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## Brazilian Journal of Medical and Biological Research

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*Print version* ISSN 0100-879X*On-line version* ISSN 1414-431X

### Braz J Med Biol Res vol.34 no.11 Ribeirão Preto Nov. 2001

#### https://doi.org/10.1590/S0100-879X2001001100017

**Braz J Med Biol Res, November 2001, Volume 34(11) 1475-1485**

**Limited-sampling strategy models for estimating the pharmacokinetic parameters of 4-methylaminoantipyrine, an active metabolite of dipyrone**

G. Suarez-Kurtz^{1,2}, F.M. Ribeiro^{1}, R.C.E. Estrela^{1}, F.L. Vicente^{1,2} and C.J. Struchiner^{1}

^{1}Divisão de Farmacologia,^{ }Coordenação de Pesquisa, Instituto Nacional de Câncer, Rio de Janeiro, RJ, Brasil

^{2}Unidade de Farmacologia Clínica, Santa Casa da Misericórdia, Rio de Janeiro, RJ, Brasil

Abstract

Introduction

Material and Methods

Results

Discussion

References

Correspondence and Footnotes

Bioanalytical data from a bioequivalence study were used to develop limited-sampling strategy (LSS) models for estimating the area under the plasma concentration versus time curve (AUC) and the peak plasma concentration (C_{max}) of 4-methylaminoantipyrine (MAA), an active metabolite of dipyrone. Twelve healthy adult male volunteers received single 600 mg oral doses of dipyrone in two formulations at a 7-day interval in a randomized, crossover protocol. Plasma concentrations of MAA (N = 336), measured by HPLC, were used to develop LSS models. Linear regression analysis and a "jack-knife" validation procedure revealed that the AUC_{0-}_{¥} and the C_{max }of MAA_{ }can be accurately predicted (R^{2}>0.95, bias <1.5%, precision between 3.1 and 8.3%) by LSS models based on two sampling times. Validation tests indicate that the most informative 2-point LSS models developed for one formulation provide good estimates (R^{2}>0.85) of the AUC_{0-}_{¥} or C_{max} for the other formulation. LSS models based on three sampling points (1.5, 4 and 24 h), but using different coefficients for AUC_{0-}_{¥} and C_{max}, predicted the individual values of both parameters for the enrolled volunteers (R^{2}>0.88, bias = -0.65 and -0.37%, precision = 4.3 and 7.4%) as well as for plasma concentration data sets generated by simulation (R^{2}>0.88, bias = -1.9 and 8.5%, precision = 5.2 and 8.7%). Bioequivalence assessment of the dipyrone formulations based on the 90% confidence interval of log-transformed AUC_{0-}_{¥} and C_{max} provided similar results when either the best-estimated or the LSS-derived metrics were used.

**Key words:** dipyrone, 4-methylaminoantipyrine, limited-sampling models, pharmacokinetics, bioequivalence

Dipyrone (noramidopyrine methanesulfonate, metamizole) is an effective analgesic, antipyretic and anti-inflammatory drug that has been widely used since its introduction in 1922. Dipyrone is a typical prodrug, and its pharmacokinetics has been extensively investigated (1). After oral administration, dipyrone is non-enzymatically hydrolyzed in the gastrointestinal tract to 4-methylaminoantipyrine (MAA), which is rapidly and nearly completely absorbed, reaching peak levels within 1-2 h. MAA is further metabolized to 4-formylaminoantipyrine, and 4-aminoantipyrine, the latter being acetylated to 4-acetylaminoantipyrine (2-4). Dipyrone is present in more than one hundred pharmaceutical products marketed in Brazil, the vast majority of which was not subjected to bioavailability studies prior to registration. Recently, however, we performed a bioequivalence study of two different formulations of dipyrone in association with caffeine and isometheptene produced by the same manufacturer (5). Because the analgesic effect of dipyrone correlates with the time course of MAA concentrations in serum (6), pharmacokinetic parameters pertaining to this active metabolite are appropriate for assessing the bioequivalence of dipyrone formulations. In the present study, the plasma concentrations of MAA were used to develop limited-sampling strategy (LSS) models to estimate both the area under the plasma concentration versus time curve (AUC) and the peak plasma concentration (C_{max}) of MAA. Strategies using a limited number of samples and proven to be sufficiently robust to allow accurate estimation of individual pharmacokinetic parameters could be very valuable for bioequivalence studies, with reduced costs of sample acquisition and analysis, reduced study duration and avoidance of sampling at "unsociable" hours (7,8).

