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r3 antibody
European Journal of Pharmaceutical Sciences 21 (2004) 261–270
Integrated pharmacokinetic–pharmacodynamic modeling and allometric scaling for optimizing the dosage regimen of the monoclonal ior EGF/r3 antibody Jorge Duconge a,∗ , Rubén Castillo a , Tania Crombet b , Daniel Alvarez a , Janet Matheu a , Gloria Vecino a , Katia Alonso a , Irene Beausoleil b , Carmen Valenzuela c , Maria A. Becquer a , Eduardo Fernández-Sánchez a a
c
Department of Pharmacology and Toxicology, Institute of Pharmacy and Foods, University of Havana, 222 St. and 23rd. Avenue, La Coronela, La Lisa, Havana 36 CP 13600, Cuba b Center of Molecular Immunology, P.O. Box 16040, Havana 10600, Cuba Center for Genetic Engineering and Biotechnology, 31st Avenue and 190 street, P.O. Box 6162, Havana 10600, Cuba Received 8 October 2002; received in revised form 24 September 2003; accepted 21 October 2003
Abstract The multiple-dose strategy with the monoclonal ior EGF/r3 antibody, in xenograft bearing nude mice, was supported upon the basis of its integrated pharmacokinetic–pharmacodynamic relationship, according to both the temporal (Ke0 = 0.0015 ± 0.000035 h−1 ) and the ss ss time-independent sensitivity (C50% , 9.23 ± 0.17 g/ml; Cmax,eff , 12.5 g/ml) components of its tumor growth delay action. This relationship was consistent with a sigmoidal Emax pharmacodynamic model postulating a hypothetical effect compartment that permits us to estimate an effective steady-state concentration range (7.5–12 g/ml). Using this information we calculated both the cumulative and non-cumulative dosage regimens to compare their response patterns with respect to the control group. It follows that the differences in the estimated tumor growth inhibition ratio were statistically significant between the control group and either of the treated ones (P < 0.05). The median survival time in treated mice under non-cumulative regimen (72 ± 10 days), predicted an increase in this parameter as compared to the control one (55 ± 6 days). Finally, using the allometric paradigm, the empiric power equation for dose scaling across mammalian species allowed the calculation of the dosage schedule for further clinical trial. The estimated maintenance dose in human (70 kg) was 200 mg/m2 to be given weekly, and the corresponding loading dose was 600 mg/m2 . © 2003 Elsevier B.V. All rights reserved. Keywords: Monoclonal antibody ior EGF/r3; Tumor growth delay; Integrated pharmacokinetic–pharmacodynamic; Survival time; Allometric scaling; Dosage regimen
1. Introduction The murine monoclonal antibody (MAb) anti-epidermal growth factor (EGF) receptor ior EGF/r3 (IgG2a isotype) recognize two conformational sequence-sites of the EGF receptor extracellular domain, with high binding affinity (Kd = 10−9 M), depending on its blocking action upon ligand binding that partially reduces the autophosphorylation of the receptor, and therefore, inhibits the receptor (hetero-)dimerization in intact tumor cells, suggesting a cytostatic response (Fernández et al., 1989). ∗
Corresponding author. Tel.: +537-271-9538; fax: +537-33-6811. E-mail address: [email protected] (J. Duconge).
0928-0987/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.ejps.2003.10.015
On the basis of data obtained in earlier pharmacokinetic (PK) and pharmacodynamic (PD) studies for the MAb ior EGF/r3, the application of PK and PD principles and procedures to the rational development of this drug will be essential. Incorporation of PD studies along with PK one, coupled with appropriate and timely evaluation so as to influence subsequent drug development procedures, may lead to earlier identification of optimal dosage regimens and may contribute to shortening the overall time of drug development program. The increased understanding of drug action derived from PK–PD-based drug development leads to more information, especially with regard to the identification of drug dosage regimens that results in optimal therapeutic outcome. Moreover, appropriate preclinical evaluation may improve
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efficacy during phase I testing. The establishment of this information during pre-marketing drug development provides an essential framework for continued refinement and improvement during post-marketing drug use (Peck, 1995; Reigner et al., 1997). Interspecies scaling can be used to reveal the underlying similarities and/or differences in drug disposition among species and to predict the PK of a drug in any particular specie, which in most cases is man (Mordenti, 1986). The use of this approach has also been subject of analysis for dose scaling (Gabrielsson and Weiner, 1997). The purpose of this study was to experimentally explore the PK–PD strategy for optimizing the multiple-dose regimen of the MAb ior EGF/r3 using the cancer-bearing nude mice as animal model of human disease, and considering the allometric scaling paradigm.
2. Material and methods 2.1. Drug The murine MAb anti-EGF receptor ior EGF/r3, from the Center of Molecular Immunology, Institute of Oncology and Radiobiology (IOR, Havana, Cuba), has been produced conforming to the standard of quality for injectable formulations. Each bulb contains 50 (±0.2) mg of sterile MAb ior EGF/r3 powder in 10 ml of neutral phosphate-buffered saline (PBS) solution. 2.2. Animal husbandry Male NmRI/ nu–nu strain nude mice (8–10 weeks old, mean weight 25 ± 3 g) were housed as a group and also were bred and maintained under controlled conditions during the experiment. Access to food and water was provided ad libitum to all animals. All studies were approved by the Institutional Animal Care and Use Committee and were performed in accordance with the guidelines of the good laboratory procedures for animal use. 2.3. Tumor cell line The HER2/neu-overexpressing cell line, H125, from a non-small cell human lung carcinoma was used. This tumor line was expanded in RPMI 1690 media (SEROMED, Berlin, FRG) supplied with 10% FBS (GIBCO, BRL, UK), 100 g/ml penicillin and 100 g/ml streptomycin. The media was maintained at 37 ◦ C and 5% CO2 conditions. 2.4. Tumor-bearing nude mice Solitary tumors were produced in the right abdominal flank by subcutaneous inoculation of 2 × 106 viable tumor cells in 0.1 ml of medium. These transplantable tumors are non-immunogenics to these hosts and therefore
growth without rejection. They were submitted to the study when the xenografts had grown up to approximately 0.5 cm3 of average diameter (∅ave ), according to the following expression: ∅ave = (π/6) × ab2 , where a (length) is the largest and b (width) is the shortest tumor diameter (Fan et al., 1993). Each diameter was measured using a vernier caliper. About the use of xenograph mice models for pharmacokinetics and pharmacodynamics, the Points to Consider in the Manufacture and Testing of Monoclonal Antibody Products for Human Use (Food and Drug Administration, CBER, 1997, section B, Preclinical pharmacology and toxicity testing: general considerations) stated: “Pharmacokinetic and pharmacodynamic properties of MAb that are dependent upon specific antigen binding may not be evident in animal studies conducted in species which do not express the antigen of interest. In some cases, xenograft models can be developed by introducing cells expressing the antigen of interest into immunodeficient mice (e.g., SCID or nude mice). Such models can provide information on specific targeting of desired cells, and the results of such testing will influence safety considerations for initial clinical trials (e.g., starting dose, dose escalation scheme, etc.)”. 2.5. Dynamic experiment Ten animals were randomized into two experimental groups (five/group). The first group was dosed with 60 mg/kg (0.1 ml) MAb ior EGF/r3 as single i.v. injection, and the second one received the same volume of saline. For further effect data analysis, the tumor growth rate of both the saline-treated and the drug-treated group was followed-up measuring two mutually orthogonal tumor diameters, by triplicate in each animal, calculating the corresponding average diameter as above mentioned, and dividing the diameter enlargement by the elapsed time, at each experimental time. Notice that the calculated growth rate at each time point is determined with regard to the previous time point. Measurements were performed on day 0 predose and at 0.5, 1, 2, 2.5, 3–6, 10, 15, 17.5, 20, 22, 25 and 30 days after treatment. Finally, the mean difference between both groups at each experimental time represents the tumor growth delay (TGD) of the drug-treated group with respect to the control one. 2.6. Pharmacokinetic data The PK parameters (i.e., K10 = 0.040 h−1 ; CL = 0.19 ml/h; Vd = 4.75 ml; K12 = 0.027 h−1 ; K21 = 0.080 h−1 ; α = 0.12 h−1 ; β = 0.027 h−1 ) were taken from a previously reported study of the systemic ior EGF/r3 disposition in xenograft-bearing nude mice, where the tissue ior EGF/r3 concentration time-course was also conveniently estimated using compartmental analysis (Duconge et al., 2002).
