Investigational New Drugs

, Volume 27, Issue 2, pp 140–152

Application of population pharmacokinetic modeling in early clinical development of the anticancer agent E7820

Authors

    • Department of Pharmacy and PharmacologyThe Netherlands Cancer Institute/Slotervaart Hospital
  • Miren K. Zamacona
    • Eisai Limited
  • Mendel Jansen
    • Eisai Limited
  • David Critchley
    • Eisai Limited
  • Jantien Wanders
    • Eisai Limited
  • Jos H. Beijnen
    • Department of Pharmacy and PharmacologyThe Netherlands Cancer Institute/Slotervaart Hospital
    • Division of Drug Toxicology, Section of Biomedical Analysis, Department of Pharmaceutical Sciences, Faculty of ScienceUtrecht University
  • Jan H. M. Schellens
    • Department of Medical OncologyAntoni van Leeuwenhoek Hospital/the Netherlands Cancer Institute
    • Division of Drug Toxicology, Section of Biomedical Analysis, Department of Pharmaceutical Sciences, Faculty of ScienceUtrecht University
  • Alwin D. R. Huitema
    • Department of Pharmacy and PharmacologyThe Netherlands Cancer Institute/Slotervaart Hospital
Phase I Studies

DOI: 10.1007/s10637-008-9164-x

Cite this article as:
Keizer, R.J., Zamacona, M.K., Jansen, M. et al. Invest New Drugs (2009) 27: 140. doi:10.1007/s10637-008-9164-x

Summary

The aim of this study was to assess the population pharmacokinetics (PopPK) of the novel oral anti-cancer agent E7820. Both a non-linear mixed effects modeling analysis and a non-compartmental analysis (NCA) were performed and results were compared. Data were obtained from a phase I dose escalation study in patients with malignant solid tumors or lymphomas. E7820 was administered daily for 28 days, followed by a washout period of 7 days prior to the start of subsequent cycles. A one compartment model with linear elimination from the central compartment was shown to give adequate fit, while absorption was described using a turnover model. Final population parameter estimates of basic PK parameters obtained with the PopPK method were (RSE): clearance, 6.24 L/h (7.1%), volume of distribution, 66.0 L (8.5%), mean transit time to the absorption compartment, 0.638 h (6.5%). The intake of food prior to dose administration slowed absorption (2.8-fold, RSE 13%) and increased relative bioavailability of E7820 by 36% (RSE 14%), although the effect on Cmax and AUC was not significant. Comparison with the NCA approach showed approximately equal PK parameter estimates and food effect measures, although specific advantages of PopPK included efficiency in use of data and more appropriate assessment of variability.

Keywords

E7820Population pharmacokineticsMixed-effects modelingNon-compartmental analysisOncologyAlpha2-integrin

Introduction

E7820 is a novel sulphonamide derivative with anti-angiogenetic activity based on inhibition of endothelial cell proliferation and tube formation. E7820 has demonstrated excellent anti-angiogenetic activity in both in-vitro and animal models of angiogenesis resulting in antiproliferative effects in breast, colon, and pancreatic cancer models [1, 2]. The drug is currently in phase I clinical development. The inhibitory action of E7820 may in part be due to the inhibition of α2-integrin expression in endothelial cells, or to its inhibition of activity of vascular endothelial growth factors (VEGF) and basic fibroblast growth factor (bFGF), both of which are known to induce tube formation [35]. Clinical results of a first-in-man study, have been published previously, and showed that E7820 was well tolerated up to 100 mg (MTD), with toxicities of grade 3 elevated liver enzymes and hemoptysis while at higher doses, haematological toxicities were observed [6, 7]. The objective of this analysis was to characterize the population pharmacokinetics (PopPK) of E7820 through assessment of PK data from this trial.

In pharmacokinetic analyses during clinical development of novel drugs, the use of the PopPK approach is encouraged by the FDA [8]. Already in early clinical stages, this tool can be very useful for gaining insight into mechanisms of drug disposition, to assess linearity in pharmacokinetics over different dosages, to identify covariates that explain between subject variability and to quantify the magnitude of unexplained variability in the population. Despite the advantageous properties of the population approach, published reports on its use in phase I trials in oncology have been only sparse [918]. In this article, a PopPK model was built for the novel oral anti-cancer agent E7820 that is currently in phase I development. Subsequently, the results obtained with the population analysis were compared to those of a classical non-compartmental pharmacokinetic analysis (NCA).