**Clinical protocol**

This open label, randomized study used a standard two-sequence, two-period crossover design in which the treatment phases were separated by a 7-day washout interval. The study protocol was approved by the Ethics Committee of Santa Casa da Misericórdia, Rio de Janeiro, and all participants provided written informed consent. Twelve healthy adult male volunteers aged 19 to 26 years (mean ± SD: 22.1 ± 2.3 years) and weighing 55-72 kg (64.1 ± 5.8 kg) completed the study. These volunteers were non-smokers 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 (blood cell count, biochemical profile and urinalysis). The enrolled volunteers had not used any investigational drug during the 6 months preceding the present study. Prescription drugs were not allowed during the study.

In each treatment phase, the volunteers arrived at the Clinical Pharmacology Unit at 7:00 pm. After an overnight (>10 h) fast, a catheter was introduced into a superficial vein, and a baseline (pre-dosing) blood sample was collected. Each volunteer then received 600 mg dipyrone, as two 300-mg tablets of one of the two formulations (A, B) under study, with 200 ml water. Six volunteers received the two formulations in one sequence, and the other six in the opposite sequence, in a balanced crossover design. Two hours after drug administration, the volunteers received a standard breakfast consisting of 200 ml homogenized milk, 200 ml orange juice, two slices of bread with ham and cheese, and one apple. Five, 8 and 12 h after drug administration, a standard lunch, snack and dinner were served. The volunteers remained at the Clinical Pharmacology Unit until collection of the 24-h blood sample and returned to the unit 48 h after drug administration.

Eight-milliliter blood samples were drawn into heparinized tubes 5-10 min before (zero time), and 0.33, 0.66, 1, 1.5, 2, 3, 4, 5, 6, 8, 10, 24 and 48 h after administration of dipyrone. The blood samples were centrifuged within 30 min after collection, and the plasma was separated and stored at -20ºC. The determination of the plasma concentrations of MAA was performed by HPLC using aminophylline (10 µg/ml) as internal standard. In this method, the internal standard was added to 1 ml plasma, and after vortex mixing for 10 s, 50 µl trichloroacetic acid (30%) was added. The sample was vortex mixed again and centrifuged at 11,000 *g* for 10 min. The supernatant (100 µl) was then applied directly to the HPLC reversed phase column ODS-23 (100 x 4.6 mm, Waters Spherisorb). The column was maintained at ambient temperature and eluted with a gradient of aqueous trifluoracetic acid (TFA) (0.15%, v/v) and 80% acetonitrile-TFA (0.05%, v/v) over a period of 15 min. The column was then allowed to re-equilibrate with TFA for 3 min before the next injection. This method has a quantification limit of 0.1 µg/ml for MAA. Standard curves were linear in the evaluated concentration range (0.1-30 µg/ml, R^{2} = 0.98) and the overall precision, as evaluated by the coefficients of variation obtained from independently prepared control plasma samples (0.5-5.0 µg/ml), ranged from 5.6% (intraday, N = 6) to 16.2% (interday, N = 8).

**Drugs**

Formulation A was commercially available as Neosaldina^{â} (batch 9811341, Knoll Produtos Químicos e Farmacêuticos Ltda., Rio de Janeiro, RJ, Brazil), while formulation B was a novel formulation under development by the same manufacturer (batch 9811368). Both formulations contained 300 mg dipyrone, 30 mg caffeine base and 50 mg isometheptene hydrochloride.

**Pharmacokinetic analysis**

The value of C_{max }and the time to reach it were determined from the individual plasma drug data. A non-compartmental model for extravascular input, provided by the Win-Nonlin Professional 3.1 software (9) was used for calculation of the pharmacokinetic parameters k_{el }(terminal elimination rate constant), t_{1/2} (terminal half-life), AUC_{0-48 }(area under the plasma drug concentration versus time curve between 0 to 48 h), and the extrapolated AUC_{0-}_{¥} (AUC from 0 to infinity). The AUC thus obtained are taken as the "best estimates" of parameter values (see below).

