1 Introduction
Ferumoxytol is approved for the treatment of iron-deficiency anaemia (IDA) in adult patients with chronic kidney disease (CKD). CKD is characterized by a decreased glomerular filtration rate, increased urinary albumin excretion, or both, and is an increasing public health issue. The prevalence of CKD is estimated at 8–16 %, worldwide [
1]. IDA is common in patients with CKD and results from decreased iron availability, blood loss and increased iron utilization for erythrocyte production in response to erythropoietin-stimulating-agent utilization in this patient group [
2,
3]. Correction of iron deficiency (ID) through iron replacement therapy is essential in the optimal management of CKD patients [
4].
Recently, ferumoxytol has been investigated for the treatment of IDA in a broader population. Multiple conditions may lead to ID, including poor nutrition status and/or diseases that restrict iron absorption (such as CKD, inflammatory bowel disease or congestive heart failure) [
5]. Irrespective of the cause, ID leads to adverse effects in patients, including anaemia and its well-documented complications. Administration of iron preparations to patients with IDA typically results in significant increases in haemoglobin [
6,
7].
Ferumoxytol is a colloidal solution of polyglucose sorbitol-carboxymethylether-coated superparamagnetic iron oxide particles [
8] and provides a source of bioactive iron [
9‐
11]. Each 510 mg ferumoxytol dose is injected over approximately 1 min. A second injection is to be administered 2–8 days after the first dose.
Approval of ferumoxytol for the treatment of IDA in adult patients with CKD was based on 11 clinical studies; seven in subjects with CKD (stages 1–5 and 5D) and four in non-CKD subjects. In three studies, two of which were performed in healthy volunteers (HV studies) and one performed in subjects with CKD stage 5D on haemodialysis (CKD study), samples for plasma pharmacokinetics (PK) were obtained.
Data from one study in HVs was previously subjected to a population PK (popPK) analysis. A two-compartment model with zero-order input and Michaelis–Menten elimination best described the PK data from this study [
12]. The model also confirmed a previously identified relationship between body weight and volume of distribution.
In the CKD study, during the first 3 h of the haemodialysis procedure ferumoxytol plasma concentrations either declined minimally or, for the 250 mg dose, increased slightly at time points following the end of intravenous ferumoxytol administration. This observation was explained by changes in plasma volume during haemodialysis, which might decrease volume of distribution for ferumoxytol [
13,
14]. However, the hypothesis that concentration increases could be fully explained by these haemodynamic changes had never been explored using a model-based approach.
The analysis objective was therefore to bridge ferumoxytol PK between HVs and CKD patients through a better understanding of the effects of haemodialysis on the PK time course of ferumoxytol via a popPK modelling approach. The analysis was performed with the intention to ultimately gain better insight into the likely ferumoxytol exposures in the general IDA population, for whom PK data are not available.
2 Methods
2.1 Ethics
Informed consent was obtained from all study participants. The studies were approved by the local Ethics Committees and were carried out in concordance with the International Conference on Harmonisation (ICH) Guidelines for Good Clinical Practice [
15].
2.2 Analysis Population and Data
An overview of the three clinical studies used in the analysis is presented in Table
1. Studies A and B were conducted in HVs. Study A was an ascending single-dose study with dosing on a per kilogram basis [
16], whereas study B, a thorough QT study, used two ferumoxytol doses of 510 mg administered 24 h apart [
12]. Study C investigated two different single doses (125 and 250 mg) in CKD patients stage 5D during haemodialysis [
16]. The HV studies provided PK data from 91 subjects (out of 93 subjects exposed), and the CKD study provided additional PK data from 20 subjects.