Methods

Study

Data were obtained from a first-in-man, open-label, dose escalation study in patients with malignant solid tumors or lymphomas aiming to determine the maximum tolerated dose (MTD) and to assess the safety, pharmacokinetics, pharmacodynamics and the food effect of E7820 when administered orally. Cycle 1 consisted of daily dosing for 28 days, followed by a 7-day washout period. Following the washout period, chronic daily dosing was recommenced after an overnight fast. Dosing of E7820 was started at 10 mg and was escalated in consecutive cohorts through doses of 20, 40, 70, 100 to a maximum of 200 mg, using a flat dosing approach. The MTD, defined as the highest dose at which dose limiting toxicities occurred in less than one third of the patients, was determined at 100 mg. No grapefruit or grapefruit-containing foods were allowed while on study and co-administration of drugs known to be modulators of the cytochrome P-450 enzymes, particularly CYP2D6, 3A4, 2C9, and 2C19 were avoided unless necessary. Use of anticoagulants/antiplatelet drugs was prohibited. A food effect study was included at the MTD level in cycle 2 of the study. Full PK curves (t = −1, 0.25, 0.5, 1, 1.5, 2, 2.5, 3, 4, 5, 6, 8, 12, 24) were recorded at the first and 28th day of cycle 1 and the first day of cycle 2, while partial curves (t = −1, 1.5, 3, 6 and 8 h) were recorded at the first day of every following cycle. Patients participating in the food-effect cohort were instructed to take a standard high fat meal on the first day of cycle 2, after which a full PK curve was recorded. Urine collections were spaced at 6-h intervals and gathered on day 1 of the first cycle.

Bioanalysis

Development and validation of the analytical method was based on the good laboratory practice (GLP) principles described in FDA’s GLP regulations and the guidance on bioanalytical method validation [19, 20]. Bioanalysis of plasma and urine samples was performed by MDS Pharma Services (Lincoln, NE, USA) using liquid chromatography-tandem mass spectrometry (LC-MS/MS). The analysis was performed on a reversed phase system using a C18 column (Waters, Milford, MA, USA) and a Perking Elmer Sciex API 3000 mass spectrometer for detection. Precision was <15% while accuracies were within the 85–115% interval. The lower limit of quantitation (LLOQ) was 1 ng/mL, while the upper limit of quantitation was established at 250 ng/mL. The calibration curve was linear over this concentration range.

Noncompartmental analysis

The NCA was performed using WinNonLin version 5.1.1 (Pharsight, Mountain View, CA). Data from full PK profiles on day 1 and 28 of cycle 1 and day 1 of cycle 2 were used, while data below the limit of quantification were discarded. Terminal parts of the curve were used to estimate the elimination half-life (t1/2). Other statistics that were recorded in the analysis were Cmax and tmax. Areas under the plasma concentration-time curves (AUC0–24, \({\text{AUC}}_{{\text{0}} - \infty } {\text{ }}\)), and area under the first moment curve (AUMC) were calculated by using the log-linear trapezoidal rule. Mean residence time was calculated as \({{{\text{AUMC}}} \mathord{\left/ {\vphantom {{{\text{AUMC}}} {{\text{AUC}}_{{\text{0}} - \infty } }}} \right. \kern-\nulldelimiterspace} {{\text{AUC}}_{{\text{0}} - \infty } }}\). Using these pharmacokinetic parameters, estimates of CL/F and steady state distribution volume (Vss/F) were calculated as \({{{\text{Dose}}} \mathord{\left/ {\vphantom {{{\text{Dose}}} {{\text{AUC}}_{{\text{0}} - \infty } }}} \right. \kern-\nulldelimiterspace} {{\text{AUC}}_{{\text{0}} - \infty } }}{\text{ }}\) and CL/F MRT respectively. The fraction excreted renally (fren) was estimated by dividing the amount of drug recovered in urine by the dose administered.

Summary statistics of these PK parameters for every patient and population mean and standard deviations were calculated for every dose level on every collection day. I.e., a standard two-stage approach in which data from each individual were weighted equally.

The effect of food intake on exposure parameters AUC0–24, \({\text{AUC}}_{{\text{0}} - \infty } \) and Cmax was evaluated by a linear mixed effect procedure in the statistical software R (http://cran.r-project.org/) using the restricted maximum likelihood estimation method (REML) included in the nlme-library [21]. In the analysis the effect of food-intake on these respective parameters was included as a fixed effect, while individual variability in the effect magnitude and residual variability (RV) were included as random effects. Before the analysis, response data were log-transformed according FDA Guidelines [20]. Mean and standard error of the estimated food effect on response parameters were calculated.