**LSS development**

All-subset linear regression analysis (10) of the AUC_{0-}_{¥} or C_{max }best estimates against C_{time} (independent variables) was carried out in order to develop LSS equations to estimate the AUC_{0-}_{¥} or C_{max }for MAA following administration of each dipyrone formulation. Computations were carried out using function leaps (11) in Splus 4.0 (12). This analysis produced equations of the form AUC_{0-}_{¥} or C_{max} = A_{0 }+ A_{1} x C_{1} + A_{2} x C_{2 }.... A_{n} x C_{n}, where A_{n} are coefficients and there is a variable number* n* of samples. Regression equations were then ranked according to the R^{2} criterion 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 the data sets of each volunteer. The bias of these LSS-derived estimates was assessed by calculating the mean percentage of difference (MD%) from the best estimates, where MD% = [(derived estimate - best estimate)/best estimate] x 100%, and precision was assessed by calculating the mean absolute percentage of difference (MAD%), where MAD% = [(derived estimate - best estimate/best estimate] x 100%.

The LSS models developed in the current study were validated by three procedures. The first is the jack-knife prediction (13), which is made when the regression equations to estimate AUC_{0-}_{¥} or C_{max} are derived using the *n* fixed concentrations of choice from 11 of the volunteers, and these equations are used to predict the AUC_{0-}_{¥} or the C_{max} of the 12th volunteer, respectively. Thus, for each subset of sample times, slightly different regression equations are used to predict the AUC_{0-}_{¥} or the C_{max} for each volunteer.

As a second validation approach (7), the 12 plasma concentration data sets for formulation B (training set) were used to estimate the regression coefficients in 2-point LSS models. These coefficients and the concentrations observed at the same respective times, but after administration of formulation A (validation set) were used to estimate the individual AUC_{0-}_{¥} or C_{max} for the latter formulation. The AUC_{0-}_{¥} and C_{max} thus obtained were then compared to the best estimates available for either parameter in each of the 12 volunteers.

As a third validation approach, we simulated new data as follows. Starting with the average plasma concentration data points obtained from a published study (14), in which 15 healthy male volunteers were given single oral doses (750 mg) of dipyrone, we used the ADAPT II software (14) to fit a two-compartment model, allowing for a lag time (model 2lagk) to the data. At the end of this step, we obtained a set of six descriptive parameters for the average plasma concentration versus time curve. Next, we used the SIM module of ADAPT II (option 4, population estimates with output noise) to generate 24 sets of plasma concentration data points at the same sampling times as used in the current study. The individual values of C_{max }and AUC_{0-}_{¥} for each simulated set were calculated as described above for the volunteer data sets and represent the best estimates for these metrics. These values were then compared with the corresponding LSS-derived metrics for the same simulated data sets.

**Bioequivalence analysis**

The 90% confidence intervals of the individual ratio (formulation A/formulation B) of the log-transformed values of the best-estimated AUC_{0-}_{¥} and C_{max} were used to assess the bioequivalence of the two dipyrone formulations administered to the volunteers (15). The same procedure was applied to the 3-point LSS-derived AUC_{0-}_{¥} and C_{max} to explore the usefulness of the LSS approach in bioequivalence studies.

**Statistical analysis**

The specific statistical tests applied to the data sets are indicated in the text. The level of significance was set at P<0.05.

Both dipyrone formulations were well tolerated by the enrolled volunteers, with no adverse effects being reported.

**Pharmacokinetic data**

The plasma MAA concentration-time curves for both dipyrone formulations are shown in Figure 1, and the pharmacokinetic parameters derived from these curves are summarized in Table 1. The data reveal large interindividual variability (coefficients of variation >30%) in several parameters, i.e., AUC_{0-48}, AUC_{0-}_{¥}, t_{1/2} and k_{el}, but no significant differences between the mean values of these parameters for each dipyrone formulation (Mann-Whitney rank sum test).

[View larger version of this image (34 K GIF file)]

**Limited-sampling models for AUC**_{0-}_{¥}

The plasma concentration data sets and an all-subset regression approach were used to identify the most informative sampling times, using 1 to 10 samples to estimate the AUC_{0-}_{¥} of MAA for each formulation tested. The results of this analysis (Table 2) indicate that the most informative strategies depend on the dipyrone formulation; in the case of two samples, the most accurate estimates of AUC_{0-}_{¥} were obtained from data points at 24 h and at 5 h (formulation A) or 4 h (formulation B). The corresponding equations are:

Formulation A:

AUC_{0-}_{¥} = 7.87 + 9.71*C_{5 }+ 50.15*C_{24}

Formulation B:

AUC_{0-}_{¥} = -3.47 + 10.48*C_{4} + 27.64*C_{24}

These equations provided accurate estimates (R^{2}>0.96, bias<1.5%, precision = 5.4 and 8.3%; Table 2) of the AUC_{0-}_{¥} for each formulation._{ }Increasing the number of sampling points to more than two increases R^{2} by <4% and adds little to the bias and the precision of the estimates of AUC_{0-}_{¥}, as compared to the respective values for 2-point sampling for each formulation (Table 2).