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2.7. Pharmacodynamic data analysis The concentration—effect data were evaluated as individual using a nonlinear sigmoidal Emax pharmacodynamic model, according to the methodology early developed by Sheiner and co-workers for simultaneous modeling of pharmacokinetic and pharmacodynamic responses (Sheiner et al., 1979). E=
N Emax · Css ss N N C50% + Css
where, Css 50% is the steady-state concentration producing 50% of maximum effect (Emax ), and N is a sigmoidicity factor. Effect (E) was expressed as above mentioned, Section 2.5. Briefly, an additional hypothetical effect-site (biophase) compartment was postulated. It was linked to the central compartment of a two-compartment mammillary pharmacokinetic model by a first-order process, while drug dissipation from it is occurring by means of a second first-order rate constant (Ke0 ). This rate constant for drug removal from the effect-site compartment will precisely account for any temporal disequilibrium of the ior EGF/r3 concentration–effect relationship. Considering that the PD models are in essence independent of time, characterizing the equilibrium (time-invariant) relationship between drug concentrations and effects, our PD model was expressed in terms of steady-state ior EGF/r3 concentrations, rather than their corresponding amounts in the hypothetical effect-site compartment. It is because, at steady-state, there will be a steady-state ior EGF/r3 serum concentration and a unique corresponding amount of ior EGF/r3 in the effect-site compartment. So, we solve for each steady-state ior EGF/r3 serum concentration that give rise to (i.e., equivalent to) each pharmacokinetically estimated amount of ior EGF/r3 in the effect-site compartment, following the mathematical algorithm earlier described by Sheiner and co-workers, where full explanation can be found (Sheiner et al., 1979). The corresponding PK parameters (see Section 2.6) were then used to generate the ior EGF/r3 serum concentrations at the same time points of TGD effect measurements, using the equation describing the steady-state ior EGF/r3 concentrations equivalent to the hypothetical effect-site ior EGF/r3 amounts for a two-compartment open model with additional effect-site compartment, after an intravenous bolus input (Holford and Sheiner, 1981). The pharmacodynamic parameters were estimated by a suitable non-linear regression, following an iterative curve-fitting algorithm by Gauss–Newton (Levenberg–Hartley adjusted) minimization method, using WinNonlin professional software (WinNonlin, ver. 2.01, 1997, Pharsight Co., Virginia, USA). The steady-state ior EGF/r3 serum concentration assoss ciated with maximum efficiency (Cmax,eff ) is derived from
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the function denoting efficiency. By definition, efficiency means production of response in relation to stimulus (input). Following Kaojarern et al. (1982), and Alvan et al. (1990), an efficiency variable which denotes drug effect per stimulus [i.e., (E − E0 )/C] was obtained by dividing both sides of the Emax PD equation by the concentration variable, Efficiency =
N−1 Emax · Css ss N N C50% + Css
ss Whence, the Cmax,eff expression (see below) is derived by calculating its maximum. Indeed, the steady-state ior EGF/r3 concentration value for which maximum efficiency ss is reached (Cmax,eff ) is just that obtained when the first ss derivative of this equation equals zero. Notice that Cmax,eff is not calculable when N < 1. ss ss Cmax,eff = C50% · (N − 1)1/N
2.8. Multiple-dose regimens Animals were randomized into three groups (five animals/group): two treatment groups either by multiple cumulative (group 1) or non-cumulative (group 2) schedule, and the control saline-treated one (group 3). All animals in this study were kept under the same experimental conditions. Five animals (group 1) received multiple intravenous bolus injection of mAb ior EGF/r3, via ocular plexus, in order to achieve the desired average drug serum concentration ss = C ss (i.e., Cave max,eff ) and also to ensure that trough concentrations remain within the upper half of the linear range, which is previously established from sensitivity aspects of the PD response. Because the superposition principle is an overlay method, the drug disposition profile plateaus when repetitive equal doses are given at a constant frequency of administration (once a day), and thus the desired average ior EGF/r3 concentration is obtained. That is, using the corresponding multiple-dose equation for cumulative dosage regimen, by intravenous bolus input and assuming first-order ss · CL · τ; where τ means dosing elimination, Dose = Cave interval (Wagner, 1965; Rowland and Tozer, 1989). To this end, the previously estimated pharmacokinetic parameters in cancer-bearing nude mice (Duconge et al., 2002) were used (see Section 2.6). Whereas, another five animals (group 2) were first dosed intravenously by an initial loading dose (DL ) that was followed by the same multiple-dose regimen as group 1 (DM , maintenance dose), given daily. In order to estimate the corresponding loading dose (DL = DM × Rac ), the required accumulation index, Rac = 1/(1 − e−K10 ·τ ), was calculated following the standard method (Wagner, 1965; Rowland and Tozer, 1989). In both schemes the duration of treatment was up to day 21st (n = 21). For practical reasons, humans are dosed weekly and, of course, the necessary dosage adjustment for allometric scaling purposes was done, using standard procedures (Rowland and Tozer, 1989).
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2.9. Tumor size and survival analysis The tumor size in each group under study was measured as previously reported for average diameter before, during and post-dose administration at the following times: 0, 6, 14, 21, 28, 35, and 42 days. These values are used to estimate the drug-induced tumor growth inhibition effect in the multiple-dose study. The tumor growth inhibition (TGI) ratio, expressed as percentage, was estimated as follows: SCav − SDav TGI ratio = × 100% SCav Where, SDav and SCav represent the slopes of the best-fitted second-degree polynomial functions (SPSS for Windows, ver. 6.0, 1993), corresponding to mean data from the drug-treated and the control group, respectively. We followed an earlier method of analysis of growth curves, where a full explanation can be found (Grizzle and Allen, 1969). Briefly, the method utilizes the technique of analysis of covariance, but adding the concept of confidence intervals for improvement of polynomial curve fitting to growth data, which yields results identical to those obtained by weighting inversely by the sample covariance matrix, but has the additional feature of allowing flexibility in weighting by choosing subsets of covariates. This approach leads to methods of estimating parameters and performing tests that can be easily implemented by standard multivariate linear model programs (Grizzle and Allen, 1969). We also followed the survival time in each group during and post-treatment, expressing the corresponding average survival time (±S.D.), in each experimental group, and estimating the survivorship directly from the continuous survival or failure times. 2.10. Dose scaling By means of the information on clearance and dose in mouse, and according to the allometric power equation that characterizes the MAb ior EGF/r3 clearance across mammalian species, the empirical relation for dose scaling (Boxenbaum and DiLea, 1995) was used in order to scale the maintenance dose (DoseM ) to man: Wman 0.85 Doseman = Dosemouse , Wmouse Where, W means the body weight and 0.85 is the allometric exponent for ior EGF/r3 clearance across mammalian species (unpublished data from the authors), and dose in mouse corresponds to the adjusted dose to be given weekly from the maintenance dose used in the above mentioned multiple-dose study. Similarly, because the loading dose (DoseL ) rather depends on volume of distribution, it was scaled using the corresponding empirical power equation for volume of
distribution of ior EGF/r3 among mammals, where the allometric exponent is unity. Wman DoseL,man = DoseL,mouse Wmouse 2.11. Statistical analysis The statistical analysis was conducted to determine significant differences among groups under study, with respect to their tumor growth rate. In this regard, the respective tumor growth curves were analyzed using a multiple likelihood ratio test (Bonferroni adjusted t-test, P < 0.05) according to the Grizzle and Allen method (Grizzle and Allen, 1969). Essentially, the methods for analyzing survival time handle censored data. Regarding that, the survival analysis was accomplished by the Kaplan–Meier’s product limit method using STATISTIC procedures (Statistic for Windows, Statsoft Inc., 1993). In order to compare more than two samples the multiple sample test implemented in survival analysis is an extension of the log-rank test. Chi-square value was computed based on the sums of the firstly assigned score to each survival time, in each group under study, using Mantel’s procedure (Mantel, 1966).
3. Results Fig. 1 (panel A), shows the measured tumor growth delay effect in tumor-bearing nude mice, treated intravenously with 60 mg/kg murine MAb ior EGF/r3. Considering that we are trying to elucidate the possible PK–PD relationship for this MAb, in order to use this information for dosing design, Fig. 1 (panels A and B) depicts comparatively the measured effect data and the earlier estimated peripheral ior EGF/r3 concentrations (Duconge et al., 2002). As can be seen, the estimated peripheral ior EGF/r3 concentrations increased immediately, but the measured effect lags behind almost 24 h and peaks approximately 4 days later, when tissue drug concentrations declined. Visually, this lag time between peripheral drug concentrations and tumor growth delay effect is clearly shown in panel B (inset rectangle) by the large degree of counterclockwise hysteresis in the concentrations-effect curve. Actually, the concentration versus effect plots using either experimentally determined ior EGF/r3 serum concentrations (result not shown) or its pharmacokinetically estimated peripheral levels (panel B) were useful for the recognition of equilibration delays, which permited us to postulate a separate effect-site compartment (i.e., biophase). The effect data were fitted to the PD model with input information being the measured tumor growth delay effect at each experimental time, and the previously estimated pharmacokinetic parameters (Duconge et al., 2002). The steady-state ior EGF/r3 concentrations-effect curve drawn in Fig. 1, panel C, represents the predicted sigmoid shape of
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Fig. 1. (A) Tumor growth delay effect (mean ± S.D., n = 5), and (B) theoretical tissue ior EGF/r3 concentrations over time, single dose, using a two-compartment pharmacokinetic model (PK parameters taken from Duconge et al., 2002). Observe the counterclockwise hysteresis loop for the tissue concentration–effect relationship (inset rectangle). (C) Equivalent steady state ior EGF/r3 concentration–effect relationship curve by sigmoid Emax . PD model, and (D) efficiency of response for the mean effect data, after single 60 mg/kg of MAb ior EGF/r3 intravenously. The linear range (20–80% Emax ) is ss delineated by vertical lines. The steady-state drug concentration for both 50% maximal effect (Css 50% ) and maximal efficiency (Cmax,eff ) are shown (arrows).