PopPK modeling

PopPK modeling was performed using the non-linear mixed effect modeling software NONMEM (version VI level 1, ICON, Ellicott City, MD, USA), using the first order conditional estimation method with η-ε interaction (FOCEI) [22]. Discrimination between hierarchical structural models was performed using the objective function value (OFV), using a significance level of p < 0.001 (ΔOFV > 10.81). Generation of goodness-of-fit plots and visual predictive checks were performed using R. After assessment of the structural model that best described the dataset, the statistical model was developed to account for between subject variation (BSV), within subject variation (WSV) and residual variability (RV). BSV and WSV in parameter estimates were modeled using an exponential variance model, e.g.
$$\left( {{{{\text{CL}}} \mathord{\left/{\vphantom {{{\text{CL}}} F}} \right.\kern-\nulldelimiterspace} F}} \right)_{ij} = \left( {{{{\text{CL}}} \mathord{\left/{\vphantom {{{\text{CL}}} F}} \right.\kern-\nulldelimiterspace} F}} \right)_{{\text{pop}}} \cdot e^{\eta + \kappa } $$
with (CL/F)ij being the apparent clearance of E7820 for the ith individual at the jth occasion after oral administration, (CL/F)pop the typical population clearance, F the (unknown) oral bioavailability, η the inter-individual random effects with mean zero and variance σ2, and κ the within individual random effects with mean zero and variance π2. Several residual error models were tested for their appropriateness: additive, proportional to the predicted concentrations, exponential or combined models. The appropriateness of the statistical submodels was assessed by inspection of objective function values, uncertainty in parameter estimates, model stability and comparison of goodness of fit plots.
A factor fren, constrained between 0 and 1, was introduced to model the fraction that was eliminated renally:
$$k_{{\text{ren}}} = f_{{\text{ren}}} \cdot \frac{{{{{\text{CL}}} \mathord{\left/{\vphantom {{{\text{CL}}} F}} \right.\kern-\nulldelimiterspace} F}}}{{{V \mathord{\left/{\vphantom {V F}} \right.\kern-\nulldelimiterspace} F}}}$$
With V/F being the volume of distribution after oral administration and kren the renal elimination rate constant. Consequently, the extra-renal fraction was defined as being 1−fren. Separate residual error magnitudes were estimated for plasma and urinary data. The effect of food on the absorption rate was estimated as a categorical covariate on the parameter(s) of the absorption models and on the relative bioavailability (Frel), e.g.: \(F_{{\text{rel}}} = 1 \cdot * f_{\operatorname{food} \sim F_{{\text{rel}}} } ^{{\text{FOOD}}} \) the binary variable FOOD indicating fasted or fed conditions and \(f_{{food \sim F_{{rel}} }} \) the coefficient quantifying the effect of the fed condition on the parameter.
Covariates weight, BSA and age were assessed for their influence on PK parameters by plotting of empirical Bayesian estimates versus CL/F, V/F and MTT. The improvement in fit when incorporated in the model was tested using the likelihood ratio test in NONMEM. Covariates were incorporated in the model as scaled to their median value, e.g.:
$${\text{CL}} = \theta _1 + \theta _2 \cdot \left( {\frac{{{\text{Weight}}}}{{70}}} \right)$$

Data handling

Data were log-transformed prior to analysis. Since PK data from up to 7 cycles was available and incorporation of patients’entire dosage histories into the dataset resulted in very long run-times of our models. As full PK curves were only collected once or twice in every 28-day cycle, we considered alternative modelling approaches that would disregard the period in between PK collections, thereby leading to less computationally intensive runs. Calculation of steady state levels by internal NONMEM routines (SS option) failed since this conflicted with the turnover absorption model that was used. Therefore, we chose to fit the amount of drug in the central compartment to the recorded pre-dose steady state levels (missing dose method) as described by Soy et al. [23]. This entailed estimation of a population steady state level at the pre-dose sampling occasion, assuming a linear relationship between steady state trough levels and dose, while allowing for BSV and WSV in the amount of drug present. To investigate the performance of this approach for this compound and study design, the parameter estimates obtained with the missing dose method were compared with those obtained using full dosing histories. Since exact day-to-day dosing histories were not known in this trial, this analysis was performed retrospectively using data from simulated trials, using the final model and parameter estimates and the same study design as in the original trial.

It was assessed if discarding data points that were below the LLOQ, as opposed to retaining them, significantly influenced estimation of PK parameters [24]. Plasma and urine concentration data below the LLOQ were included in the dataset and modeled by fitting the model parameters to likelihoods of the observed data points, as described by Beal [25], This was done using the F_FLAG option under the LAPLACE estimation method to simultaneously model concentration predictions for predictions above the LLOQ and likelihoods for predictions below the LLOQ. The likelihood of the predicted concentration being under the limit of quantification was estimated using an approximation to the cumulative normal distribution [26]. The parameter estimates thus obtained were compared to parameter estimates obtained when data below the LLOQ data were discarded.