Diagnostic jack-knife plots (Methods) of the best-estimated AUC_{0-}_{¥} versus the LSS-derived AUC_{0-}_{¥} for either formulation (Figure 2A,B) show agreement (R^{2}>0.90, bias <3.5%, precision <11.9%) between observed and predicted quantities. Residual plots (data not shown) indicate no need to search for either additional variable transformations or non-linear relationships for either data set. Figure 2C shows another validation approach of the 2-point LSS models, in which the most informative LSS equation developed for formulation B and the concentrations observed at the same respective times, but after administration of formulation A, were used to estimate the individual AUC_{0-}_{¥} for the latter formulation (Methods). The AUC_{0-}_{¥}_{ }thus obtained showed good correlation (R^{2} = 0.85, P<0.001) with the best-estimated parameter values.

The most-informative 2-point LSS models (Table 2) include the 24-h data points, which occur at a late time in the elimination phase of the plasma concentration versus time curve (Figure 1), when the MAA concentrations are close to or below the quantification limit of the analytical method used. To circumvent this limitation, LSS equations derived for two sampling points, but excluding the 24-h sample, were evaluated for their ability to predict the AUC_{0-}_{¥} for either formulation. As shown in Table 3, sampling at 3 h and either 10 h (formulation A) or 8 h (formulation B) allows a good estimation of the AUC_{0-}_{¥}_{ }in each case (R^{2} = 0.93, bias <1.2%, precision = 7.3%).

[View larger version of this image (20 K GIF file)]

**Limited-sampling models for C**_{max}

All-subset regression analysis of the plasma concentration data sets (Table 4) revealed that the C_{max }for MAA following the administration of either dipyrone formulation can be accurately estimated (R^{2}>0.95, bias = 0.1%, precision <3.6%) by 2-point LSS equations using data collected at 2 h and either at 3 h (formulation A) or 1.5 h (formulation B). Increasing the number of sampling points to more than two increases R^{2} by 4%, adds little (<3%) to the precision and the bias of the estimates of C_{max} of MAA, as compared to the respective values for 2-point sampling for each formulation. The jack-knife approach indicated good agreement (R^{2}>0.92) between the best-estimated C_{max }and* *the 2-point LSS-derived C_{max} for either formulation (Figure 3A,B). Figure 3C shows that the most informative 2-point LSS equation developed for formulation B (training set; Methods) predicted well (R^{2 }= 0.90) the individual C_{max} values for formulation A.

[View larger version of this image (19 K GIF file)]

**Limited-sampling models for both AUC**_{0-}_{¥}_{ }**and C**_{max}

Because AUC_{0-}_{¥}_{ }and C_{max }are the standard pharmacokinetic metrics for assessing bioavailability and bioequivalence, it is of practical interest to develop LSS models based on the same sampling times for estimation of these metrics. For this purpose, the plasma MAA concentration data sets for both formulations were pooled and all-subset regression analyses were performed for AUC_{0-}_{¥}_{ }and C_{max}. These analyses revealed that a minimum of three sampling points are required for accurate prediction of both pharmacokinetic metrics, the most informative points being 1.5, 4 and 24 h (Table 5) for estimating both parameters. Diagnostic jack-knife plots of the best-estimated versus the LSS-derived AUC_{0-}_{¥} or C_{max} individual values (Figure 4A,B) showed good agreement (R^{2}>0.90, bias <0.8%, precision between 3.9 and 7.7%) between observed and predicted quantities.