Table 1
Overview of clinical studies used in popPK analysis
| Phase I, randomized, double-blind, placebo-controlled, single-centre, ascending dose | Healthy subjects | Part 1: | | Part 1: | Pre-dose, 5, 10, 15, and 30 min, and 1, 4, 8, 24, 48, 72, and 168 h (n = 12) |
1 mg/kg | 8 | 60 mg/min |
2 mg/kg | 8 | Part 2: |
4 mg/kg | 8 | 30 mg/20 s |
Part 2: | | 30 mg/10 s |
4 mg/kg | 11 | 30 mg/s |
| Phase I, randomized, double-blind, active- and placebo-controlled, parallel group, single-centre | Healthy subjects | 2 × 510 mg | 58 | 17 mL over 17 s | Pre-dose, 5, 10, 15 and 30 min, 1, 4, 8, 12, 24, 24.08, 24.167, 24.25, 24.5, 25, 28, 32, 36, 48, 72, 96, 120, and 144 h after first dose (n = 23) |
| Phase I, open-label, non-randomized, parallel group, ascending dose, single-centre | CKD stage 5D on HD | 1 × 125 mg | 10 | Over 5 min within 30 min after dialysis start | Pre-dose, 5, 10, 15, and 30 min, and 1, 2, 3, 48, and 96 h (n = 10) |
1 × 250 mg | 10 |
2.3 Analytical Methods
Plasma from blood samples was collected within 30 min of collection and was kept frozen (−20 °C) until analysis. Samples were analysed at 39.5 °C using relaxivity measurements on a 20 MHz NMR. Method validations using spiked plasma samples showed that the data was accurate (97–112 %) over the range of concentrations studied, with a coefficient of variation between 0.5 and 16.5 % (repeatability). The lower limit of quantification (LLOQ) was set at five times the mean relaxivity of normal pooled plasma: 5.83, 6.0 and 11.16 μg/mL for studies A, B and C, respectively.
2.4 Pharmacokinetic Analysis
2.4.1 Development of Structural and Error Model
PopPK analysis of ferumoxytol plasma concentrations was performed using NONMEM software [
17] (version 7, ICON Development Solution LLC, Hanover, MD, USA), with visualization performed in R (version 2.12.2). Samples with ferumoxytol concentration less than LLOQ were treated as missing. The first-order conditional estimation method with interaction was used throughout model development. Model development was initiated using a model previously developed for ferumoxytol study B [
12]. This model was extended by exploring additional between-subject variability (BSV), assuming lognormal distribution of individual parameter estimates and additive/proportional residual error structures, in addition to exploring structural elements of the model. Models were evaluated using standard goodness-of-fit plots (observed concentrations versus population and individual-predicted concentrations and plots assessing the conditional and individual weighted residuals), decrease in objective function value (OFV), parameter variance, individual plots and biological plausibility of parameter estimates. In order to evaluate whether the model could reproduce the observed data with respect to central tendency and observed variability, visual predictive checks (VPCs) [
18] were performed during model development.
2.4.2 Covariate Model Development
The effect of the following covariates on ferumoxytol PK was investigated:
-
Demographics: age, body weight (WGT), body mass index (BMI), sex (SEX), ethnicity
-
Study population (i.e. healthy subjects vs. CKD patients)
-
Measures of iron: baseline serum iron, ferritin, transferrin saturation (TSAT), total iron binding capacity (TIBC), unsaturated iron binding capacity (UIBC), haemoglobin
-
Haemodialysis (yes/no)
-
Body weight loss due to haemodialysis (WLO, obtained from pre- and post-dialysis weight assessment, zero for all non-haemodialysis subjects)
As a general rule, the confounding effects of highly correlated covariates were considered in covariate identification and the interpretation of covariate effects. A covariate was tested if justified from plots showing individual empirical Bayes estimates of the parameters of interest against possible covariates. In addition, physiologically plausible relations (e.g. measures of iron against parameters related to ferumoxytol clearance from the circulation, body weight on volume, haemodialysis on clearance or volume) were tested irrespective of the visual plot assessment. Models were compared using a likelihood ratio test, using the minimum OFV as an approximation to −2 times the log-likelihood. The covariate analysis followed the forward inclusion (p ≤ 0.05)/backward elimination (p ≤ 0.001) procedure.
Continuous covariates were implemented into the model using a linear relation, centered around a typical covariate value, and expressed as percentage change:
$$ \theta_{\text{ind}} = \theta_{\text{pop}} \left( {1 + \frac{{\left( {{\text{Cov}} - {\text{Cov}}_{\text{norm}} } \right)\theta_{\text{Cov}} }}{100}} \right) $$
(1)
where
\( \theta \)
ind is the individual model-predicted PK parameter (e.g. clearance) for an individual with covariate value Cov,
\( \theta \)
pop represents the population central tendency for the respective PK parameter, Cov
norm represents the normalization value (e.g. population median) of the covariate, and
\( \theta \)
Cov represents the covariate effect in percentage.