Model evaluation

The model that was developed was subsequently evaluated by estimation-based diagnostics as well as simulation-based diagnostics [27]. These included plots of predicted versus observed concentration, conditional weighted residuals (CWRES) versus time and time after dose, etc. For the calculation of CWRES, the PsN toolkit and the R-package Xpose were used [29, 30]. At the 100 mg level, at which the most patients were included, visual predictive checks were constructed by plotting the 90% confidence interval of the model predictions, obtained by simulating from the model on the same dataset, overlaid by observed plasma concentrations. This was done for the plasma concentrations in the first 24 h of cycle 1 and for plasma concentrations at steady state (after >10 days of consecutive dosing).

Standard errors of parameters were obtained from the NONMEM covariance step but also by a bootstrapping procedure, automated by Perl (ActiveState, Vancouver BC, Canada) scripts and R. Due to the long run time of the model, the number of bootstrap runs was limited to 150. Urine data were not included in the bootstrap analysis since this resulted in large numbers of unsuccessful runs. Therefore, and for the fact that only from a selection of patients urine collections were available, a standard error for the renal fraction was not calculated in the bootstrap analysis. Shrinkage in random effects was calculated as \(1 - \frac{{{\text{SD}}_{{\text{EBE}}} }}{\omega }\) for η-shrinkage and \(1 - {\text{SD}}\left( {\frac{{{\text{OBS}} - {\text{IPRED}}}}{\sigma }} \right)\)for ε-shrinkage, SDEBE describing the standard deviation of the empirical Bayesian estimates, ω the square root of the estimated between- or within-subject variance in parameters, and OBS and IPRED the observed and individual model predictions respectively [27].

Simulation of food effect studies

FDA’s guidance on food effects studies specifies AUC and Cmax as the relevant statistics for evaluating effects of food intake on drug exposure [20]. When simple models are applied, these statistics can be obtained by reparametrization of the PopPK-model to use AUC and/or Cmax as model parameters. However, this approach becomes more complicated when more sophisticated models are used. Alternatively, these statistics and their confidence intervals can be obtained from stochastic simulation of food effect trials. Therefore, using the final model, 1,000 simulations of food effect trials in six patients were performed. To account for uncertainty in the parameter estimates of the final model, the 1,000 trial-simulations were performed 1,000 times, each time with a new set of model-parameters sampled from the multivariate parameter distribution obtained from the covariance matrix, output by the NONMEM covariance step of the final model. Food effects on response parameters Cmax, AUC0–24 and \({\text{AUC}}_{{\text{0}} - \infty } \) were assessed by calculating medians of the ratios of these (log transformed) parameters and their respective confidence intervals. To ensure comparability to these statistics obtained in the NCA, Cmax and AUCs were calculated by the same method as in the NCA, i.e. the Cmax observed at discrete timepoints and AUCs calculated by the log-linear trapezoidal rule.

Results

Dataset

Data from 36 patients were available for analysis, whose characteristics are listed in Table 1. From these patients, 1,421 plasma samples were available, collected from up to 7 cycles, while urinary concentration data was available from 21 patients (82 samples). In the dataset, 95 out of 1,503 (6.3%) of the samples were reported as being under the LLOQ.
Table 1

Patient characteristics

 

Value (range)

Total number

36

Dose level:

10 mg

3

20 mg

4

40 mg

3

70 mg

3

100 mg

17

200 mg

6

Sex:

Male

20

Female

16

Race

Caucasian

31

Black

1

Hispanic

4

Weight (kg)

 

70.9 (43.2–113.6)

Height (cm)

 

167.3 (150.5–182.9)

BSA (m2)

 

1.805 (1.375–2.402)

Age (years)

 

64.8 (40.0–82.0)

Continuous variables given as mean (range) and categorical data as counts

NCA

Summary statistics at different dose levels are shown in Table 2. Elimination half-lives were around 6–7 h at all dose levels, on all collection days on which full PK curves were obtained. AUC0–24 and Cmax increased with increasing dose. Remarkably, the mean AUC and Cmax were higher in the 70 mg subset than in the 100 mg subset, which could be explained by the small number of patients at the 70 mg level. From plots of AUC0–24 and Cmax against dose level (Fig. 1), the linearity in exposure over the studied dose-range was evaluated. Minor plateauing was observed at higher dose levels. However, the small number of patients at dose levels of 70 mg and 200 mg obstructed a thorough assessment of linearity over the entire dose range. Mean CL/F and Vss/F were estimated at 6.67 L/h and 67.4 L respectively, calculated over all dose levels and collection days.
https://static-content.springer.com/image/art%3A10.1007%2Fs10637-008-9164-x/MediaObjects/10637_2008_9164_Fig1_HTML.gif
Fig. 1

Plots of recorded AUC0–24 and Cmax versus dose level, recorded in the NCA on day 1

