Model‐based approach for methoxy polyethylene glycol‐epoetin beta drug development in paediatric patients with anaemia of chronic kidney disease

Abstract

Aims

Methoxy polyethylene glycol‐epoetin beta (continuous erythropoietin receptor activator, C.E.R.A.) is used for the treatment of anaemia in adults with chronic kidney disease (CKD). Patients treated with shorter‐acting erythropoiesis‐stimulating agents up to three times weekly can be switched to once‐monthly C.E.R.A.. Doses can be adjusted on a monthly basis based on haemoglobin (Hb) levels during the preceding period. A model‐based approach was applied to optimise C.E.R.A. development, more specifically the confirmatory trial of the paediatric plan.

Methods

Pharmacokinetic and pharmacodynamic data from a phase II paediatric study and phase II and III adult studies were analysed together using modelling and simulation to determine the pharmacokinetic/pharmacodynamic characteristics of C.E.R.A. in a broad population. Model‐based simulations of C.E.R.A. treatment outcomes in paediatric patients were performed, notably when administered subcutaneously and compared to clinical and real‐world data.

Results

Age and body weight explained differences in pharmacokinetics, while the pharmacodynamic characteristics of C.E.R.A. were similar between adult and paediatric populations. Simulated Hb levels (mean and 95% prediction interval 10.9 [10.6, 11.2] g dL⁻¹) and C.E.R.A. doses (median and 95% prediction interval 105 [72, 159] μg) 20 weeks after switching to subcutaneous C.E.R.A. were confirmed by observed real‐world data from International Pediatric Dialysis Network registries (mean Hb was 10.8 g dL⁻¹ and median C.E.R.A. dose was 100 μg).

Conclusions

These analyses have facilitated optimisation of the C.E.R.A. development programme in paediatric patients with anaemia of CKD to provide this patient population with faster access to the drug while avoiding unnecessary clinical trial exposure and related monitoring burden in children.

What is already known about this subject

• Adult patients with anaemia of chronic kidney disease switching to C.E.R.A. from other erythropoiesis‐stimulating agents receive 120 μg, 200 μg or 360 μg every 4 weeks, depending on the dose of the previous agent.

• Doses can be adjusted on a monthly basis, based on haemoglobin levels during the preceding period.

• In paediatric patients, a conversion factor has been identified to define the intravenous starting dose for C.E.R.A..

What this study adds

• The exposure‐response relationship for C.E.R.A. is similar in adult and paediatric patients.

• Model‐based simulations confirmed by real‐world data support a similar C.E.R.A. subcutaneous starting dose in paediatric patients to the intravenous dose.

• The results have helped to optimise paediatric drug development plans approved by health authorities, with reduced drug exposure and treatment burden for children.

1. INTRODUCTION

Patients with chronic kidney disease (CKD) frequently experience anaemia and require treatment with erythropoiesis‐stimulating agents (ESAs) to correct and maintain haemoglobin (Hb) levels.1, 2 Such treatment may constitute a considerable burden for patients, in that ESAs such as https://www.guidetopharmacology.org/GRAC/LigandDisplayForward?ligandId=4921 alfa, epoetin beta and darbepoetin alfa generally require frequent dosing, up to three times weekly.3, 4, 5 Methoxy polyethylene glycol‐epoetin beta (continuous erythropoietin receptor activator, C.E.R.A.) is a synthetic ESA that contains a polyethylene glycol moiety, conferring a longer half‐life compared with other ESAs and allowing stable Hb levels to be achieved with less‐frequent (once‐monthly) dosing.6, 7

C.E.R.A. has been approved in Europe and the United States for the treatment of anaemia of CKD in adults since 2007, and is indicated either intravenously (IV) or subcutaneously (SC) for the correction and maintenance of Hb levels in patients with anaemia associated with CKD both on dialysis and not on dialysis.8, 9 Adult patients receiving epoetin alfa/beta or darbepoetin alfa for maintenance of Hb levels can be switched to C.E.R.A., with a recommended C.E.R.A. starting dose of 120 μg, 200 μg or 360 μg every 4 weeks, depending on the dose of the previous ESA.8, 9 During treatment, doses can be adjusted on a monthly basis based on absolute Hb levels and changes in Hb levels during the preceding period. The target range of Hb levels is 10–12 g dL⁻¹.