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Table 1 Summary of the ior EGF/r3 pharmacodynamic parameters, in tumor bearing nude mice after single intravenous dose (60 mg/kg) Parameters (mm3 /h)
Emax ss C50% (g/ml) N (shape factor) Ke0 (h−1 ) ss Cmax,eff (g/ml)
Values (± S.E.) 0.49 9.23 5.42 0.0015 12.5
± ± ± ±
0.012 0.17 0.36 0.000035
Values are expressed as mean ± S.E. Parameters estimates were determined for the mean effect data (n = 5) using the sigmoid Emax . PD model.
the pharmacodynamic relationship for the best fit of these data to our model and Table 1 shows the corresponding pharmacodynamic parameters. Using the so-called linking approach an integrated model of PK–PD drug responses was proposed, which allowed characterization of the temporal aspects of its pharmacodynamic (Ke0 and t1/2ke0 ) as well as the time-independent ss ss sensitivity component (C50% and Cmax,eff ), as can be seen in Table 1. Interestingly, the first-order rate constant for equilibration of ior EGF/r3 effect (i.e., tumor growth delay) and its effect-site concentration was 0.0015 ± 0.000035 h−1 , which demonstrates that effect is not directly proportional to the amount of drug either in the central or in the peripheral compartment (K21 Ke0 ) of the PK model. The mean steady-state ior EGF/r3 concentration required to produce 50% growth delay is 9.23 ± 0.17 g/ml, a measure of the sensitivity to the drug. As can be seen from Fig. 1, panel D, the course of efficiency is shifted rightward from effect. The steady-state ior EGF/r3 serum concentration associated with maximal ss efficiency, Cmax,eff , 12.5 g/ml, was then proposed as the ss ) for dose calculation. optimal level (i.e., Cave
In utilizing this approach, the first group (group 1) was dosed intravenously by a cumulative regimen with 2.3 mg/kg murine MAb ior EGF/r3, once a day. Whereas, the second group (group 2) was treated using a non-cumulative regimen, with a 4 mg/kg loading dose at the first day, followed by 2.3 mg/kg daily maintenance dosage. The estimated index of the extent of accumulation (Rac = 1.62, τ = 24 h) revealed a cumulative pattern that suggests just a two-fold higher dose as first input to reach immediately the required steady-state values. Fig. 2 displays the tumor growth rate in each group under study, after a multiple-dose strategy. In the light of this result we are able to appreciate that the control group showed a faster tumor growth rate than either of the drug-treated groups. It concerns with the fact that both treatments showed a significant tumor size reduction with respect to control. The tumor growth rate, in the treated group with cumulative scheme, displayed a plateau during about 20 days (30 days for the non-cumulative scheme), and then suddenly showed a slow recovery. As can be seen in Table 2, the statistical analysis shows significant differences between groups under study, each other. These differences were remarked by the estimated tumor growth inhibition ratio (TGI) parameter, which showed a percentage of about 50% for the cumulative schedule, whereas the non-cumulative group exhibited a higher percentage (i.e., 85%), as compared to control one. On the other hand, Fig. 3 depicts the survivorship analysis using the survival percentage after treatment in each group studied. The mean survival time was estimated according to the Kaplan–Meier product limit method. This method estimates the survivorship, and the resulting estimates don’t depend on the grouping of the data into a certain number of time intervals as it’s using the life table method. Interestingly, current survival projection in treated mice, under
Fig. 2. Mean tumor size over time from a multiple-dose study of the MAb ior EGF/r3-treated and non-treated (control) tumor-bearing nude mice. Five animals were dosed in each drug-treated group. Up to day 36, n = 5 for the control group. On other days, n is less, since mice dropped out due to death. Dosing (arrows) protocol was established as a 21-days exposure to 2.3 mg/kg intravenous ior EGF/r3 once daily, using both cumulative and non-cumulative (DL = 4 mg/kg) dosage regimens. The horizontal bar shows the steady state condition for cumulative scheme. Dotted line represents the consecutive dosing up to day 21. Symbols are the experimentally measured mean values and curves represent the simulated values based on the best-fitted quadratic functions.
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Table 2 Statistical analysis of tumor growth curves corresponding to each group under study, after a multiple-dose scheme Parametersa
Cumulative (group 1)
Non-cumulative (group 2)
Control (group 3)
Observed differences 1 vs. 2
1 vs. 3
2 vs. 3
Intercept (cm3 ) Slope (cm3 /days) Acceleration (cm3 /days2 )
0.0376 0.0364 0.0043
0.0248 0.0092 0.0012
0.1433 0.0618 0.0098
0.0128 0.0272b 0.0031
0.1057b 0.0254b 0.0055
0.1185b 0.0526b 0.0086
A multiple likelihood ratio test (Bonferroni adjusted t-test, P < 0.05) was used conforming to Grizzle and Allen method. a Parameters were estimated using an unweighted least square method from the best-fitted quadratic function for experimental data in each tumor growth curve (Wilks-test probability: 0.76, Roy’s probability: 0.91). b Means statistically significant differences between groups.
Fig. 3. Survival percentage for each group under study from a multiple-dose schedule. Solid line corresponds to the control (non-treated) group. Dotted and dashed lines represent the drug-treated groups by cumulative and non-cumulative regimens, respectively. Observe the survival time differences between control and non-cumulative regimen at the end.
non-cumulative dosage regimen (median survival time: 72 ± 10 days), predicts an increment of about 17 days in the surviving proportion as compared to the control (median survival time: 55 ± 6 days). Whereas, the treated group using cumulative dosage regimen (median survival time: 66 ± 11 days) showed a slight but significant increment (P = 0.049) in survival with respect to the control. Indeed, according to the multiple-sample log rank test for analyzing survival time data, the statistical difference between the non-cumulative group and the control one was remarkably the highest (P = 0.007), but there is not any significant difference between both groups of treatment (P = 0.083). After that, the allometric power equation for dose scaling across mammalian species allowed the calculation of the dosage schedule for further clinical trial. The estimated maintenance dose in human (70 kg) was 200 mg/m2 to be given weekly, and the corresponding loading dose was 600 mg/m2 .
4. Discussion Because we need to use concentrations in our PD characterization which reflect the drug action at the effect site, and our pharmacokinetic model alone may not be able to predict
such values directly, even when peripheral drug level were considered, we developed a more complicated linked modeling approach, which is conceptually similar to the methodology previously reported by Sheiner et al. (1979). As was earlier suggested by Sheiner et al. (1979), it is more meaningful to relate the tumor growth delay effect to the serum concentrations of the MAb ior EGF/r3, rather than to an amount of drug in the hypothetical effect-site compartment. The effect equation obtained deals directly in (equivalent) steady-state ior EGF/r3 serum concentrations for sensitivity, and this aspect of its pharmacodynamic is isolated from the kinetic aspects, quantified by the Ke0 parameter. The optimal biological dose (OBD) has been postulated by regulatory agencies as the most clinically relevant dose for survey the rational drug developmental programs of novel biological entities (FDA, Point to consider in the manufacturing and testing of MAb products for human use: Preclinical Studies, 1999). Regarding to achieve a relevant selection criterion about the most reliable therapeutic range, we must pay great attention upon the clinical support of the tumor growth delay as pharmacodynamic marker, according to the oncotherapeutic endpoints of the murine MAb ior EGF/r3 treatment. In this sense, the steady-state ior EGF/r3 concentration range, from 7.5 to 12 g/ml (see Fig. 1, panel C), which is the linear range (i.e., within 20–80% Emax ) of this sigmoid-shape nonlinear PD curve, between threshold and plateau values, could be assumed as the probabilistic interval that results in proportional percentages of contribution to the desired response per increment of drug amount. The sensitive parameter Css 50% is midpoint of this interval, which produces 50% of the maximal TGD response. This PD value is a measure of the subject’s sensitivity to the MAb ior EGF/r3. At this point, the expression for maximum efficiency gives the concentration value at which the highest yield of effect per stimulus is obtained. It is also a “money-saving” approach that permits us a more rational use of this drug. Considering that, instead of using an arbitrary level within the linear range or even the value for maximum effect, we decided to draw the dosage scheme by using the estimated ss Cmax,eff value (i.e., 12.5 g/ml). As far as we know, the concentration of a drug at the site of action, whether directly
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corresponding to the serum concentration or to a kinetically associated compartment such as a deep target organ is heavily dependent on drug input. Therefore, the input variable should be controlled in order to attain optimal drug effect. In this context, we need to adjust the dosing rate (i.e., dose/τ) of the multiple-dose regimen in order to achieve the ss desired average ior EGF/r3 serum concentration, Cmax,eff = 12.5 g/ml and also to ensure that trough concentrations remain within the upper half of the linear range, as established from sensitivity aspects of the PD response. In fact, we thought that this extreme value allows estimation of the dose size more closely associated with the optimal biological dose (OBD), early suggested by FDA (point to consider, 1999). During the drug administration the clinician must appreciate to what degree drug concentration in the biophase lags behind that in the blood. Thus, drug dosing must be designed to reach the maximum efficiency concentration in the biophase when it is clinically important to achieve the maximally efficient tumor growth delay effect. Accordingly, a cumulative dosage schedule was designed as first choice because we were encouraged to assess whether this cumulative pattern is required for the antitumoral response. That is, if therapeutic success would be dependent more on cumulative response than moment-to-moment activity, then the use of extended dosing intervals might markedly reduce the effectiveness of the same average dose. Therefore, it is a kind of information that we need in order to suggest an appropriate dosing interval for clinical testing. On the other hand, in order to reduce the onset time—that is, the time drug takes to achieve its minimum effective serum concentration—a loading (priming) dose was given. The main objective is to achieve the desirable average ior EGF/r3 serum concentration for maximum efficiency as quickly as possible, which is generally most useful for clinical outcome. We decided to put both schedules into practice in order to compare each other and therefore make the best choice for dose scaling. In our case, the dosing interval (τ, once a day) was chosen for practical reasons. The usual “rule of thumb” of dosing every half-life is a conservative strategy for limiting wide fluctuations in drug effect, but demands more in terms of dosing frequency than may be necessary to achieve consistent drug action. The dosage interval should be spaced conveniently for better dosing and sampling, and also in order to reduce animal stress. Concerning both treated-groups, a possible explanation for the terminal behavior observed in Fig. 2 is related to the heterogeneous and asynchronous distribution of macromolecules in tumors (Jain and Baxter, 1988; Jain, 1990). Alternatively, this tendency may also be due to cell-cycle specificity or depending upon the proposed time and dose-dependent mechanisms of auto- and paracrine release of EGF-like peptides, which are induced through up-regulation of their encoding genes after EGF-receptor signaling reduction by monoclonal anti-EGF receptor antibodies (Mendelsohn, 1987). These results stressed the