Table 2

Variables obtained in NCA analysis

Dose level

Recorded statistics

Calculated parameters

n

AUC0–24, ng h/mL (CV%)

Cmax, ng h/mL (CV%)

n

t1/2, h (CV%)

CL/F, L h−1 (CV%)

Vss/F, L (CV%)

Cycle 1, day 1

10 mg

3

1,186 (46%)

190 (21%)

2

5.61 (61%)

10.8 (11%)

84.6 (51%)

20 mg

4

2,809 (45%)

447 (26%)

4

6.37 (21%)

7.76 (51%)

67.0 (31%)

40 mg

3

5,261 (49%)

740 (69%)

2

7.05 (17%)

5.37 (3%)

54.5 (14%)

70 mg

4

17,628 (40%)

1,770 (33%)

2

6.30 (2%)

3.20 (41%)

29.3 (43%)

100 mg

17

14,760 (52%)

1,487 (46%)

9

6.58 (26%)

8.44 (62%)

76.7 (61%)

200 mg

7

21,650 (48%)

1,863 (39%)

1

8.61 (–)

6.05 (–)

75.2 (–)

Mean

37

20

6.45 (25%)

7.67 (46%)

68.2 (47%)

Variability in observed AUC0–24 and Cmax were moderate to high at most dose levels (range 8–77%). In calculated parameters, BSV for CL/F and Vss/F was ∼50%, while BSV in t1/2 was 25%.

In Table 3, the results of assessment of the food effect are shown. These results show that, although all log transformed estimators of exposure were slightly lower in the fed state, a significant food effect could not be proven by the mixed effects analysis: all confidence intervals for the effect of food on the bio-availability statistics contained 1 and were also well within the 80–125% interval laid down by the FDA as the test for absence of food effects [20]. Due to the low number of full PK curves in the food effect cohort, the effect on AUC0–inf could not be calculated.
Table 3

Assessment of food effect on bioavailability parameters using NCA and compartmental analysis

  Response parameter

NCA

PopPK simulation

Ratio fed/fasted

90% CI

Median ratio

90% CI

ln (Cmax)

1.057

0.913–1.087

1.027

0.966–1.067

ln (AUC0–24)

1.031

0.971–1.028

1.031

1.005–1.054

ln (AUC0–inf)

1.033

1.010–1.055

PopPK modeling

Several types of absorption models were tested: linear absorption to the central compartment (with and without lag-time), zero order absorption, linear absorption through a chain of transit compartments (turnover model) and use of Weibull functions (one or two). No time dependencies were assessed in the modeling of the absorption process. In Table 4, an overview is provided of key decisions in model development based on model fits. It was found that the turnover model described absorption best, with the lowest number of parameters. Using this model, the absorption process was defined by the mean transit time (MTT), the number of transition compartments (N) and the absorption rate constant (ka) [27]. The number of transit compartments that best described the absorption process was found by using an analytical solution to the transit compartment model with a 2nd order Stirling’s series approximation of the factorial term [28]. With this method, it is assumed that during the dose interval, all drug has been absorbed. The number of compartments that best fit the data was estimated at 2.98 (RSE 45%), but since the number of compartments could not be estimated accurately, the population estimate for this parameter was fixed to 3. In fitting these parameters, it was observed that all three absorption parameters could not be estimated independently (with or without inter-individual variability): although significant improvements in fit were observed, nonsensical parameter estimates were obtained, and/or BSV was estimated at extremely high values. Therefore the absorption rate parameter ka was defined to equal the transition rate parameter ktr, defined as (N + 1)/MTT. Figure 2 depicts four absorption profiles of patients at the 100 mg dose levels and the population and individual model fit, which shows that the absorption model was able to describe the variability in absorption rate and onset adequately. To assess further if the our model was able to describe the observed data well, we used stochastic simulations using final model parameters to construct a predictive check for Cmax, which is shown in Fig. 3. This figure shows that the model is able to adequately predict the observed Cmax’s.
https://static-content.springer.com/image/art%3A10.1007%2Fs10637-008-9164-x/MediaObjects/10637_2008_9164_Fig2_HTML.gif
Fig. 2

Model fit in absorption phase. Black dots are observed E7820 plasma concentrations, grey lines are population predictions, black lines are individual predictions

https://static-content.springer.com/image/art%3A10.1007%2Fs10637-008-9164-x/MediaObjects/10637_2008_9164_Fig3_HTML.gif
Fig. 3

a, b Predictive checks of Cmax, showing model predicted Cmax (grey histogram) and the observed 25th, 50th, and 75th percentile

Table 4

Objective function values (OFV) of pivotal models in development of the structural model

