INTRODUCTION

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Amoxicillin, a well-known amino-substituted penicillin, enjoys widespread clinical use, not only because of its broad antibacterial spectrum but also because of its high oral bioavailability (>90%), which makes it relatively unaffected by food or by other concomitantly administered drugs. The pharmacokinetics of amoxicillin has been extensively investigated (reviewed in reference 15) , and the compounded data indicate that an oral dose of 500 mg produces peak concentrations in plasma of about 10 µg/ml within 1 to 1.5 h, reaches adequate therapeutic concentrations in pleural, synovial, and ocular fluids, and accumulates in the amniotic fluid, but penetrates poorly into the central nervous system unless inflammation is present. Excretion of amoxicillin is predominantly renal, and >80% of an intravenous dose is recoverable in the urine, leading to very high urinary concentrations. The drug's terminal half-life (t_1/2) of elimination is 1 to 1.5 h.

Amoxicillin is the single active principle of at least 26 formulations marketed in Brazil (4), the vast majority of which were not subjected to bioavailability studies prior to registration. Recently, however, the Brazilian agency for drug control, Agência Nacional da Vigilância Sanitária, decreed that bioequivalence studies are mandatory for the registration of generic products and issued guidelines for such studies, which can be performed only at accredited centers (2). This prompted an immediate increase in the demand for such studies, two of which, carried out by our group, assessed the bioequivalence of generic formulations of amoxicillin. The concentration-in-plasma data points (n = 1,152 samples) obtained from 48 subjects enrolled in these studies were then used to develop and validate limited-sampling strategy (LSS) models (21, 22) to estimate the major bioequivalence metrics, namely, the area under the concentration-time curve (AUC) and the maximum concentration of drug in plasma (C_max) of amoxicillin. In addition, a similar linear regression approach was carried out in order to develop an LSS for predicting the time interval that amoxicillin concentrations in plasma exceed MIC susceptibility breakpoints (T>MIC), chosen as a dynamically linked variable. The results indicate that three-point LSS models, based on the same sampling times, provide accurate estimates of both AUC from 0 h to infinity (AUC_0-) and C_max, whereas two-point models are strong predictors of T>MICs of 0.25 and 2.0 µg/ml. These findings support the notion that strategies using a limited number of samples and proven to be sufficient robust to allow accurate estimation of individual pharmacokinetic parameters could be valuable for bioequivalence assessment as well as for investigation of pharmacokinetic-pharmacodynamic relationships, at reduced costs of sample acquisition and analysis and avoiding sampling at "unsociable" hours (21, 22, 24, 25).

	MATERIALS AND METHODS

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Clinical protocol. The two open-label, randomized studies described here used a standard two-sequence, two-period crossover design, in which the treatment phases were separated by a 7-day washout interval. Each study protocol was approved by the Ethics Committee of Instituto Nacional de Câncer, Rio de Janeiro, Brazil, and all participants provided written, informed consent. Two groups of 24 healthy volunteers (12 men and 12 women per group) were enrolled in the studies. The demographic characteristics of these 48 volunteers were as follows: (i) study 1, age range, 19 to 26 years; mean ± standard deviation [SD] of age, 25.5 ± 4.4 years; weight range, 50.7 to 84.5 kg; mean ± SD of weight, 62.0 ± 11.3 kg; and (ii) study 2, age range 19 to 43 years; mean ± SD of age, 25.7 ± 5.6 years; weight range, 48.2 to 99.1 kg; mean ± SD of weight, 65.2 ± 11.6 kg. All enrolled volunteers were nonsmokers and had no clinically significant abnormalities, as determined 2 weeks before the start of the study, based on medical history, physical examination, electrocardiogram, and standard laboratory test results (i.e., blood cell count, biochemical profile, sorological tests for human immunodeficiency virus, hepatitis B and C, and urinalysis). The volunteers had not used any investigational drugs in the 6 months preceding the present studies. Prescription drugs other than oral contraceptives or acetaminophen as an analgesic were not allowed during either study.