idea about a cyclic dosing strategy for optimal clinical outcome, in order to avoid the long-term saturation of the cell surface EGF-receptors, which probably is associated with the above-mentioned time-dependent mitogenic upstream programs. Strikingly, the equilibration time parameter (t1/2ke0 = ln (2)/Ke0 = 19.3 days) is telling us that the ior EGF/r3 dissipation kinetic out of its effect-site compartment is near to the end of the treatment (21 days) and also to the major difference in survival. Perhaps, the most obvious and simple explanation could be the end of the treatment after 21 days. Although, care must be taken in speculating which one is the most correct explanation to this terminal behaviour (see Fig. 2), considering the tremendous heterogeneity of tumor xenografts and their complex response over time. In this context, the significant difference between the non-cumulative and the cumulative group after the dosing has stopped is probably a consequence of the initial loading dose of 4 mg/kg, which had a tremendous effect compared to the initial dose of 2.3 mg/kg (cumulative scheme). In our opinion, it is due at least in part to the fact that a relatively higher tumor drug availability at the begining of the treatment should be expected. It is well-established that smaller tumors, like those at the begining of the treatment, are highly vascularized and have reduced necrosis areas when comparing to larger tumors. Hence, we should dose the largest amount of drug at this time point because tumors become more necrotic over time and therefore drug availability will be lower. The cumulative schedule only achieved the effective concentration after three days and at this point the tumor biology is remarkable different and drug availability is reduced. On the other hand, there is a difference between both groups with regard to the time elapsed upon binding of ior EGF/r3 at effective concentration. Perhaps, the EGF receptor has an internal clock that times how long it is occupied and such a kinetic-reading will shift the cell signal toward an specific fate (e.g., cell death or cell-cycle arrest). Of course, further studies must be accomplished to support such a hypothesis or elucidate more appropriated explanations. Indeed, tumor response is extremely difficult to understand. The fact of the matter is that the higher percentage (i.e., 85%) of tumor growth inhibition (TGI) was observed in the non-cumulative group. It means that the tumor growth in the group treated by non-cumulative scheme lag behind the control one, representing only a 15% of the tumor growth rate in the control group. The results corroborated our hypothesis about the key role played by this MAb ior EGF/r3 as modulator of some biosignal controlling tumor growth pathway. Thereby, we were encouraged to scale this dose because it was considered quite appropriate to satisfy the requirements for optimal antitumoral effect, in spite of incomplete inhibition. The survival time for mouse might become into human time using the equivalent biological time. Biological time is defined as a species-dependent unit of chronological time
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required for the completion of a species-independent physiological event and this relates also to pharmacokinetic. Comparing maximum lifespan potential (MLP) in man (i.e., 98 years old) to MLP in mouse (i.e., 2.7 years old) was a factor of 40 (Gabrielsson and Weiner, 1997). Taking only MLP into account a concentration of unity in the mouse during 1 h corresponds to a 40 h period in man at the same concentration level, therefore the survival time will be 40 times greater in man (Boxenbaum, 1982; Gabrielsson and Weiner, 1997). The results brought forth a median survival time increment representing about two years in human, according to the equivalent biological time across mammalian species from mouse to man. However, we must bear in mind that this is a speculation based on the concept of MLP and therefore it should be accepted with some reserves. The body weight rule offers the investigator a very powerful tool with which to obtain general guidelines for making reasonable interspecies predictions of the optimal therapeutic scheme. Using the allometric equation for dose scaling (see Section 2.10) we have a scaling factor of 851.3, which was multiplied by the maintenance dose in mouse (0.025 kg), but just that to be administered weekly (i.e., 16 mg/kg weekly). Accordingly, the maintenance dose in human (70 kg) will be 340.5 mg/week = 190 mg/m2 weekly ≈200 mg/m2 to be administered weekly. Concerning the loading dose, it was scaled assuming to be proportional to body weight as aforementioned in Section 2.10, where the body weight ratio is the corresponding scaling factor. However, we also took the dosing interval into consideration because the next dose will be administered after a week instead of daily. Notice that a larger dose is necessary if the drug is given at longer intervals. So, any change in dosing interval must be corrected by a proportional change in dose size. Under such an interpretation, we were encouraged to scale an adjusted loading dose in mouse (0.025 kg) of 16 mg/kg (i.e., DoseL = DoseM [1/(1 − e−K10 τ )] = 16 mg/kg weekly × 1.001 = 16 mg/kg), rather than 4 mg/kg (i.e., 2.3 mg/kg daily × 1.62 = 4 mg/kg). The last one is valid only for continuing dosing once a day, which is not the case. Therefore, using a dose scaling factor of (70 kg/0.025 kg)1 = 2800, the correct loading dose in man (70 kg) will be 0.4 mg × 2800 = 1120 mg = 622.2 mg/m2 ≈ 600 mg/m2 . Interestingly, we do believe that taking the murine MAb ior EGF/r3 studies into account a reasonable dose scale-up for the humanized variant is possible, even though this should be done with great caution. As a matter of facts, we really ought to use the murine entity in tumor-bearing mice models in order to override recurrent species-specific clearance mechanisms such as human anti-mouse immunological response and thus obtain a reliable prediction of the recombinant humanized MAb (rhuMAb) behavior in cancer patients. It’s true because murine MAbs administered in mouse resemble more efficiently the pharmacokinetic of humanized MAbs used in human, at a similar pace, measured by their own internal biological clock, than if we had
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used rhuMAbs themselves in mouse. This sort of anti-sense prediction is based upon one of the underlying assumptions of the allometric scaling approach, which is related with the absence of species-specific clearance mechanisms in the disposition, under the precept that a representative animal species is used and scaled appropriately, with respect to elimination and sensitivity of drug. Pioneers like Boxenbaum and co-workers have provided excellent overviews to this field (Boxenbaum, 1986). Finally, as Levy (1993) has argued, “It is unfortunate that comparative information on the effective concentrations of new drugs in various species of animals and (eventually) humans is either not obtained or not fully utilized. Knowledge of effective drug concentrations in animal models can greatly facilitate dose ranging in phase I clinical studies”. In this regard, a dose scaling strategy using PK–PD data from preclinical study in a xenograft mice model was developed for the murine MAb ior EGF/r3. The results allowed us to recommend a dosage scheme (DL = 600 mg/m2 ; DM = 200 mg/m2 to be given weekly) for clinical testing based on estimation of the effective ior EGF/r3 concentration through the PK–PD approach.
Acknowledgements This investigation was supported by Center of Molecular Immunology and funded by grant 2002/A02–23 from Alma-Mater project of the University of Havana. The authors would like to thank the technical assistance of MsC. Hussam Ajamieh, MsC. Ilys Rodriguez, Mr. Armando López, and Mr. Dariel Morales, for their excellent contributions to this survey. References Alvan, G., Helleday, L., Lindholm, A., Sanz, E., Villen, T., 1990. Diuretic effect and diuretic efficiency after intravenous dosage of furosemide. Br. J. Clin. Pharmacol. 29, 215–219. Boxenbaum, H., 1982. Interspecies scaling, allometry, physiological time and the ground plan for pharmacokinetics. J. Pharmacokin. Biopharm. 10, 201–207. Boxenbaum, H., 1986. Time concepts in physics, biology and pharmacokinetics. J. Pharm. Sci. 75 (11), 1053–1062. Boxenbaum, H., DiLea, C., 1995. First time in human dose selection: allometric thoughts and perspectives. J. Clin. Pharmacol. 35, 957–965. Duconge, J., Fernández-Sánchez, E., Macias, A., Castillo, R., Garcia, I., Beausoleil, I., Amador, J.F., Matheu, J., 2002. Monoclonal anti-egf receptor antibody (ior-R3) pharmacokinetic study in tumor bearing nude mice: role of the receptor-mediated endocytosis on drug clearance. Eur. J. Drug Metab. Pharmacokinet. 27 (2), 101–105. Fan, Z., Baselga, J., Masui, H., Mendelsohn, J., 1993. Antitumor effect of anti-EGF receptor monoclonal antibodies plus cis-diamminedichloroplatinum on web established A431 cell xenografts. Cancer Res. 53, 4637–4642. Fernández, A., Pérez, R., Mac´ıas, A., Velanda, A., Alvarez, I., Ramos, M., Velozo, A., 1989. Generación y caracterización primaria de anticuerpos monoclonales contra el receptor del factor de crecimiento epidérmico. Interferón y Biotecnolog´ıa 6 (3), 289–298.