Absorption

Distribution

Elimination

OFV

Implication

1st order

1 comp

1st order

\(\left. {\matrix {52.3} \\ { - 174.1} \\ {205.0} \\ \begin{aligned} & - 167.7 \\ & - 154.6 \\ & - 341.1 \\ & {\text{ - }} \\ & - 629.6 \\ \end{aligned} \ } \right\}{\text{Turnover absorption model gave best fit}}\)

1st order with lag-time

1 comp

1st order

Zero order

1 comp

1st order

Combined 1st-zero order

1 comp

1st order

Two 1st order processes

1 comp

1st order

1 Weibull function

1 comp

1st order

2 Weibull functions

1 comp

1st order

Turnover model, ka=ktr

1 comp

1st order

Turnover model, estimate ka

1 comp

1st order

−632.8

Separate ka not significantly better

Turnover model

2 comp, linear distribution

1st order

−629.6

No peripheral compartment

Turnover model

1 comp

Emax

−634.0

No non-linear elimination

*= no successful minimization

In the distribution and elimination phase, the observed data were adequately described using a one-compartment PK model, with linear elimination from this compartment. Including one or more peripheral compartments in the model did not result in an improved fit. Also no improvement was observed by non-linear elimination (Emax-model) from the plasma compartment.

Urinary data could be modeled simultaneously with plasma data and the fraction eliminated in urine (fren) could be estimated with appropriate precision at 0.011% (RSE 18%).

In patients that were allowed to take a standard high fat meal, the MTT was estimated a factor 2.78 (RSE 13%) higher, indicating a decreased absorption rate in presence of food. Furthermore, relative bioavailability was estimated 36% (RSE 14%) higher in the fed state.

BSV could be estimated on PK parameters of distribution (V/F) and elimination (CL/F), while also covariance between these parameters was found to be significant. BSV could not be estimated on the absorption parameters (MTT or N), since this resulted in unstable models and/or very wide confidence intervals for the estimates. Estimation of BSV in fren decreased the stability of the model, probably due to the low number of patients with urinary data available, and was therefore abandoned. Incorporation of WSV improved model-fit when included on all PK parameters when tested univariately. The improvement was however most pronounced when included on MTT and N. Since WSV could not be estimated on all parameters simultaneously, it was chosen to include WSV only on the absorption parameters MTT and N. WSV was also estimated for the estimated steady state trough levels. No covariates were found that could describe part of the observed BSV in any of the basic PK parameters, although the number of patients in the current dataset was probably too low to draw conclusions for the entire patient population.

The error model, relating predictions to observed concentrations, was a combined proportional and additive model. Separate proportional and additive residual errors were estimated for the urinary data. Furthermore, despite efforts mentioned above, the absorption phase could only be modeled with moderate precision. Therefore a factor was included on the proportional residual error for plasma concentrations during the absorption phase (arbitrarily set at the first 3 h post-dose). This way, fitting of data in the absorption phase was allowed to be less strict and estimation of parameters for distribution and elimination relied more heavily on data from the elimination phase. The relative error was estimated 23% higher in the absorption phase than in the elimination phase.

Using an intermediate model and including data below the LLOQ by means of likelihood estimation, no relevant influence was observed on the estimation of the PK parameters, relative to discarding those data. The differences in parameter estimates between the two methods were less than 1% for all parameters. Therefore, in further model development, data below the LLOQ data were discarded. Using the final model, the influence of data below the LLOQ data was assessed again and confirmed to have no relevant influence on parameter estimates (Table 5).
Table 5

Final parameter estimates PopPK

PK parameter

Estimate (RSE%)

Bootstrap geometric mean (CV%)

Shrinkage

Structural model

   

 CL/F

6.24 L h−1 (7.1%)

6.46 L h−1 (16%)

 

 V/F

66.0 L (8.5%)

64.0 L (12%)

 

 MTT

0.638 h (6.5%)

0.695 h (19%)

 

 Na

3

3

 

 ffood∼MTT

2.78 (13%)

2.91 (23%)

 

 ffood∼F_rel

1.36 (14%)

1.39 (19%)

 

 frenb

0.011% (18%)

BSV

 ωCL

51.1% (12%)

53.2% (17%)

2.3%

 ωV

48.1% (17%)

47.2% (13%)

1.3%

 ρCL∼V

62.1% (12%)

69.0% (21%)

 

WSV

 κMTT

62.8% (8%)

67.2% (7%)

28%

 κN

137% (17%)

121% (12%)

55%

 κSS

120% (15%)

143% (14%)

61%

Residual error plasma

  

9.1%

Proportional error h

30.2% (9.1%)

27.4% (11%)

 

Prop. error factor t < 3 h

1.23 (9.0%)

1.41 (19%)

 

Additive error

4.2 ng/mL (7.0%)

5.0 ng/mL (47%)