Microbiological assay. Amoxicillin concentrations were determined by a validated microbiological method (agar well diffusion) using Micrococcus luteus (ATCC 9341) as the test organism (6, 20) and Antibiotic Medium 2 (Difco Laboratories). Fresh stock solutions of amoxicillin at 1,000 µg/ml were made up in 0.1 M phosphate buffer (pH 6.0) for each set of assays. All samples were assayed in triplicate at appropriate dilutions in pooled human plasma, and all the samples from each volunteer were tested in parallel. The detection limit in plasma was 0.01 µg/ml, the standard curve of log concentration against the inhibitory halo diameter was linear between 0.03 and 5 µg/ml (correlation coefficient R was >0.98), the intraday coefficients of variation were 2.3% (0.3 µg/ml; n = 8) and 1.7% (3 µg/ml; n = 8), and the interday coefficients of variation were 4.4% (0.3 µg/ml; n = 6) and 1.6% (3 µg/ml; n = 6), respectively.

Drugs. The formulations tested were called reference (Amoxil, 500-mg capsules, batch BA0095, and 250 mg/5 ml of suspension, batch AD0164; SmithKline Beecham) and test (Amoxicilina-Basf Generix, 500-mg capsules, batch 9911004, and 250 mg/5 ml of suspension, batch 9911026; Knoll Produtos Químicos Farmacêuticos Ltda.).

Pharmacokinetic and statistical analyses. The C_max of amoxicillin and the time it was reached (T_max) were determined from the individual drug concentration in plasma data. A noncompartmental model provided by the software WinNonlin Professional 3.1 (Pharsight Corporation, Cary, N.C.) was used for the calculation of the pharmacokinetics parameters k_el (terminal elimination rate constant), t_1/2 (the terminal half-life), AUC_0-10 or AUC_0-12 (AUC from 0 to 10 h or 0 to 12 h), and the extrapolated AUC_0-. The AUCs thus obtained were taken as the "best estimates" of parameter values (see below).

LSS development for AUC_0- and C_max All-subsets linear regression analysis (9) of the AUC_0- or C_max best estimates against the concentration at a particular time (C_time) (independent variables) was carried out in order to develop LSS to estimate the individual values of AUC_0- or C_max for amoxicillin following administration of each formulation. Computations were carried out using function leaps (5) in Splus 4.0 (12). This analysis produced equations of the following form: AUC_0- or C_max = A₀ + A₁ × C₁ + A₂ × C₂ ... . A_n × C_n, where A_n are coefficients and there are a variable number of samples. Regression equations were then ranked according to the R² criterium in order to identify those that provided the best fit for 1 to 10 timed plasma samples. The LSS-derived AUC_0- or C_max estimates were then compared with the best estimates of these parameters for each of the 24 volunteers' data sets. The bias of these LSS-derived estimates was assessed by calculating the mean percentage of difference (MD%) from the best estimates as follows: percentage difference = [(derived estimate  best estimate)/best estimate] × 100%. Precision was assessed by calculating the mean absolute percentage of difference (MAD%) as follows: absolute percentage of difference = (|derived estimate  best estimate|/best estimate) × 100%.

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Bioequivalence analysis. The 90% confidence interval (CI) of the individual ratio (reference formulation/test formulation) of the log-transformed values of the best-estimated AUC_0- and C_max were used for bioequivalence assessment (23). The same procedure was applied to the three-point LSS-derived AUC_0- and C_max to explore the usefulness of the LSS approach in bioequivalence studies.

LSS development for T>MIC. We started by choosing two amoxicillin MIC susceptibility breakpoints representative of susceptible (0.25 µg/ml) and resistant (2.0 µg/ml) microorganisms, such as Staphylococcus aureus, Streptococcus pneumoniae, or Neisseria gonorrhoeae (16). We then calculated by linear interpolation the times when the individual amoxicillin concentration in plasma crossed each of these MICs, both in the absorption and the elimination phases of the concentration-time curves. The T>MIC for each MIC breakpoint, each individual ratio and each formulation was calculated as the difference between these two crossing-time points. A linear regression analysis of these T>MICs against the amoxicillin concentrations in plasma was performed to develop (training set; reference capsules) and to validate (the other three formulation data sets) LSS models for T>MIC, using the procedures described above for LSS modelling of AUC_0- and C_max.

