependent on blood sampling frequency.2 Recently, other metrics have been proposed, [e.g., partial area under the curve of concentration versus time fromzero to t, (AUC,)? C--t, and C,~AUCm11. Endrenyi et al.1 provided strong arguments, based on simulated experiments, why CmIU/AUCm might be a superior measure to C., Our investigations build on the work of Endrenyi et al. by comparing different metrics, including C,JAUC,, with simulated experiments. Importantly, we have extended these investigations to the results of actual pharmacokinetic studies with Glaxo drugs.

Experlmental SectIon Metrics-The following metrics of rate of drug absorption were investigated the observed maximum drug concentration (C,,,), for each C,,JAUC,, AUC from time zero to the time of C-Ct,,) treatment separately (AUC,), AUC,/AUC,, and C,.t,. AUC, was used as the measure of extent of absorption. Theory-Let C(t) = concentration a t time t , k, = first-order rate of absorption, k = first-order rate of elimination, F = oral bioavailability, V = apparent volume of distribution, and A = F-Dosel V. Then, for a one-compartmental model with first-order rate of absorption, the following relationship exists: C(t) = [A-k,.(exp(-k.t) - exp(-k,-t))l/(k, - k) (1) For this model: the following relationships exist: Abstract published in Advance ACS Abstracts, November 15,1993. 2 12 / Journal of PtKlrrnaceutical Sciences Vol. 83, No. 2, February 1994

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C,/AUC, = k;(k,/k)' (5) In eq 5, P = kJ(k - k,). C, is directly related to F-Dose, as is AUC,. Thus, these parameters should be highly correlated. In contrast, t, and C&AUC, are only dependent on k, and k. Pharmacostatistical Model-The one-compartmental model (eq 1) was used to generate simulated data for crossover studies. The lognormal distribution was used for the within-subject variability in the pharmacokinetic model parameters. The expected geometric mean (GM) values of the model parameters, with their associated within-subject coefficients of variation (CV) were as follows: GM of A = 80 units, CV of A = 20%; GM of k = 0.25 h-l, CV of k = 10%; GM of k. = 1.25 h-1, CV of k. = 30%. Standard deviations (SD) for the log parameters were obtained' according to the following equation: (6) SD,- = (log (CV2 + 1))'l2 Residual error was introduced into the model by a multiplicative term to eq 1 according to a log-normal distribution, with CV = 20%. For the purposes of assessing the metrics of rate of absorption, it is not necessary to include in the model between-subject variability, sequence effects, or period effects, as these would be eliminated in the standard analysis of variance for two-period crossover studies.5 Sampling times were set as 0.0,0.25,0.5,1.0,1.5,2.0,2.5,3.0,3.5,4.0, 5.0, 6.0, 8.0, 10.0, 12.0, and 16.0 h post-dose. Simulations-Two sets of simulated experiments were carried out. Each involved generating data from 100 separate two-period crossover studies. There were 24 subjects per study, which is a typical number of subjects used in actual bioequivalence studies. In the first set of simulations, the model parameter values were the same for both treatments and are as given above. Thus, in this simulation the two treatments were truly bioequivalent. In the second set of simulations, the expected geometric mean values for k. were 1.26 h-1 for the first (standard) treatment and 0.625 h-l for the second (test) treatment, a 50% decrease. Data from Actual Studies of Glaxo Drugs-A suitable Glaxo drug was identified and 11of the most recently performed two-way, crossover, oral relative bioavailability studies were used to assess the different metrics of rate of drug absorption. The studies involved between 12 and 36 subjects, with a median of 24 subjects per study. With one exception, the same standard treatment was used in all studies. For these studies all the metrics given above were calculated and compared. In addition, four studies with other Glaxo drugs were used specifically to compare C d A U C , with.,,C Eachstudy involved between 16 and 24 subjects. StatisticalAnalysis and Bioequivalence Assessment-Standard analysis of variance methods6 were used to obtain the treatment mean ratios of the log transformed metrics, with associated 90% confidence intervals. Bioequivalence was deemed to have occurred if the 90% confidence interval for the treatment mean ratios of the metric was within the range 80 to 125%.' For the second set of simulations only, t,, was compared between treatments by the Wilcoxon signed rank test.