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Gabrielsson, J., Weiner, D., 1997. Pharmacokinetic and Pharmacodynamic Data Analysis: Concepts and Applications. Swedish Pharmaceutical Press, Stockholm. Grizzle, J.E., Allen, D.M., 1969. Analysis of growth and dose response curves. Biometrics 25, 357–381. Holford, N.H.G., Sheiner, L.B., 1981. Understanding the dose–effect relationship: clinical application of pharmacokinetic–pharmacodynamic models. Clinical Pharmacokin 6, 429–453. Jain, R.K., Baxter, L.T., 1988. Mechanism of heterogeneous distribution of MAb and other macromolecules in tumors: Significance of elevated interstitial pressure. Cancer Res. 48, 7022–7032. Jain, R.K., 1990. Physiological barriers to delivery of MAb and other macromolecules in tumors. Cancer Res. 50, 814–819. Kaojarern, S., Day, B., Brater, D.C., 1982. The time course of delivery of furosemide into urine: an independent determinant of overall response. Kidney Int. 22, 69–74. Levy, G., 1993. The case for preclinical Pharmacodynamic. In: Yacobi, A., Skelly, J.P., Shah, V.P., Benet, L.Z. (Eds.), Integration of Pharmacokinetic, Pharmacodynamic and Toxicokinetics in Rational Drug Development. Plenum Press, New York, pp. 7–13. Mantel, N., 1966. Evaluation of survival data and two new rank order statistics arising in its considerations. Cancer Chemother. Rep. 50, 163–170.
Mendelsohn, J., 1987. Anti-EGF receptor MAb may inhibit A431 tumor cell proliferation by blocking on autocrine pathway. Trans. Assoc. Am Physicians 100, 173–178. Mordenti, J., 1986. Man versus beast: pharmacokinetic scaling in mammals. J. Pharm. Sci. 75 (11), 1028–1040. Peck, C.C., 1995. Rationale for the effective use of pharmacokinetic and pharmacodynamic in early drug development. In: Yacobi, A., Skelly, J.P., Shah, V.P. (Eds.), Integration of Pharmacokinetic, Pharmacodynamic and Toxicokinetics in Rational Drug Development. Plenum Press, New York, pp. 1–5. Reigner, B.G., Williams, P.E.O., Patel, I.H., Steimer, J.L., Peck, C.C., Van Brummelen, P., 1997. An evaluation of the integration of pharmacokinetic and pharmacodynamic principles in clinical drug development: Experience within Hoffmann La Roche. Clin. Pharmacokinet 33 (2), 142–151. Rowland, M., Tozer, T.N., 1989. Multiple-dose regimens. In: Clinical Pharmacokinetics: Concepts and Applications, 2nd edition. Lea and Febiger, Philadelphia, pp. 78–100. Sheiner, L.B., Staski, R., Vozeh, A., Miller, R.D., Ham, J., 1979. Simultaneous modeling of pharmacokinetic and pharmacodynamic: Application to d-tubocurarine. Clin. Pharmacokinet 1, 358–371. Wagner, J.G., 1965. Blood levels of the equilibrium state after multiple dosing. Nature 107, 1391–1402.
Integrated pharmacokinetic–pharmacodynamic modeling and allometric scaling for optimizing the dosage regimen of the monoclonal ior EGF/r3 antibody Jorge Duconge a,∗ , Rubén Castillo a , Tania Crombet b , Daniel Alvarez a , Janet Matheu a , Gloria Vecino a , Katia Alonso a , Irene Beausoleil b , Carmen Valenzuela c , Maria A. Becquer a , Eduardo Fernández-Sánchez a a
c
Department of Pharmacology and Toxicology, Institute of Pharmacy and Foods, University of Havana, 222 St. and 23rd. Avenue, La Coronela, La Lisa, Havana 36 CP 13600, Cuba b Center of Molecular Immunology, P.O. Box 16040, Havana 10600, Cuba Center for Genetic Engineering and Biotechnology, 31st Avenue and 190 street, P.O. Box 6162, Havana 10600, Cuba Received 8 October 2002; received in revised form 24 September 2003; accepted 21 October 2003
Abstract The multiple-dose strategy with the monoclonal ior EGF/r3 antibody, in xenograft bearing nude mice, was supported upon the basis of its integrated pharmacokinetic–pharmacodynamic relationship, according to both the temporal (Ke0 = 0.0015 ± 0.000035 h−1 ) and the ss ss time-independent sensitivity (C50% , 9.23 ± 0.17 g/ml; Cmax,eff , 12.5 g/ml) components of its tumor growth delay action. This relationship was consistent with a sigmoidal Emax pharmacodynamic model postulating a hypothetical effect compartment that permits us to estimate an effective steady-state concentration range (7.5–12 g/ml). Using this information we calculated both the cumulative and non-cumulative dosage regimens to compare their response patterns with respect to the control group. It follows that the differences in the estimated tumor growth inhibition ratio were statistically significant between the control group and either of the treated ones (P < 0.05). The median survival time in treated mice under non-cumulative regimen (72 ± 10 days), predicted an increase in this parameter as compared to the control one (55 ± 6 days). Finally, using the allometric paradigm, the empiric power equation for dose scaling across mammalian species allowed the calculation of the dosage schedule for further clinical trial. The estimated maintenance dose in human (70 kg) was 200 mg/m2 to be given weekly, and the corresponding loading dose was 600 mg/m2 . © 2003 Elsevier B.V. All rights reserved. Keywords: Monoclonal antibody ior EGF/r3; Tumor growth delay; Integrated pharmacokinetic–pharmacodynamic; Survival time; Allometric scaling; Dosage regimen
1. Introduction The murine monoclonal antibody (MAb) anti-epidermal growth factor (EGF) receptor ior EGF/r3 (IgG2a isotype) recognize two conformational sequence-sites of the EGF receptor extracellular domain, with high binding affinity (Kd = 10−9 M), depending on its blocking action upon ligand binding that partially reduces the autophosphorylation of the receptor, and therefore, inhibits the receptor (hetero-)dimerization in intact tumor cells, suggesting a cytostatic response (Fernández et al., 1989). ∗
Corresponding author. Tel.: +537-271-9538; fax: +537-33-6811. E-mail address: [email protected] (J. Duconge).
0928-0987/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.ejps.2003.10.015
On the basis of data obtained in earlier pharmacokinetic (PK) and pharmacodynamic (PD) studies for the MAb ior EGF/r3, the application of PK and PD principles and procedures to the rational development of this drug will be essential. Incorporation of PD studies along with PK one, coupled with appropriate and timely evaluation so as to influence subsequent drug development procedures, may lead to earlier identification of optimal dosage regimens and may contribute to shortening the overall time of drug development program. The increased understanding of drug action derived from PK–PD-based drug development leads to more information, especially with regard to the identification of drug dosage regimens that results in optimal therapeutic outcome. Moreover, appropriate preclinical evaluation may improve
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efficacy during phase I testing. The establishment of this information during pre-marketing drug development provides an essential framework for continued refinement and improvement during post-marketing drug use (Peck, 1995; Reigner et al., 1997). Interspecies scaling can be used to reveal the underlying similarities and/or differences in drug disposition among species and to predict the PK of a drug in any particular specie, which in most cases is man (Mordenti, 1986). The use of this approach has also been subject of analysis for dose scaling (Gabrielsson and Weiner, 1997). The purpose of this study was to experimentally explore the PK–PD strategy for optimizing the multiple-dose regimen of the MAb ior EGF/r3 using the cancer-bearing nude mice as animal model of human disease, and considering the allometric scaling paradigm.
2. Material and methods 2.1. Drug The murine MAb anti-EGF receptor ior EGF/r3, from the Center of Molecular Immunology, Institute of Oncology and Radiobiology (IOR, Havana, Cuba), has been produced conforming to the standard of quality for injectable formulations. Each bulb contains 50 (±0.2) mg of sterile MAb ior EGF/r3 powder in 10 ml of neutral phosphate-buffered saline (PBS) solution. 2.2. Animal husbandry Male NmRI/ nu–nu strain nude mice (8–10 weeks old, mean weight 25 ± 3 g) were housed as a group and also were bred and maintained under controlled conditions during the experiment. Access to food and water was provided ad libitum to all animals. All studies were approved by the Institutional Animal Care and Use Committee and were performed in accordance with the guidelines of the good laboratory procedures for animal use. 2.3. Tumor cell line The HER2/neu-overexpressing cell line, H125, from a non-small cell human lung carcinoma was used. This tumor line was expanded in RPMI 1690 media (SEROMED, Berlin, FRG) supplied with 10% FBS (GIBCO, BRL, UK), 100 g/ml penicillin and 100 g/ml streptomycin. The media was maintained at 37 ◦ C and 5% CO2 conditions. 2.4. Tumor-bearing nude mice Solitary tumors were produced in the right abdominal flank by subcutaneous inoculation of 2 × 106 viable tumor cells in 0.1 ml of medium. These transplantable tumors are non-immunogenics to these hosts and therefore
growth without rejection. They were submitted to the study when the xenografts had grown up to approximately 0.5 cm3 of average diameter (∅ave ), according to the following expression: ∅ave = (π/6) × ab2 , where a (length) is the largest and b (width) is the shortest tumor diameter (Fan et al., 1993). Each diameter was measured using a vernier caliper. About the use of xenograph mice models for pharmacokinetics and pharmacodynamics, the Points to Consider in the Manufacture and Testing of Monoclonal Antibody Products for Human Use (Food and Drug Administration, CBER, 1997, section B, Preclinical pharmacology and toxicity testing: general considerations) stated: “Pharmacokinetic and pharmacodynamic properties of MAb that are dependent upon specific antigen binding may not be evident in animal studies conducted in species which do not express the antigen of interest. In some cases, xenograft models can be developed by introducing cells expressing the antigen of interest into immunodeficient mice (e.g., SCID or nude mice). Such models can provide information on specific targeting of desired cells, and the results of such testing will influence safety considerations for initial clinical trials (e.g., starting dose, dose escalation scheme, etc.)”. 2.5. Dynamic experiment Ten animals were randomized into two experimental groups (five/group). The first group was dosed with 60 mg/kg (0.1 ml) MAb ior EGF/r3 as single i.v. injection, and the second one received the same volume of saline. For further effect data analysis, the tumor growth rate of both the saline-treated and the drug-treated group was followed-up measuring two mutually orthogonal tumor diameters, by triplicate in each animal, calculating the corresponding average diameter as above mentioned, and dividing the diameter enlargement by the elapsed time, at each experimental time. Notice that the calculated growth rate at each time point is determined with regard to the previous time point. Measurements were performed on day 0 predose and at 0.5, 1, 2, 2.5, 3–6, 10, 15, 17.5, 20, 22, 25 and 30 days after treatment. Finally, the mean difference between both groups at each experimental time represents the tumor growth delay (TGD) of the drug-treated group with respect to the control one. 2.6. Pharmacokinetic data The PK parameters (i.e., K10 = 0.040 h−1 ; CL = 0.19 ml/h; Vd = 4.75 ml; K12 = 0.027 h−1 ; K21 = 0.080 h−1 ; α = 0.12 h−1 ; β = 0.027 h−1 ) were taken from a previously reported study of the systemic ior EGF/r3 disposition in xenograft-bearing nude mice, where the tissue ior EGF/r3 concentration time-course was also conveniently estimated using compartmental analysis (Duconge et al., 2002).