In the DOLPHIN study (NH19707, NCT00717366) in a paediatric population, patients aged 5–17 years on haemodialysis with stable chronic anaemia being treated with epoetin alfa/beta or darbepoetin alfa were switched to IV C.E.R.A. for 20 weeks.10 This study established a dose conversion factor of four times the previous weekly dose (IU) of epoetin beta divided by 125, or four times the previous weekly dose of darbepoetin alfa (μg) divided by 0.55 to give the 4‐weekly starting dose (in μg) of C.E.R.A. when switching from these ESAs.10

Population pharmacokinetic (PK) analysis of phase III studies has demonstrated that the PK parameters of C.E.R.A. in adult patients remain stable over time and the same dosing regimen applies for both routes of administration (IV and SC).11 The current analysis was conducted to determine the PK and pharmacodynamic (PD) properties of C.E.R.A. in paediatric patients with anaemia of CKD on haemodialysis to assess whether they differ from those in adults and to simulate clinical outcomes in paediatric patients receiving SC C.E.R.A. to support the design of a confirmatory trial in paediatric patients.

2. METHODS

A modelling and simulation framework consisting of PK and PK/PD models (historical models) was previously developed for adult patients11 using data from three phase III randomised trials evaluating C.E.R.A. vs other ESAs in patients on dialysis who were ESA‐naïve (the AMICUS trial,12 with PK data from 135 patients treated with IV C.E.R.A.) or who were already on maintenance treatment (the PROTOS trial,13 with PK data from 143 patients receiving SC C.E.R.A., and the MAXIMA trial,14 with PK data from 122 patients receiving IV C.E.R.A.). This framework has been updated using data from two further phase II trials of SC C.E.R.A. in the anaemia correction setting, one in patients on dialysis15 (PK data from 59 patients) and one in patients not on dialysis16 (PK data from 65 patients), and from the DOLPHIN study of IV C.E.R.A. in paediatric patients10 (PK data from 63 patients). Details of the studies and data used in this analysis are shown in Table 1. In the DOLPHIN study, two conversion factors were tested sequentially.10 In group 1 (intermediate conversion factor, first 16 patients), the starting dose was 4 μg every 4 weeks for each weekly dose of 250 IU epoetin alfa/beta or 1.1 μg darbepoetin alfa. After the first 16 patients had completed at least 16 weeks of treatment, a preliminary assessment of efficacy and safety was conducted. This analysis showed that the lower limit of the 95% confidence interval for average change in Hb concentration was below −1.0 g dL⁻¹ and a second group with a conversion factor yielding higher drug exposure was tested. In this group (group 2, higher conversion factor), the starting dose was doubled to 4 μg every 4 weeks for each weekly dose of 125 IU epoetin alfa/beta or 0.55 μg darbepoetin alfa.10

Table 1.

Summary of the studies included in the analysis

Study	Phase	Route	Treatment setting	Total number of patients	Number of patients included in the analysis	Target population	Number of patients on peritoneal dialysis
BA16260	II	SC	Correction	133	59	On dialysisb	21, 19 with PK data
BA16528	II	SC	Correction	324	65	Not on dialysis	0
AMICUSa	III	IV	Correction	182	135	On dialysis	3 with PK data
MAXIMAa	III	IV	Maintenance	673	122	On dialysis	0
PROTOSa	III	SC	Maintenance	572	143	On dialysis	28, 11 with PK data
DOLPHIN	II	IV	Maintenance	64	63	On dialysis	0

Abbreviations: IV, intravenous; SC, subcutaneous.

^aUsed to developed historical models.

^b“on dialysis” means on haemodialysis by default throughout the table.

Both PK and the PK/PD models were initially developed using a population approach,11 which was also applied in this analysis.

Analyses were performed according to the following sequence:

1. PK analysis: base PK model without covariates; final PK model with covariates: age and body weight were initially tested according to the historical model11; the potential need for additional covariates was assessed; PK model qualification.

2. PK/PD analysis: Bayesian feedback; re‐evaluation of covariate effects.

3. Building of the modelling and simulation framework: implementation of PK and PK/PD models; study design, notably dose‐adjustment rules.