 

Residual error urine

  

<1%

Proportional error

90% (9.1%)

  

Additive error

180 ng (31%)

  

RSE% relative standard error as obtained by COVARIANCE option of NONMEM, CV% coefficient of variation observed in bootstrap analysis

aFixed parameter

bNot estimated in bootstrap analysis

Model evaluation

The fixed effect parameters could be estimated with adequate precision (RSE 7–18%, estimated by covariance step) while random effects also could be estimated precisely (RSE 12–31%). BSV was moderate to high for all pharmacokinetic parameters with BSV in CL/F and V/F around 50%, while WSV on absorption parameters MTT (63%) and N (137%), and estimated steady state levels (120%) were high. Means of all inter-individual variability estimates were not significantly different from 0 (p > 0.05) and the condition number of the final model was low (<100). Low shrinkage was seen in ε’s (<10%), while shrinkage in η’s was small for IIV’s (1–3%) and fairly high for IOV (28–61%). Magnitudes of standard errors for both fixed and random effects calculated in the bootstrap analysis corresponded well with those obtained from the covariance step.

Plots of observations versus population/individual predictions are shown in Fig. 4a,b, which showed good correlation. In Fig. 4c,d, conditionally weighted residuals (CWRES) are plotted against time after dose. From all goodness-of-fit plots no pronounced bias was observed confirming adequate model fit. Visual predictive checks (VPCs) for the MTD dose level (100 mg) are shown in Fig. 5: observed plasma concentrations are plotted and the 90% confidence interval of model predictions for: (a) the first dose administered on day 1 in cycle 1, and (b) patients at steady state (after >10 days of consecutive dosing). By visual inspection, both VPCs showed no pronounced bias, while also the simulated confidence intervals of the predictions were considered satisfactory. The fact that the confidence interval at steady state seem slightly too wide, might be explained by the fact that only part of the data (patient at the 100 mg level) are depicted, while the model is conditioned on the entire dataset.
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Fig. 4

ad Goodness of fit plots. From upper left, clockwise: observed versus population predictions, observed versus individual (log transformed), CWRES versus time after dose and CWRES versus population predictions

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Fig. 5

a Visual predictive check for cycle 1, day 1, at 100 mg. The shaded area shows the 90% confidence interval of the model predicted concentrations. b Visual predictive check for patients at steady state (>10 days consecutive dosing). The shaded areas show the 90% confidence intervals of the model predicted concentrations

Retrospective assessment of the missing dose method showed that parameter estimates thus obtained were comparable (<5% different) to those obtained with full dosing histories, indicating that the use of the missing dose method in the PK analysis of the real phase I data was justifiable.

Simulation of food effect studies

Estimates for the parameters Frel and MTT indicated that food intake prior to administration of E7820 both decreased the absorption rate and increased bioavailability. Results of the simulation study showed increases in (log transformed) exposure variables Cmax, AUC0–24 and \({\text{AUC}}_{{\text{0}} - \infty } \) (Table 3) in the fed state. However, as in the NCA, these results showed no evidence of significant food effect measured by these statistics, according to FDA definitions: confidence intervals for food effects on AUC an Cmax were well within the 80–125% interval.

Comparison of NCA and PopPK results

As can be seen in Tables 2 and 3, the results for elimination (CL/F) and distribution (V/F) parameters obtained in both methods show close agreement. Elimination half-life in the PopPK analysis, estimated by reparametrization, was 7.10 h (RSE 8%), while the mean t1/2 in the NCA calculated over all days was 6.42 (CV 26%). In the NCA, the t1/2, CL/F and V/F could not be calculated in profiles where not sufficient samples were collected, which was the case in 26 out of 66 profiles. The estimate for fren was also approximately the same in both methods. In both approaches no significant food effect on exposure parameters AUC and Cmax was found. BSV for CL/F and V/F in the PopPK analysis as well as in the NCA were both estimated at about 50%. WSV in absorption parameters was high in the PopPK analysis and was not estimated in the NCA due to the low number of occasions (three or less for every patient).

Discussion

In the present study we described the assessment of the PK characteristics of the new oral anti-cancer agent E7820. Both population based non-linear mixed effect modelling, and a traditional NCA were performed.

PopPK modeling

A model that could describe all available data simultaneously, was developed. A rapid absorption was observed, with approximately half of the absorption process being completed after 1 h in the typical patient. The effect of food-intake prior to dose administration showed an effect on absorption kinetics: in the presence of food, the rate of absorption was decreased (increased MTT) and relative bioavailability was increased modestly. Both effects could be explained by delayed passage through the intestinal system due to the food intake. These effects did not result in significant changes in exposure measures AUC and Cmax. Elimination half-life of E7820 was estimated at 7 h, thereby supporting qd or bid dosing. While high within patient variability in absorption rate and onset was observed, between-patient variability in clearance and distribution was moderate to high.