Categorical covariates were incorporated using a fractional change model, estimating percentage difference to the reference category. For covariates with two categories (encoded as 1 and 2), this would be described by the following equation:
$$ \theta_{\text{ind}} = \theta_{\text{pop}} \left( {1 + \frac{{\left( {{\text{Cov}} - 1} \right)\theta_{\text{Cov}} }}{100}} \right) $$
(2)
where
\( \theta \)
ind is the individual model-predicted PK parameter (e.g. clearance) for an individual with covariate value Cov,
\( \theta \)
pop represents the popPK parameter of the reference category, and
\( \theta \)
Cov represents the covariate effect in percentage.
2.5 Model Evaluation
The final model was evaluated by VPC [
18] and non-parametric bootstrapping methods.
For the VPC, new individual plasma concentration–time profiles were simulated based on 200 simulations from the original dataset and the parameter estimates from the final model, respectively. All measured concentrations were visually compared with the corresponding median and 90 % prediction interval. The plots were stratified by treatment, defined as dose in mg.
The non-parametric bootstrap re-sampling technique was applied to assess the robustness of the model. Similar to VPC, sampling was performed stratified on treatment to assure a similar population in each data set. The final model was fit to 1,000 bootstrap data sets. Results were evaluated by means of summary statistics and comparison with the final model-predicted parameter estimates, using final parameter estimates for all runs.
2.6 Simulations and Statistical Analysis
The final model was used to simulate plasma concentration–time profiles with the intention of comparing ferumoxytol exposures in HVs with those of patients with CKD. For CKD patients on haemodialysis, PK profiles were simulated such that drug administration took place after completion of 1 h of haemodialysis, as per the product label [
19]. For comparison, simulations were also performed following a single dose in healthy subjects and in CKD patients without haemodialysis.
To create the simulation data set, three subsets were initially created which used the same number of subjects and same covariate information as in the data sets for studies B and C. For CKD patients not on haemodialysis, WLO was set to zero. The data set merged from all subsets was simulated 100 times, using the final covariate model.
To illustrate the approved dosing regimens, an additional simulation was performed for the combined data set of HVs and CKD patients not on haemodialysis, at a dose of 510 mg. For each simulation scenario, ferumoxytol was administered twice: once on day one, followed by a second administration 2, 5 or 8 days later.
All simulated profiles were subjected to a non-compartmental analysis (NCA) using Pheonix WinNonlin 6.3 (Pharsight Corporation, St Louis, MO, USA), and the PK parameters generated were summarized using descriptive statistics.
4 Discussion
The described popPK model was developed in an effort to bridge ferumoxytol plasma PK across populations through a model-based approach. The present model is an expansion of a previously available two-compartment model with saturable elimination [
12], using additional data from healthy subjects (study A) and CKD patients on haemodialysis (study C). Some minor modifications were introduced into the model, e.g. a Hill factor was temporarily included on the Michaelis–Menten elimination term and models for BSV and residual error were reassessed. In addition, the influence of body weight on central volume was included during base model development as this covariate had previously been related to central volume. The final model was a two-compartment model with a concentration-dependent maximum effect (
E
max) term used to describe capacity-limited ferumoxytol elimination from plasma. The model resulted in adequate characterization of the ferumoxytol data under most conditions. Small doses of 1 mg/kg (approximately 70 mg) were overpredicted by the model, which was considered acceptable given that the approved dose of 510 mg is about sevenfold higher.
The final parameter estimates suggest that ferumoxytol is mainly constrained to plasma volume, with a total estimated volume of 3.13 L [
23]. This was expected given the large molecular weight of ferumoxytol (750 kDa), and is in line with previous results [
12] which reported a similar volume of distribution of 3.15 L. As in the previous analysis, a saturable elimination process was found to adequately describe ferumoxytol plasma concentrations, and absolute values in
V
max and Km differed only slightly from previous results.
Different covariate relations were incorporated into the current model in an attempt to explain the BSV in model parameters. While none of the baseline laboratory values related to iron metabolism displayed a significant relationship to any of the model parameters across the ranges studied, the demographic parameters sex and body weight were related to central volume of distribution. The relationship between body weight and volume of distribution had been reported previously, with a relative increase in
V1 of 0.84 % per kilogram body weight [
12]. The slightly smaller relative increase in
V1 of 0.61 % per kilogram body weight identified in this analysis might be explained by the additional influence of sex on volume, as males, in addition to their general difference in body composition, tend to be heavier than females. Sex was not investigated as a potential covariate in the previously published model [
12], thus the results of the current analyses are considered to be plausible. The European Summary of Product Characteristics for ferumoxytol [
24] includes dose adjustment for patients with a body weight of less than 50 kg. The identified effects of body weight and sex on central volume are not considered to warrant any further dose adjustment.