Statistical analysis. The specific statistical tests applied to the data sets are indicated in the text. Significance level was set at a P value of <0.05.

	RESULTS

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All subjects completed the study protocol, and the four amoxicillin formulations were well tolerated with no adverse effects being reported.

Pharmacokinetic data. The plasma amoxicillin concentration-time curves for the reference and test formulations in each study are shown in Fig. 1, and the pharmacokinetic parameters derived from these curves are summarized in Table 1. The data reveal large interindividual variability (coefficients of variation >30%) for C_max, AUC_0-t, and AUC_0-, but there were no significant differences between the mean values of these parameters or the other pharmacokinetic parameters reported in Table 1 for the formulations tested in each study (Mann-Whitney rank sum test). The T_max for the reference capsule formulation did not differ from that obtained for the test capsule but was significantly longer than the T_max values for either the reference (P < 0.002; Student's t test) or the test amoxicillin suspension (P < 0.01).

View larger version (17K): [in this window] [in a new window]   FIG. 1.   Mean (± standard error of the mean) concentrations of amoxicillin in the plasma of healthy volunteers, after single oral doses (500 mg) of reference and test amoxicillin capsules (study 1, n = 24) (A) or suspensions (study 2, n = 24) (B).

Limited-sampling models for AUC_0-. The concentration in plasma data sets from the 24 volunteers enrolled in each study and an all-subsets regression approach were used to identify the most informative sampling times using 1 to 10 samples for estimating the AUC_0- of each formulation tested. The results of this analysis (Table 2) show that the most informative strategies depend on the formulation, although in the case of three-point models, the best equations for all formulations included sampling at 1 and 2 h and taking a third sample at 3, 4, or 5 h. The AUC_0- derived from the most informative three-point LSS correlated closely (R², >0.95; bias, <0.5%; precision, <5.0%; Table 2) with the corresponding best estimates of the AUC_0- for each formulation. Increasing the number of sampling points to more than three increased R² marginally and added little to the bias or the precision of the estimates of AUC_0-, compared to the respective values for three-point sampling for each formulation. From this analysis, we conclude that LSS models based on three samples are adequate for estimating amoxicillin's AUC_0-. The most informative three-point strategy for each formulation (Table 2) was used to construct the diagnostic, jack-knife plots (see Materials and Methods) shown in Fig. 2. In each case, the LSS-derived AUC_0- correlates closely (R² > 0.92) with the best estimated AUC_0-.

View this table: [in this window] [in a new window]   TABLE 2.   R2, bias, and precision of the best linear equations for n sample times derived by using the all-subset regression approach to estimate the AUC0- for each of the 24 subjects in study 1 (capsules) and study 2 (suspensions)

View larger version (20K): [in this window] [in a new window]   FIG. 2.   Scatter plot of the relationship between the best estimated AUC0- (microgram · hour · milliliter1; abscissa) and the corresponding AUC0- derived from the three-point LSS model for each volunteer (ordinate), using the jack-knife approach (described in Materials and Methods) for the four formulations tested: reference capsule (A), test capsule (B), reference suspension (C), test suspension (D). The continuous line in each plot is the identity line. R2 = correlation coefficient.

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View this table: [in this window] [in a new window]   TABLE 3.   R2, bias, and precision of the five best linear equations on three sample times derived by the all-subset regression approach to estimate the AUC0- for each of the 24 subjects in study 1 (capsules) and study 2 (suspensions)

View this table: [in this window] [in a new window]   TABLE 4.   R2, bias, and precision of LSS-derived AUC0-a

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View larger version (13K): [in this window] [in a new window]   FIG. 3.   Scatter plot of the best estimated AUC0- (microgram · hour · milliliter1) for amoxicillin in 11 previously published studies (1, 3, 7, 10, 13, 14, 17-20, 26), and the corresponding AUC0- derived from the three-point LSS model developed for the reference capsule formulation in the present study (Table 3, equation 1, adjusted for the dose). In the 11 studies examined, amoxicillin was given in single doses of 250 mg (+, ), 500 mg (open symbols), or 1 g (solid symbols); in some studies, more than one amoxicillin dose or formulation was tested. The best estimated and the LSS-derived AUC0-'s were obtained as described in Materials and Methods. The continuous line is the identity line. The symbols (and references of the data) are as follows:  (1), + (3),  (7),  (10),  (13),  (14),  and  (17),  (18),  (19),  (20),  (26).