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2.7. Pharmacodynamic data analysis The concentration—effect data were evaluated as individual using a nonlinear sigmoidal Emax pharmacodynamic model, according to the methodology early developed by Sheiner and co-workers for simultaneous modeling of pharmacokinetic and pharmacodynamic responses (Sheiner et al., 1979). E=
N Emax · Css ss N N C50% + Css
where, Css 50% is the steady-state concentration producing 50% of maximum effect (Emax ), and N is a sigmoidicity factor. Effect (E) was expressed as above mentioned, Section 2.5. Briefly, an additional hypothetical effect-site (biophase) compartment was postulated. It was linked to the central compartment of a two-compartment mammillary pharmacokinetic model by a first-order process, while drug dissipation from it is occurring by means of a second first-order rate constant (Ke0 ). This rate constant for drug removal from the effect-site compartment will precisely account for any temporal disequilibrium of the ior EGF/r3 concentration–effect relationship. Considering that the PD models are in essence independent of time, characterizing the equilibrium (time-invariant) relationship between drug concentrations and effects, our PD model was expressed in terms of steady-state ior EGF/r3 concentrations, rather than their corresponding amounts in the hypothetical effect-site compartment. It is because, at steady-state, there will be a steady-state ior EGF/r3 serum concentration and a unique corresponding amount of ior EGF/r3 in the effect-site compartment. So, we solve for each steady-state ior EGF/r3 serum concentration that give rise to (i.e., equivalent to) each pharmacokinetically estimated amount of ior EGF/r3 in the effect-site compartment, following the mathematical algorithm earlier described by Sheiner and co-workers, where full explanation can be found (Sheiner et al., 1979). The corresponding PK parameters (see Section 2.6) were then used to generate the ior EGF/r3 serum concentrations at the same time points of TGD effect measurements, using the equation describing the steady-state ior EGF/r3 concentrations equivalent to the hypothetical effect-site ior EGF/r3 amounts for a two-compartment open model with additional effect-site compartment, after an intravenous bolus input (Holford and Sheiner, 1981). The pharmacodynamic parameters were estimated by a suitable non-linear regression, following an iterative curve-fitting algorithm by Gauss–Newton (Levenberg–Hartley adjusted) minimization method, using WinNonlin professional software (WinNonlin, ver. 2.01, 1997, Pharsight Co., Virginia, USA). The steady-state ior EGF/r3 serum concentration assoss ciated with maximum efficiency (Cmax,eff ) is derived from
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the function denoting efficiency. By definition, efficiency means production of response in relation to stimulus (input). Following Kaojarern et al. (1982), and Alvan et al. (1990), an efficiency variable which denotes drug effect per stimulus [i.e., (E − E0 )/C] was obtained by dividing both sides of the Emax PD equation by the concentration variable, Efficiency =
N−1 Emax · Css ss N N C50% + Css
ss Whence, the Cmax,eff expression (see below) is derived by calculating its maximum. Indeed, the steady-state ior EGF/r3 concentration value for which maximum efficiency ss is reached (Cmax,eff ) is just that obtained when the first ss derivative of this equation equals zero. Notice that Cmax,eff is not calculable when N < 1. ss ss Cmax,eff = C50% · (N − 1)1/N
2.8. Multiple-dose regimens Animals were randomized into three groups (five animals/group): two treatment groups either by multiple cumulative (group 1) or non-cumulative (group 2) schedule, and the control saline-treated one (group 3). All animals in this study were kept under the same experimental conditions. Five animals (group 1) received multiple intravenous bolus injection of mAb ior EGF/r3, via ocular plexus, in order to achieve the desired average drug serum concentration ss = C ss (i.e., Cave max,eff ) and also to ensure that trough concentrations remain within the upper half of the linear range, which is previously established from sensitivity aspects of the PD response. Because the superposition principle is an overlay method, the drug disposition profile plateaus when repetitive equal doses are given at a constant frequency of administration (once a day), and thus the desired average ior EGF/r3 concentration is obtained. That is, using the corresponding multiple-dose equation for cumulative dosage regimen, by intravenous bolus input and assuming first-order ss · CL · τ; where τ means dosing elimination, Dose = Cave interval (Wagner, 1965; Rowland and Tozer, 1989). To this end, the previously estimated pharmacokinetic parameters in cancer-bearing nude mice (Duconge et al., 2002) were used (see Section 2.6). Whereas, another five animals (group 2) were first dosed intravenously by an initial loading dose (DL ) that was followed by the same multiple-dose regimen as group 1 (DM , maintenance dose), given daily. In order to estimate the corresponding loading dose (DL = DM × Rac ), the required accumulation index, Rac = 1/(1 − e−K10 ·τ ), was calculated following the standard method (Wagner, 1965; Rowland and Tozer, 1989). In both schemes the duration of treatment was up to day 21st (n = 21). For practical reasons, humans are dosed weekly and, of course, the necessary dosage adjustment for allometric scaling purposes was done, using standard procedures (Rowland and Tozer, 1989).
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2.9. Tumor size and survival analysis The tumor size in each group under study was measured as previously reported for average diameter before, during and post-dose administration at the following times: 0, 6, 14, 21, 28, 35, and 42 days. These values are used to estimate the drug-induced tumor growth inhibition effect in the multiple-dose study. The tumor growth inhibition (TGI) ratio, expressed as percentage, was estimated as follows: SCav − SDav TGI ratio = × 100% SCav Where, SDav and SCav represent the slopes of the best-fitted second-degree polynomial functions (SPSS for Windows, ver. 6.0, 1993), corresponding to mean data from the drug-treated and the control group, respectively. We followed an earlier method of analysis of growth curves, where a full explanation can be found (Grizzle and Allen, 1969). Briefly, the method utilizes the technique of analysis of covariance, but adding the concept of confidence intervals for improvement of polynomial curve fitting to growth data, which yields results identical to those obtained by weighting inversely by the sample covariance matrix, but has the additional feature of allowing flexibility in weighting by choosing subsets of covariates. This approach leads to methods of estimating parameters and performing tests that can be easily implemented by standard multivariate linear model programs (Grizzle and Allen, 1969). We also followed the survival time in each group during and post-treatment, expressing the corresponding average survival time (±S.D.), in each experimental group, and estimating the survivorship directly from the continuous survival or failure times. 2.10. Dose scaling By means of the information on clearance and dose in mouse, and according to the allometric power equation that characterizes the MAb ior EGF/r3 clearance across mammalian species, the empirical relation for dose scaling (Boxenbaum and DiLea, 1995) was used in order to scale the maintenance dose (DoseM ) to man: Wman 0.85 Doseman = Dosemouse , Wmouse Where, W means the body weight and 0.85 is the allometric exponent for ior EGF/r3 clearance across mammalian species (unpublished data from the authors), and dose in mouse corresponds to the adjusted dose to be given weekly from the maintenance dose used in the above mentioned multiple-dose study. Similarly, because the loading dose (DoseL ) rather depends on volume of distribution, it was scaled using the corresponding empirical power equation for volume of
distribution of ior EGF/r3 among mammals, where the allometric exponent is unity. Wman DoseL,man = DoseL,mouse Wmouse 2.11. Statistical analysis The statistical analysis was conducted to determine significant differences among groups under study, with respect to their tumor growth rate. In this regard, the respective tumor growth curves were analyzed using a multiple likelihood ratio test (Bonferroni adjusted t-test, P < 0.05) according to the Grizzle and Allen method (Grizzle and Allen, 1969). Essentially, the methods for analyzing survival time handle censored data. Regarding that, the survival analysis was accomplished by the Kaplan–Meier’s product limit method using STATISTIC procedures (Statistic for Windows, Statsoft Inc., 1993). In order to compare more than two samples the multiple sample test implemented in survival analysis is an extension of the log-rank test. Chi-square value was computed based on the sums of the firstly assigned score to each survival time, in each group under study, using Mantel’s procedure (Mantel, 1966).