Results First Set of Simulated Experiments (No Difference between Treatments)-Representative examples of simulated

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plasma concentration-time profiles obtained in a subject following both treatments are given in Figure 1. Table I shows the percentage of studies that demonstrated bioequivalence for each metric. It is apparent that AUC,, AUCJAUC,, and ,&,C rarely demonstrated bioequivalence and that C,JAUC, dem.,C onstrated bioequivalence more frequently than A plot of the treatment mean ratios for,C against AUC, shows that these variables are highly correlated, whereas C,,/AUC, plotted against AUC, shows no such correlation (Figure 2). The CVs for within-subject variability in each of these parameters was calculated from the residual mean square error obtained from the analysis of variance. Box-Whisker plots of these values (Figure 3) show that the largest CVs occurred for AUC,, AUC,/AUC,, and C,,-t,, and that C,JAUC, tended to result in lower CVs than for C ,,,,. Second Set of Simulated Experiments (50% Decrease in k,)-Table I shows the percentage of studies which demonstrated bioequivalence for each metric. Both ,C and C,JAUC, demonstrated bioequivalence in only a minority of cases. Table I1shows the distribution of p values associated with each metric.

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It is apparent that the smallest p values occurred most frequently with CmJAUCmand least frequently with AUC,, AUCJAUC,, and C,.t,,. This demonstrates that C,dAUC, is the most sensitivemetric at detecting true differencesin rate of absorption. Otherwise, similar results were obtained with this set of simulations as were obtained with the first set: the frequency distributions for mean ratio values of AUC,, AUCJAUC,, and C,,.t,, were very broad, but were much tighter for,C and especially for C,JAUC,. The metrics,C and AUC, were highly correlated, whereas CJAUC, and AUC, were not. The lowest CVs for within-subject variability tended to occur with C,,,/AUC,, and t h e highest CVs occurred with AUC,, AUC,/AUC,, and C,-t,,. Actual Studies with a Glaxo Drug-A total of 11studies with a particular Glaxo drug were analyzed. The 90% ’ confidence C C,JAUC,, and AUC, intervals obtained for the AUC,, ,, mean ratios are given in Figure 4. Within subject variabilities for AUC, were so high that bioequivalence was never demonstrated; similar results were obtained for AUCJAUC,, and C,-t,. Bioequivalence was more frequently demonstrated with C,dAUC, than with C,. The observed,C ratios were similar in value to the corresponding AUC, ratios, and bioequivalence was not demonstrated with ,C when AUC, failed the bioequivalence criteria. As with the simulated experiments, a plot of the treatment mean ratio for,C against AUC, shows that these parameters are highly correlated, whereas a plot of CJAUC, against AUC, shows no such correlation (Figure 5). Actual Studies with Other Glaxo Drugs-We have also compared,,C and CJAUC, in a further four actual studies with other Glaxo drugs. Figure 6 shows that CJAUC, consistently has a tighter 90% confidence interval than C ., Study D shows an example where the treatment mean ratio for AUC, is close to unity, but a difference in the observed,C is reflected in a difference of comparable magnitude in C,&AUC,. Journal of Pharmaceutical Sciences / 213 Vol. 83, No. 2, February 1994

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As stated by Endrenyi et al.,l C, is not suitable for assessing differences in absorption rate because it is confounded by extent of absorption. In addition, recent meetings have identified other problems, such as imprecision in C, estimates of treatment differences.8 This has caused problems in the international harmonizationof bioequivalence criteria. For example, current CPMP guidelines9have no specific guidance in relation to C, whereas FDA criteria' require the 90% confidence interval for the mean ratio to be within the range 80-125 % . The t,, value is only dependent on the rates of absorption and disposition of a drug and is not affected by the extent of absorption. In certain cases, t,, can be a useful parameter for assessing absorption rate.lOJ1 However, it suffers from shortcomings,being a discrete variable dependent on blood sampling frequency. The parameter t , is not normally expressed in 214 /Journal of pharmaceutlcsl Sciences Vol. 83, No. 2, February 1994

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consistently demonstrated that the mean ratio for partial areas and for C,,.t, were very imprecisely estimated and very insensitiveto real differencesin absorption rate. However, other partial area metrics have recently been proposed13and require evaluation before their role in the measurement of rate of absorption in comparative pharmacokinetic studies can be properly assessed. The mean ratio for C,/AUC, was consistently shown to be more precisely estimated than the C, mean ratio. This makes C,JAUC, a more powerful parameter for assessing differences in rate of absorption and, therefore, it should be a more suitable metric for bioequivalence testing, especially for drugs that are highly variable in their pharmacokinetics. Both C, and AUC, are dependent on the extent of drug absorption and should therefore be highly correlated. This was observed in both the simulated and actual studies (Figure 2 and 5). Theoretical considerations given in the Appendix show that it is this high degree of correlation between,C and AUC, that is responsible for the C,JAUC, mean ratio being more precisely estimated than the C, mean ratio. It should be noted that when treatments do not differ in their extent of absorption, the / , C AUC, mean ratio will tend to give the same estimate as the C, mean ratio. The results of this paper concentrate on one Glaxo drug. Limited work with other Glaxo drugs would suggest that the advantage of C,JAUC, over other metrics of rate of absorption is not limited to specificdrugs. All this work involved immediaterelease dosage forms and therefore further work is required in the assessment of these metrics for prolonged-release dosage forms. Whereas these metrics are most often discussed in the context of bioequivalence studies, our findings are not specific to such studies but can be applied to any comparative pharmacokinetic study that involves the comparison of rates of drug absorption.