Figure 4. |

[View larger version of this image (38 K GIF file)]

**Validation of the LSS models using simulated data**

The best-estimated AUC_{0-}_{¥} and C_{max }for the 24 simulated data sets (Methods) were 56.2 ± 19.5 (mean ± SD) and 8.45 ± 1.52, respectively. The corresponding values for the LSS-estimated metrics using the 3-point LSS equations shown in Table 5 were 54.8 ± 18.3 and 9.18 ± 0.86. The best-estimated and the LSS-derived metrics were closely correlated: R^{2} = 0.98 and 0.88, bias = -1.93% and 8.54%, precision = 8.65% and 5.16%, for AUC_{0-}_{¥} and C_{max}, respectively.

**Bioequivalence analysis**

The 90% confidence intervals of the individual percent ratios (formulation A/formulation B) of the log-transformed C_{max} and AUC_{0-}_{¥}_{ }of MAA, calculated for the best-estimated and for the LSS-derived metrics, were closely similar and within the accepted bioequivalence range of 80-125% (Table 6). The power of ANOVA was also comparable for the best-estimated and the LSS-generated data sets.

This paper describes for the first time the development of LSS for predicting both the plasma AUC_{0-}_{¥} and C_{max }of MAA, the main active metabolite of the prodrug dipyrone. These strategies were developed using data from a bioequivalence study in which a relatively large number of plasma samples (N = 336) were collected from closely monitored healthy volunteers. Our LSS analysis and validation procedures show that the AUC_{0-}_{¥} and C_{max }of MAA following oral administration of single 600 mg doses of dipyrone can be determined accurately using only two plasma samples. Choosing three or more samples adds little to the accuracy and precision of the estimates (Tables 2 and 4). The statistical principle of parsimony advises in favor of models with fewer parameters and therefore we settled for 2-sample regressions for independent estimation of MAA AUC_{0-}_{¥} or C_{max}. Validation tests, namely the jack-knife prediction and the use of training sets, provided strong support for the conclusion that both the AUC_{0-}_{¥} and the C_{max }of MAA following administration of single doses of dipyrone can be accurately estimated by the 2-point LSS models developed in this study. The fact that the interindividual variability in several pharmacokinetic parameters was relatively large heightens the methodological and practical value of the proposed LSS models.

Although the most informative 2-point regression equations for predicting the AUC_{0-}_{¥} require sampling at 24 h, when the MAA plasma concentrations are close to the quantification limit of the analytical method used, we showed that accurate estimates of AUC_{0-}_{¥} can also be obtained using 2-point LSS models, which exclude the 24-h sample. Other criteria that determine the practical value of LSS models include avoiding sampling at "unsocial" hours or long after drug administration (to reduce the duration of the study) and to use the same sampling times but different regression coefficients to obtain the pharmacokinetic metrics of interest. In the case of bioequivalence studies, these metrics are AUC_{0-}_{¥} and C_{max}, and the present study reveals that 3-point LSS models based on sampling at 1.5, 4 and 24 h provide the information required for accurate estimation of both of these metrics for MAA following the administration of dipyrone. The corresponding LSS equations were validated in the same group of volunteers using the jack-knife approach, and also in a simulated group of 24 "subjects" generated by a pharmacokinetic model applied to concentration-in-plasma data from a previously published study in which the reference dipyrone formulation (Novalgin^{â}) was used (6). The latter observation suggests to us that the applicability of the LSS models developed here is not limited to the formulations and population studied. Nevertheless, we are aware of the potential limitations of these LSS models when applied to other dipyrone formulations, which could change the absorption profile of the drug, and consequently the pharmacokinetic parameters being analyzed.

Finally, the AUC_{0-}_{¥} and C_{max} of MAA derived by the 3-point LSS models developed in the present study allowed precise assessment of the bioequivalence between the two dipyrone formulations tested. This observation adds support to previous proposals (7,8,16) that LSS models are valuable tools for bioequivalence trials, with the advantage of reducing the costs of sampling and analysis, as well as the time required for completion of the trial.

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**Address for correspondence:** G. Suarez-Kurtz, Instituto Nacional de Câncer, CPQ, Praça da Cruz Vermelha, 23, 20130-230 Rio de Janeiro, RJ, Brasil. Fax: +55-21-506-6376. E-mail: kurtz@inca.org.br

Research supported by CNPq, Fundação Ary Frauzino (FAF) and FAPERJ. G. Suarez-Kurtz and C.J. Struchiner are Senior Investigators of CNPq. R.C.E. Estrela and F.M. Ribeiro were recipients of fellowships from CNPq/PIMED. Received March 8, 2001. Accepted August 21, 2001.