Some identified covariates were specific to the haemodialysis process. Prior to this analysis, it had been assumed that central volume would change during the course of haemodialysis due to the fluid loss, and this hypothesis was tested during model development. A typical volume reduction of 0.59 L over the haemodialysis period of 3 h was estimated. This is in line with reported blood volume reduction of ~10 % during haemodialysis [
20]. In addition, the extent of weight loss during haemodialysis was identified as an indicator of the initial central volume as subjects with larger differences between pre- and post-dialysis weight initially had a higher volume of distribution. From a physiological point of view, this relationship appears reasonable as a higher weight loss would be expected in subjects with a high fluid retention and thus higher volume at the start of dialysis. In principle, a relationship between WLO and VSLOPE might also be reasonable as most dialysis machines are generally volumetric [
25], meaning they allow dialysate pressure to change to achieve the prescribed target weight. Indeed, when using such equipments, weight loss can occur in a linear manner per unit of time with high precision. However, as BSV on VSLOPE was not included during model development, its relationship with WLO was not tested. Remaining plasma PK variability, which is currently described using BSV terms, indicates that other covariates not included in the present analysis could assist in further reducing unexplained variability.
It is acknowledged that the developed model is empirical in nature. This means that ferumoxytol plasma clearance is considered to mostly represent iron sequestration into the reticuloendothelial system and not a systemic clearance [
26]. Covariate analysis showed that baseline iron panel parameters did not influence plasma ferumoxytol PK. Differences in the plasma concentration–time profiles across populations could be explained by the effects of haemodialysis on the central volume of distribution alone, indicating comparable ferumoxytol plasma PK between populations, even if iron panel baseline values differ. It should nonetheless be noted that the sample size of the CKD population included in the model was limited. Therefore, the results presented in this manuscript should be regarded as supportive evidence for the similarities in ferumoxytol plasma PK between populations, not as proof thereof. It should also be noted that the iron disposition itself has not been investigated as part of this popPK analysis. While the final model was considered appropriate for the intended purpose of describing and comparing ferumoxytol plasma PK across populations, more physiological approaches may be warranted to better describe the fate of the iron once it has been released from the ferumoxytol complex, including potential differences between HVs and CKD populations.
Simulation of repeated dosing with varying dosing intervals demonstrated that ferumoxytol accumulation is small. Simulations were also performed to illustrate exposure differences that arise as a result of haemodialysis and to compare these with exposures in HVs and non-haemodialysis CKD patients. While maximum concentrations and AUC values were marginally lower for the haemodialysis patients, no difference in exposure was predicted between HVs and non-haemodialysis CKD patients.
Overall, CKD is an example of a chronic disease, with a predictable prognosis and course, where IDA can be caused by decreased iron availability, blood loss and increased iron utilization in response to erythropoietin-stimulating-agent utilization [
2,
3]. It was therefore an appropriate population to explore PK via modelling approaches and to extrapolate this to an all-cause IDA population, where ID is caused by a variety of mechanisms. Given that the differences in plasma PK profiles between CKD patients and HVs are not related to intrinsic factors and were overall very marginal, it is expected that the PK of these two groups is representative of that of other populations, including patient subgroups of all-cause IDA, provided there are no other extrinsic factors causing clinically significant perturbations on the PK parameters, in particular
V1 (e.g. extreme blood loss). This bridging strategy was used to support the Marketing Authorization Application for ferumoxytol in the all-cause IDA indication, and the methodology was deemed as acceptable to this Regulatory Agency for registration and labelling purposes.
5 Conclusions
Body weight and sex were found to influence the central volume of distribution but did not warrant any further dose adjustment. Differences in plasma PK profiles between HVs and CKD patients with haemodialysis could be fully explained by the volume loss during haemodialysis, and it was shown that the overall effect of haemodialysis on ferumoxytol PK is small.
The results from the present popPK meta-analysis support the hypothesis that underlying pathology investigated in this analysis is not relevant for explaining variability in plasma PK, and that CKD patients are similar to HVs. It is thus expected that the PK of these two groups is representative of other populations, including patient subgroups with all-cause IDA. The analysis thus increased the understanding of the likely ferumoxytol plasma exposures in the general IDA population and provided valuable support for the bridging strategy in the respective Marketing Authorization Application for ferumoxytol.