Conclusions The following conclusions can be drawn from our results. (I) As an indirect measure of rate of drug absorption in comparative pharmacokinetic studies, C,,JAUC, isnot confounded by extent of absorption, unlike C ., (2) The treatment ratio of / ,C AUC, is more precisely estimated than the treatment ratio of ? ,I, This makes C,JAUC, a more powerful measure than ,C in establishing bioequivalence when the formulations are truly bioequivalent and more sensitive at detecting differences in rate of absorption when they are present. Therefore, C,J AUC, should be used instead of C, in bioequivalence testing. (3) The treatment ratios for the partial areas tested and for C,,-t, are very imprecisely estimated. However,further work is needed in the evaluation of other partial area metrics that have recently been proposed.

Appendix Let A = log treatment mean ratio for AUC,. Let B = log treatment mean ratio for C., Thus, B - A = log treatment mean ratio for C,JAUC,. Let p = correlation between A and B. Now, var(B - A) = var(B) + var(A) - 2.cov(A,B) = var(B) + var(A) - 2.p.[var(A).~ar(B)11/~.So, var(B - A) < var(B), if 2-p.[var(A).~ar(B)]~/~ > var(A). In the simulations, the observed values were as follows (simulation 1,simulation 2): p (0.77,0.75); UA (0.061,0.061); UB (0.064,0.066); UA-B (0.043,0.045). Thus, in these simulations, for var(B - A) to be less than var(B), the correlation coefficient between A and B needed to be >0.48 (simulation 1)and >0.46 (simulation 2), which was the clearly the case. Similar considerations apply within a study. For the 11Glaxo studies with a single drug, variability of the treatment ratio for AUC, was always less than that for C ;, the median correlation coefficient was 0.75 (range 0.67 t o 0.88).

References and Notes 1. Endrenyi, L.; Fritsch, S.;Yan, W. Int. J. Clin. Pharmacol. Ther. Toxicol. 1991, 29, 394-399. 2. Proceedings of the September 26, 1991, generic drugs advisory committee meeting, Food and Drug Administration, Center for D Evaluation and Research,Office of Generic Drugs; proceedings by?.A.S.E.T Associates, Fairfax, VA. 3. Gibaldi, M.; Perrier, D. Pharmacokinetics, Volume 15, 2nd ed.; Marcel Dekker: New York, 1982. 4. Diletti, E.; Hauschke,D.;Steinijans,V. W. Int. J. Clin.Pharmacol. Ther. Toxicol. 1991,29, 1-8. 5. Pabst, G.; Jaeger, H. Eur. J. Clin. Phormacol. 1990, 38, 5-10. 6. Schuirmann, D. J. J. Pharmacokinet. Biopharm. 1987, 15,657680. 7. Guidance: Statistical procedures for bioequivalencestudies using a standard two-treatmentcrossoverdesign;Office of GenericDrugs, FDA, July 1992. 8. McGilveray, I. J.; Midha, K.; Skelly, J. P.; Dighe, S.; Doluisio, J. T.; French, I. W.; Karim, A.; Burford, R. J. Pharm. Sci. 1990,79, 945-946. 9. CPMP Guideline: "Investi ation of Bioavailabilityand Bioequivalence". Doc: 111/54/89-E%. 10. Khoo, K.-C.;Gibaldi, M.; Brazzell, R. K. J. Phorm. Sci. 1985,74, 1340-1342. 11. Aarons, L. J. Pharm. Sci. 1987, 76,853-855. 12. Cartwright, A. C. Drug Info. J. 1991,25,473-482. 13. Chen, M.-L. Pharm. Res. 1992,9(11), 1380-1385. 14. SAS Institute Inc., Release 6.04 Edition, Cary, NC, 1987.

Acknowledgments We acknowledge the excellent contribution made by Brenda Miller, who wrote the SAS" programs used in this research.

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