3. Results Fig. 1 (panel A), shows the measured tumor growth delay effect in tumor-bearing nude mice, treated intravenously with 60 mg/kg murine MAb ior EGF/r3. Considering that we are trying to elucidate the possible PK–PD relationship for this MAb, in order to use this information for dosing design, Fig. 1 (panels A and B) depicts comparatively the measured effect data and the earlier estimated peripheral ior EGF/r3 concentrations (Duconge et al., 2002). As can be seen, the estimated peripheral ior EGF/r3 concentrations increased immediately, but the measured effect lags behind almost 24 h and peaks approximately 4 days later, when tissue drug concentrations declined. Visually, this lag time between peripheral drug concentrations and tumor growth delay effect is clearly shown in panel B (inset rectangle) by the large degree of counterclockwise hysteresis in the concentrations-effect curve. Actually, the concentration versus effect plots using either experimentally determined ior EGF/r3 serum concentrations (result not shown) or its pharmacokinetically estimated peripheral levels (panel B) were useful for the recognition of equilibration delays, which permited us to postulate a separate effect-site compartment (i.e., biophase). The effect data were fitted to the PD model with input information being the measured tumor growth delay effect at each experimental time, and the previously estimated pharmacokinetic parameters (Duconge et al., 2002). The steady-state ior EGF/r3 concentrations-effect curve drawn in Fig. 1, panel C, represents the predicted sigmoid shape of
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Fig. 1. (A) Tumor growth delay effect (mean ± S.D., n = 5), and (B) theoretical tissue ior EGF/r3 concentrations over time, single dose, using a two-compartment pharmacokinetic model (PK parameters taken from Duconge et al., 2002). Observe the counterclockwise hysteresis loop for the tissue concentration–effect relationship (inset rectangle). (C) Equivalent steady state ior EGF/r3 concentration–effect relationship curve by sigmoid Emax . PD model, and (D) efficiency of response for the mean effect data, after single 60 mg/kg of MAb ior EGF/r3 intravenously. The linear range (20–80% Emax ) is ss delineated by vertical lines. The steady-state drug concentration for both 50% maximal effect (Css 50% ) and maximal efficiency (Cmax,eff ) are shown (arrows).
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Table 1 Summary of the ior EGF/r3 pharmacodynamic parameters, in tumor bearing nude mice after single intravenous dose (60 mg/kg) Parameters (mm3 /h)
Emax ss C50% (g/ml) N (shape factor) Ke0 (h−1 ) ss Cmax,eff (g/ml)
Values (± S.E.) 0.49 9.23 5.42 0.0015 12.5
± ± ± ±
0.012 0.17 0.36 0.000035
Values are expressed as mean ± S.E. Parameters estimates were determined for the mean effect data (n = 5) using the sigmoid Emax . PD model.
the pharmacodynamic relationship for the best fit of these data to our model and Table 1 shows the corresponding pharmacodynamic parameters. Using the so-called linking approach an integrated model of PK–PD drug responses was proposed, which allowed characterization of the temporal aspects of its pharmacodynamic (Ke0 and t1/2ke0 ) as well as the time-independent ss ss sensitivity component (C50% and Cmax,eff ), as can be seen in Table 1. Interestingly, the first-order rate constant for equilibration of ior EGF/r3 effect (i.e., tumor growth delay) and its effect-site concentration was 0.0015 ± 0.000035 h−1 , which demonstrates that effect is not directly proportional to the amount of drug either in the central or in the peripheral compartment (K21 Ke0 ) of the PK model. The mean steady-state ior EGF/r3 concentration required to produce 50% growth delay is 9.23 ± 0.17 g/ml, a measure of the sensitivity to the drug. As can be seen from Fig. 1, panel D, the course of efficiency is shifted rightward from effect. The steady-state ior EGF/r3 serum concentration associated with maximal ss efficiency, Cmax,eff , 12.5 g/ml, was then proposed as the ss ) for dose calculation. optimal level (i.e., Cave
In utilizing this approach, the first group (group 1) was dosed intravenously by a cumulative regimen with 2.3 mg/kg murine MAb ior EGF/r3, once a day. Whereas, the second group (group 2) was treated using a non-cumulative regimen, with a 4 mg/kg loading dose at the first day, followed by 2.3 mg/kg daily maintenance dosage. The estimated index of the extent of accumulation (Rac = 1.62, τ = 24 h) revealed a cumulative pattern that suggests just a two-fold higher dose as first input to reach immediately the required steady-state values. Fig. 2 displays the tumor growth rate in each group under study, after a multiple-dose strategy. In the light of this result we are able to appreciate that the control group showed a faster tumor growth rate than either of the drug-treated groups. It concerns with the fact that both treatments showed a significant tumor size reduction with respect to control. The tumor growth rate, in the treated group with cumulative scheme, displayed a plateau during about 20 days (30 days for the non-cumulative scheme), and then suddenly showed a slow recovery. As can be seen in Table 2, the statistical analysis shows significant differences between groups under study, each other. These differences were remarked by the estimated tumor growth inhibition ratio (TGI) parameter, which showed a percentage of about 50% for the cumulative schedule, whereas the non-cumulative group exhibited a higher percentage (i.e., 85%), as compared to control one. On the other hand, Fig. 3 depicts the survivorship analysis using the survival percentage after treatment in each group studied. The mean survival time was estimated according to the Kaplan–Meier product limit method. This method estimates the survivorship, and the resulting estimates don’t depend on the grouping of the data into a certain number of time intervals as it’s using the life table method. Interestingly, current survival projection in treated mice, under
Fig. 2. Mean tumor size over time from a multiple-dose study of the MAb ior EGF/r3-treated and non-treated (control) tumor-bearing nude mice. Five animals were dosed in each drug-treated group. Up to day 36, n = 5 for the control group. On other days, n is less, since mice dropped out due to death. Dosing (arrows) protocol was established as a 21-days exposure to 2.3 mg/kg intravenous ior EGF/r3 once daily, using both cumulative and non-cumulative (DL = 4 mg/kg) dosage regimens. The horizontal bar shows the steady state condition for cumulative scheme. Dotted line represents the consecutive dosing up to day 21. Symbols are the experimentally measured mean values and curves represent the simulated values based on the best-fitted quadratic functions.
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Table 2 Statistical analysis of tumor growth curves corresponding to each group under study, after a multiple-dose scheme Parametersa
Cumulative (group 1)
Non-cumulative (group 2)
Control (group 3)
Observed differences 1 vs. 2
1 vs. 3
2 vs. 3
Intercept (cm3 ) Slope (cm3 /days) Acceleration (cm3 /days2 )
0.0376 0.0364 0.0043
0.0248 0.0092 0.0012
0.1433 0.0618 0.0098
0.0128 0.0272b 0.0031
0.1057b 0.0254b 0.0055
0.1185b 0.0526b 0.0086
A multiple likelihood ratio test (Bonferroni adjusted t-test, P < 0.05) was used conforming to Grizzle and Allen method. a Parameters were estimated using an unweighted least square method from the best-fitted quadratic function for experimental data in each tumor growth curve (Wilks-test probability: 0.76, Roy’s probability: 0.91). b Means statistically significant differences between groups.
Fig. 3. Survival percentage for each group under study from a multiple-dose schedule. Solid line corresponds to the control (non-treated) group. Dotted and dashed lines represent the drug-treated groups by cumulative and non-cumulative regimens, respectively. Observe the survival time differences between control and non-cumulative regimen at the end.
non-cumulative dosage regimen (median survival time: 72 ± 10 days), predicts an increment of about 17 days in the surviving proportion as compared to the control (median survival time: 55 ± 6 days). Whereas, the treated group using cumulative dosage regimen (median survival time: 66 ± 11 days) showed a slight but significant increment (P = 0.049) in survival with respect to the control. Indeed, according to the multiple-sample log rank test for analyzing survival time data, the statistical difference between the non-cumulative group and the control one was remarkably the highest (P = 0.007), but there is not any significant difference between both groups of treatment (P = 0.083). After that, the allometric power equation for dose scaling across mammalian species allowed the calculation of the dosage schedule for further clinical trial. The estimated maintenance dose in human (70 kg) was 200 mg/m2 to be given weekly, and the corresponding loading dose was 600 mg/m2 .