Limited-sampling models for C_max C_max is a standard pharmacokinetic metric for estimating the rate of drug absorption in bioavailability and bioequivalence studies. It is, therefore, of practical interest to evaluate whether the same sampling times (1, 2, and 5 h) used in the most-informative LSS model for the AUC_0-which is the other major bioequivalence metricprovided adequate LSS strategies for the prediction of C_max. Our approach to this question consisted of using the amoxicillin concentrations in plasma from the training set to develop the most informative three-point LSS equation for predicting the corresponding individual C_max's. This equation is as follows: C_max = 0.38 + 0.47 × C₁ + 0.68 × C₂ + 0.35 × C₅; the LSS-derived C_max's correlate well (R² = 0.79; bias, <1.5; precision, <9.9) with the best-estimated C_max's. This equation was then applied to the concentrations observed at the same respective times, but after administration of the three other formulations (validation sets) in order to predict the individual C_max for the latter formulations (24, 25). The results revealed a correlation coefficient (R²) of 0.88 between the LSS-derived and the best-estimated C_max's (n = 72, bias = 3.39, precision = 11.52).

Bioequivalence analysis. The 90% CI's of the individual percent ratios (reference formulation/test formulation) of the ln-transformed C_max and AUC_0- of amoxicillin capsules or suspensions, calculated for the best-estimated or the LSS-derived metrics, were in close similarity and were within the accepted bioequivalence range of 80 to 125% (Table 5). The power of the analysis of variance was also comparable for the best-estimated and the LSS-generated data sets.

LSS for estimating T>MIC. The concentrations in plasma of the training set and an all-subsets regression approach were used to develop LSS models for estimating T>MIC for MICs of 0.25 or 2.0 µg/ml (Table 6). The most informative sampling times differed between these two MICs and for two-point LSS models, which provided accurate estimates of T>MIC (R², >0.90; precision, <4.5%), the best sampling pairs were 5 and 8 h or 1 and 3 h for MICs of 0.25 or 2.0 µg/ml, respectively. The corresponding regression equations were as follows: T>MIC (0.25 µg/ml) = 4.61 + 1.29 × C₅ + 6.83 × C₈; T>MIC (2.0 µg/ml) = 0.92 + 0.12 × C₁ + 0.46 × C₃. Figure 4 shows a correlation plot of the T>MIC that was calculated from all the available data points (best estimated T>MIC) or by using these two-point LSS models (LSS-derived T>MIC). As a validation approach of these models, the corresponding descriptive linear regression equations were applied to the concentrations observed at the same respective times, but after the administration of the three other formulations, in order to estimate the individual T>MIC in each case (see Materials and Methods). The results, shown in Table 7, indicate that the two-point LSS models developed for the reference capsule in study 1 accurately predicted T>MIC for the test capsule in the same group of volunteers (R² = 0.95; precision, 6.7%). The estimates of T>MIC for the suspension formulations were less precise, especially when the MIC breakpoint was set at 2.0 µg/ml (R², 0.86; precision, 9.9 to 14.1%).

View larger version (15K): [in this window] [in a new window]   FIG. 4.   Scatter plot of the relationship between the best estimated T>MIC (hours; abscissa) and the corresponding T>MIC (hours; ordinate) that was derived from the most informative two-point LSS models for each volunteer in the training set. , MIC = 2.0 µg/ml (sampling times, 1 and 3 h); , MIC = 0.25 µg/ml (sampling times, 5 and 8 h). The continuous line is the identity line.