The PopPK model was evaluated by bootstrapping, assessment of shrinkage [27], and evaluation of goodness-of-fit plots and visual predictive checks. The low degree of η-shrinkage in BSV on CL/F and V/F indicated that the data at hand werre rich enough to accurately estimate the degree of variability in these parameters. The higher degree of η-shrinkage in WSV-measures indicated that the dataset was not informative enough to determine this type of variability with a high degree of accuracy.

Plots of population predictions versus observed plasma concentrations showed some bias, which was not present in the plots of individual predictions versus observations (Fig. 4a,b). This might indicate some degree of misspecification by the final structural model. However, as described, extensions or modification to the structural model did not result in improved fit. Plots of CWRES versus time after dose and CWRES versus time (Fig. 4c,d) showed no apparent bias in residual errors, indicating that the model is unbiased in its predictions. Visual predictive checks at the MTD, shown in Fig. 5a,b, demonstrated that model predicted confidence intervals corresponded adequately with the observed data.

Comparison of PopPK approach with NCA

Since both of the approaches taken here entail specific advantages and limitations, it is important to recognize the difference in aim and applicability in drug development. While PopPK modeling aims to develop models describing drug disposition and to gain insight into mechanisms by which disposition occurs, the aim of a NCA is generally the estimation of elimination rates and the gathering of information about exposure statistics (AUC and Cmax) over several dose levels. Below, two key differences between the two methods that we encountered are discussed.

The first important difference involves the efficiency in use of data. Attaining high efficiency is especially relevant in phase I of clinical development as at this stage, PK data of only a small number of patients are available. In the present study, at every dose level only few patients were available, except at the MTD level. In contrast with the NCA, data from several occasions could be used to obtain overall parameter estimates.Because the NCA requires at least several data points in the elimination curve and Cmax levels, only full PK curves could be used to estimate elimination parameters and statistics. Therefore, PK data recorded in cycles 2 and up, had to be discarded in the NCA, while also PK curves that were incompletely recorded could not be used to estimate t1/2 (26 out of 66 curves). In addition, data points in an NCA are imperatively discarded, or handled in a less correct manner. When significant portions of the elimination part of the curve are under the LLOQ, which is often the case at lower dose levels, estimates of PK parameters might be biased. In our PopPK analysis, it could be confirmed that the influence of discarding these points was marginal. Furthermore, in the PopPK analysis a model was jointly fitted to plasma and urine data thereby using the extra information obtained from the urine samples in fitting of the model while, simultaneously, information from the plasma compartment is used in estimation of a renal elimination fraction.

The second important issue is the approach by which variability was addressed. In the NCA, parameters were calculated separately for each recorded PK curve for each individual, and pooled afterwards to obtain mean and variatibility measures for every dose level on every occasion, weighing data from each individual equally. This resulted in low numbers of patients for each doselevel/occasion, and therefore high variability and low precision in parameter estimates. In contrast, in the PopPK approach, data from all patients on all occasions were used simultaneously to obtain parameter distributions for the fixed and random effects, accordingly leading to more accurate estimates. Furthermore, the PopPK provided uncertainty measures for all parameter estimates, whereas the NCA could only provide point estimates and variation measures.

It must be stated however, that in the present analysis, population estimates for basic PK parameters showed fairly good agreement between both methods. Also, the fact that performing a NCA requires less effort and can be performed much faster, does offer an advantage over performing a PopPK analysis. However, it is our opinion that the advantages discussed above demonstrate the benefits of implementation of PopPK modeling, already in phase I of drug development. It is anticipated that when data from subsequent clinical trials are included in the analysis, applying the PopPK approach will become even more advantageous, e.g. in the assessment of covariate and genotype effects.

Conclusion

In this study, we presented the first population pharmacokinetic analysis of the novel anticancer agent E7820. This analysis shows that population pharmacokinetic modeling can be used in phase I oncology trials to gather early information about pharmacokinetics. The developed PK model can be used, e.g. to simulate different dosage regimes and in the design optimalization of sampling schemes for phase II trials. Data collected from subsequent phase I/II trials should be used to update and refine the current PK model. Combining the PK model with models for that describe the pharmacodynamics (PD) of the drug, may aid in limiting toxicity.

We showed in this article that the PopPK method has marked advantages over classical non-compartmental PK analyses, such as the incorporation of sparse data and data below the LLOQ, as well as the possibility to simulate from the model. However, the NCA has the advantage of being more easily applicable, and can be applied to gain information about disposition prior to a PopPK analysis.

Copyright information

© Springer Science+Business Media, LLC 2008