4. Discussion Because we need to use concentrations in our PD characterization which reflect the drug action at the effect site, and our pharmacokinetic model alone may not be able to predict
such values directly, even when peripheral drug level were considered, we developed a more complicated linked modeling approach, which is conceptually similar to the methodology previously reported by Sheiner et al. (1979). As was earlier suggested by Sheiner et al. (1979), it is more meaningful to relate the tumor growth delay effect to the serum concentrations of the MAb ior EGF/r3, rather than to an amount of drug in the hypothetical effect-site compartment. The effect equation obtained deals directly in (equivalent) steady-state ior EGF/r3 serum concentrations for sensitivity, and this aspect of its pharmacodynamic is isolated from the kinetic aspects, quantified by the Ke0 parameter. The optimal biological dose (OBD) has been postulated by regulatory agencies as the most clinically relevant dose for survey the rational drug developmental programs of novel biological entities (FDA, Point to consider in the manufacturing and testing of MAb products for human use: Preclinical Studies, 1999). Regarding to achieve a relevant selection criterion about the most reliable therapeutic range, we must pay great attention upon the clinical support of the tumor growth delay as pharmacodynamic marker, according to the oncotherapeutic endpoints of the murine MAb ior EGF/r3 treatment. In this sense, the steady-state ior EGF/r3 concentration range, from 7.5 to 12 g/ml (see Fig. 1, panel C), which is the linear range (i.e., within 20–80% Emax ) of this sigmoid-shape nonlinear PD curve, between threshold and plateau values, could be assumed as the probabilistic interval that results in proportional percentages of contribution to the desired response per increment of drug amount. The sensitive parameter Css 50% is midpoint of this interval, which produces 50% of the maximal TGD response. This PD value is a measure of the subject’s sensitivity to the MAb ior EGF/r3. At this point, the expression for maximum efficiency gives the concentration value at which the highest yield of effect per stimulus is obtained. It is also a “money-saving” approach that permits us a more rational use of this drug. Considering that, instead of using an arbitrary level within the linear range or even the value for maximum effect, we decided to draw the dosage scheme by using the estimated ss Cmax,eff value (i.e., 12.5 g/ml). As far as we know, the concentration of a drug at the site of action, whether directly
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corresponding to the serum concentration or to a kinetically associated compartment such as a deep target organ is heavily dependent on drug input. Therefore, the input variable should be controlled in order to attain optimal drug effect. In this context, we need to adjust the dosing rate (i.e., dose/τ) of the multiple-dose regimen in order to achieve the ss desired average ior EGF/r3 serum concentration, Cmax,eff = 12.5 g/ml and also to ensure that trough concentrations remain within the upper half of the linear range, as established from sensitivity aspects of the PD response. In fact, we thought that this extreme value allows estimation of the dose size more closely associated with the optimal biological dose (OBD), early suggested by FDA (point to consider, 1999). During the drug administration the clinician must appreciate to what degree drug concentration in the biophase lags behind that in the blood. Thus, drug dosing must be designed to reach the maximum efficiency concentration in the biophase when it is clinically important to achieve the maximally efficient tumor growth delay effect. Accordingly, a cumulative dosage schedule was designed as first choice because we were encouraged to assess whether this cumulative pattern is required for the antitumoral response. That is, if therapeutic success would be dependent more on cumulative response than moment-to-moment activity, then the use of extended dosing intervals might markedly reduce the effectiveness of the same average dose. Therefore, it is a kind of information that we need in order to suggest an appropriate dosing interval for clinical testing. On the other hand, in order to reduce the onset time—that is, the time drug takes to achieve its minimum effective serum concentration—a loading (priming) dose was given. The main objective is to achieve the desirable average ior EGF/r3 serum concentration for maximum efficiency as quickly as possible, which is generally most useful for clinical outcome. We decided to put both schedules into practice in order to compare each other and therefore make the best choice for dose scaling. In our case, the dosing interval (τ, once a day) was chosen for practical reasons. The usual “rule of thumb” of dosing every half-life is a conservative strategy for limiting wide fluctuations in drug effect, but demands more in terms of dosing frequency than may be necessary to achieve consistent drug action. The dosage interval should be spaced conveniently for better dosing and sampling, and also in order to reduce animal stress. Concerning both treated-groups, a possible explanation for the terminal behavior observed in Fig. 2 is related to the heterogeneous and asynchronous distribution of macromolecules in tumors (Jain and Baxter, 1988; Jain, 1990). Alternatively, this tendency may also be due to cell-cycle specificity or depending upon the proposed time and dose-dependent mechanisms of auto- and paracrine release of EGF-like peptides, which are induced through up-regulation of their encoding genes after EGF-receptor signaling reduction by monoclonal anti-EGF receptor antibodies (Mendelsohn, 1987). These results stressed the
idea about a cyclic dosing strategy for optimal clinical outcome, in order to avoid the long-term saturation of the cell surface EGF-receptors, which probably is associated with the above-mentioned time-dependent mitogenic upstream programs. Strikingly, the equilibration time parameter (t1/2ke0 = ln (2)/Ke0 = 19.3 days) is telling us that the ior EGF/r3 dissipation kinetic out of its effect-site compartment is near to the end of the treatment (21 days) and also to the major difference in survival. Perhaps, the most obvious and simple explanation could be the end of the treatment after 21 days. Although, care must be taken in speculating which one is the most correct explanation to this terminal behaviour (see Fig. 2), considering the tremendous heterogeneity of tumor xenografts and their complex response over time. In this context, the significant difference between the non-cumulative and the cumulative group after the dosing has stopped is probably a consequence of the initial loading dose of 4 mg/kg, which had a tremendous effect compared to the initial dose of 2.3 mg/kg (cumulative scheme). In our opinion, it is due at least in part to the fact that a relatively higher tumor drug availability at the begining of the treatment should be expected. It is well-established that smaller tumors, like those at the begining of the treatment, are highly vascularized and have reduced necrosis areas when comparing to larger tumors. Hence, we should dose the largest amount of drug at this time point because tumors become more necrotic over time and therefore drug availability will be lower. The cumulative schedule only achieved the effective concentration after three days and at this point the tumor biology is remarkable different and drug availability is reduced. On the other hand, there is a difference between both groups with regard to the time elapsed upon binding of ior EGF/r3 at effective concentration. Perhaps, the EGF receptor has an internal clock that times how long it is occupied and such a kinetic-reading will shift the cell signal toward an specific fate (e.g., cell death or cell-cycle arrest). Of course, further studies must be accomplished to support such a hypothesis or elucidate more appropriated explanations. Indeed, tumor response is extremely difficult to understand. The fact of the matter is that the higher percentage (i.e., 85%) of tumor growth inhibition (TGI) was observed in the non-cumulative group. It means that the tumor growth in the group treated by non-cumulative scheme lag behind the control one, representing only a 15% of the tumor growth rate in the control group. The results corroborated our hypothesis about the key role played by this MAb ior EGF/r3 as modulator of some biosignal controlling tumor growth pathway. Thereby, we were encouraged to scale this dose because it was considered quite appropriate to satisfy the requirements for optimal antitumoral effect, in spite of incomplete inhibition. The survival time for mouse might become into human time using the equivalent biological time. Biological time is defined as a species-dependent unit of chronological time
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required for the completion of a species-independent physiological event and this relates also to pharmacokinetic. Comparing maximum lifespan potential (MLP) in man (i.e., 98 years old) to MLP in mouse (i.e., 2.7 years old) was a factor of 40 (Gabrielsson and Weiner, 1997). Taking only MLP into account a concentration of unity in the mouse during 1 h corresponds to a 40 h period in man at the same concentration level, therefore the survival time will be 40 times greater in man (Boxenbaum, 1982; Gabrielsson and Weiner, 1997). The results brought forth a median survival time increment representing about two years in human, according to the equivalent biological time across mammalian species from mouse to man. However, we must bear in mind that this is a speculation based on the concept of MLP and therefore it should be accepted with some reserves. The body weight rule offers the investigator a very powerful tool with which to obtain general guidelines for making reasonable interspecies predictions of the optimal therapeutic scheme. Using the allometric equation for dose scaling (see Section 2.10) we have a scaling factor of 851.3, which was multiplied by the maintenance dose in mouse (0.025 kg), but just that to be administered weekly (i.e., 16 mg/kg weekly). Accordingly, the maintenance dose in human (70 kg) will be 340.5 mg/week = 190 mg/m2 weekly ≈200 mg/m2 to be administered weekly. Concerning the loading dose, it was scaled assuming to be proportional to body weight as aforementioned in Section 2.10, where the body weight ratio is the corresponding scaling factor. However, we also took the dosing interval into consideration because the next dose will be administered after a week instead of daily. Notice that a larger dose is necessary if the drug is given at longer intervals. So, any change in dosing interval must be corrected by a proportional change in dose size. Under such an interpretation, we were encouraged to scale an adjusted loading dose in mouse (0.025 kg) of 16 mg/kg (i.e., DoseL = DoseM [1/(1 − e−K10 τ )] = 16 mg/kg weekly × 1.001 = 16 mg/kg), rather than 4 mg/kg (i.e., 2.3 mg/kg daily × 1.62 = 4 mg/kg). The last one is valid only for continuing dosing once a day, which is not the case. Therefore, using a dose scaling factor of (70 kg/0.025 kg)1 = 2800, the correct loading dose in man (70 kg) will be 0.4 mg × 2800 = 1120 mg = 622.2 mg/m2 ≈ 600 mg/m2 . Interestingly, we do believe that taking the murine MAb ior EGF/r3 studies into account a reasonable dose scale-up for the humanized variant is possible, even though this should be done with great caution. As a matter of facts, we really ought to use the murine entity in tumor-bearing mice models in order to override recurrent species-specific clearance mechanisms such as human anti-mouse immunological response and thus obtain a reliable prediction of the recombinant humanized MAb (rhuMAb) behavior in cancer patients. It’s true because murine MAbs administered in mouse resemble more efficiently the pharmacokinetic of humanized MAbs used in human, at a similar pace, measured by their own internal biological clock, than if we had
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used rhuMAbs themselves in mouse. This sort of anti-sense prediction is based upon one of the underlying assumptions of the allometric scaling approach, which is related with the absence of species-specific clearance mechanisms in the disposition, under the precept that a representative animal species is used and scaled appropriately, with respect to elimination and sensitivity of drug. Pioneers like Boxenbaum and co-workers have provided excellent overviews to this field (Boxenbaum, 1986). Finally, as Levy (1993) has argued, “It is unfortunate that comparative information on the effective concentrations of new drugs in various species of animals and (eventually) humans is either not obtained or not fully utilized. Knowledge of effective drug concentrations in animal models can greatly facilitate dose ranging in phase I clinical studies”. In this regard, a dose scaling strategy using PK–PD data from preclinical study in a xenograft mice model was developed for the murine MAb ior EGF/r3. The results allowed us to recommend a dosage scheme (DL = 600 mg/m2 ; DM = 200 mg/m2 to be given weekly) for clinical testing based on estimation of the effective ior EGF/r3 concentration through the PK–PD approach.
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