	DISCUSSION

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In the present study, LSS strategies were developed for prediction of the AUC_0-, C_max, and T>MIC of the widely used antibiotic amoxicillin. A large number of plasma samples (n = 1,152) collected from 48 closely monitored, healthy volunteers in two bioequivalence studies allowed the development and subsequent validation of LSS models by using several different procedures. The results show that the AUC_0- of amoxicillin, following administration of single oral doses (500 mg) as capsules or suspensions, can be determined accurately using three plasma samples. Increasing the number of samples added little to the accuracy and precision of the estimates of the AUC_0- (Table 2). The statistical principle of parsimony advises in favor of models with fewer parameters; thus, we settled for three-sample regressions for independent estimation of amoxicillin's AUC_0-. Jack-knife validation tests of the most informative three-point LSS models developed for each formulation indicated that the observed and the predicted quantities correlated closely (R² > 0.92). The use of the reference capsule formulation data as a training set allowed accurate estimation of amoxicillin's AUC_0- after administration of either the test capsule formulation to the same subjects or both the reference and test amoxicillin suspensions to another group of subjects.

The robustness of the three-point LSS regression equation derived from the capsule formulation data set as a predictor of the plasma amoxicillin AUC_0- was confirmed when tested on data from 11 published studies (1, 3, 7, 10, 13, 14, 17-20, 26), encompassing a large range of amoxicillin single doses (250 to 1,000 mg) and AUC_0-'s (9 to 55 µg · h · ml¹). This result not only validates our proposed three-point LSS model but also extends its applicability to a variety of experimental conditions, both clinical and analytical, which prevailed in the 11 studies examined.

The most informative three sampling points (1, 2, and 5 h) for LSS estimation of amoxicillin's AUC_0- supported the development of LSS models which estimate adequately this drug's C_max following administration of each of the four formulations tested in the current investigation. The possibility of LSS estimation of both AUC_0- and C_max using the same sampling timesalbeit with different regression coefficients and intercepts in the corresponding regression equationsis valuable, especially for bioavailability and bioequivalence studies, which are based on the determination of these two pharmacokinetic metrics. Indeed, the present results revealed that the 90% CI for the individual ratio (reference/test formulations) of the LSS-derived and the best-estimated AUC_0- and C_max for amoxicillin capsule and suspension formulations were comparable (Table 5). Accordingly, the use of LSS-derived metrics leads to the correct conclusion that both test amoxicillin formulations (capsule or suspension) are bioequivalent to the respective reference formulations. This extends previous observations (11, 24, 25) of the validity of LSS methods for the assessment of bioequivalence between drug formulations, with the advantage of reducing the costs of sampling and analysis as well as the time required for completion of the trial.

Finally, this study supports the notion that LSS approaches are useful for investigating pharmacokinetic-pharmacodynamic relationships. Thus, we show that two-point LSS models allow accurate estimation of a dynamically linked variable, namely T>MIC for amoxicillin. This was demonstrated for MIC breakpoints at 0.25 and 2.0 µg/ml, representative of amoxicillin-susceptible and -resistant strains of microorganisms, such as S. aureus, S. pneumoniae or N. gonorrhoeae (16). It is significant that the LSS models developed for the reference capsule formulation were excellent predictors of the T>MIC for the test capsule formulation (R², 0.95) and provided good estimates (R², 0.86 to 90) of T>MIC of amoxicillin suspensions. The less accurate estimates of T>MIC for the latter might be related to differences in the amoxicillin concentration-time profiles for capsules versus suspensions due to faster rates of absorption from the latter formulations. Accordingly, small but significant differences in T_max between the reference capsule and both amoxicillin suspensions were observed, whereas t_1/2 was not affected by formulation, as anticipated from basic pharmacokinetic principles. Consequently, the amoxicillin concentrations in plasma crossed the MIC susceptibility breakpoints in both the absorption and elimination phases at later times when the capsules were used, compared to the suspensions. This will impact on the C_time values in the model equations for LSS estimation of T>MIC, explaining, at least in part, the relatively lower accuracy of the LSS models for suspensions, compared to that for the capsule formulations.