4. Qualification of the modelling and simulation framework and of the PK/PD model.

5. Exploratory simulations for SC C.E.R.A. and comparison to real‐world data.

2.1. PK analysis

The PK analysis was performed on 6559 data points in 587 patients: 5883 data points from 524 adults and 676 data points from 63 children. The original PK model developed from adult data was a one‐compartment model with first‐order absorption and elimination processes according to the following equations:

For SC administration: $C\left(t\right)=\frac{D}{V/F}·\frac{\mathit{Ka}}{\mathit{Ka}-\mathit{Ke}}·\left({\mathrm{e}}^{-\mathit{Ka}·t}-{\mathrm{e}}^{-\mathit{Ke}·t}\right)$

For IV administration: $C\left(t\right)=\frac{D}{V}·{\mathrm{e}}^{-\mathit{Ke}·t}$

$$\mathit{\text{Ke}}=\frac{CL}{V}$$

where:

D (μg)

= dose of C.E.R.A.Ka (day⁻¹)

= first‐order absorption rate constantKe (day⁻¹)

= first‐order elimination rate constantF

= absolute bioavailability following SC dosingCL (L day⁻¹)

= drug clearanceV (L)

= volume of distribution.At time 0, C(0)

= 0.

To avoid any aberrant results, specifically Ka being estimated to a lower value than Ke, Ka was parameterized as Ka = Kh + Ke. F, Kh (hybrid constant), CL and V are estimated parameters.

Inter‐individual variability was modelled assuming a lognormal distribution of the parameters as follows:

$$P_{i=\mathrm{\theta }·{\mathrm{e}}^{{\mathrm{\eta }}_i}}$$

where:

θ

= typical value of the PK parameter P (eg, CL) in the populationP _i

= individual value for P in the ith individualη_i

= random variable with a mean of zero and variance ω² _P.

In the update, the structural PK model (without covariates) was kept. All parameters were re‐estimated to ensure that the updated model would adequately characterize C.E.R.A. pharmacokinetics across the complete range of the data, including those obtained in paediatric patients. After reassessment of previously identified covariates of body weight and age, the need for further covariate effects to explain potential remaining differences between adult and paediatric patients was investigated. A prediction‐corrected visual predictive check using 1000 replicates of the PK dataset was used to qualify the PK model as several studies with different designs and population were included in this analysis.

2.2. PK/PD analysis

The PK/PD analysis was performed on the same patient population as the PK analysis and comprised 14 366 data points: 12 786 from adults and 1580 from paediatric patients. The original PK/PD model developed from adult data was a sequential model where individual empirical Bayes estimates of PK parameters for C.E.R.A. were used to derive the concentration of C.E.R.A. at any time (C(t)), which drove the drug effect11:

$$\mathrm{H}{\mathrm{b}}^{\prime }\left(t\right)=S\left(t\right)-S\left(t-\mathit{LS}\right)+S_{\mathrm{ESA}}$$

$$S\left(t\right)=\frac{\mathrm{H}{\mathrm{b}}_0}{\mathrm{LS}}.\left(1+\mathrm{E}\left(C\left(t\right)\right)\right)$$

$$S_{\mathrm{ESA}}=\frac{\mathrm{H}{\mathrm{b}}_0-\mathrm{H}{\mathrm{b}}_{\mathrm{SW}}}{\mathrm{LS}}\text{if}0\le t\le \mathrm{LS}\text{otherwise}{S}_{\mathrm{ESA}}=0$$

$$\mathrm{E}\left(C\left(t\right)\right)=\frac{S_{\max }·C\left(t\right)}{\mathrm{S}{\mathrm{C}}_{50}+C\left(t\right)}$$

where:

Hb'(t) (g dL⁻¹ day⁻¹)

= change in Hb concentration over time

S(t) (g dL⁻¹ day⁻¹)

= rate of production of Hb

S(t – LS) (g dL⁻¹ day⁻¹)

= rate of elimination of Hb produced one lifespan earlier

S_ESA (g dL⁻¹ day⁻¹)

= Hb loss rate due to the interruption of former ESA

Hb_SW (g dL⁻¹)

= Hb concentration at switch

time

= 0 corresponds to the switch time point and first C.E.R.A. administration

S_max

= maximum increase in Hb production rate after switch to C.E.R.A., relative to production rate in the absence of any ESA treatment

SC₅₀

= C.E.R.A. concentration at which 50% of S _max is achieved

Hb₀ (g dL⁻¹)

= Hb concentration in the absence of any ESA treatment

LS (day)

= apparent lifespan of red blood cells

Hb₀/LS (g dL⁻¹ day⁻¹)

= rate of production of Hb in the absence of any ESA treatment.

This is a semi‐physiological PK/PD model based on previous works from Krzyzanski et al,17, 18, 19 who developed the lifespan concept. CKD patients tend to have a shorter lifespan of red blood cells (around 60 days) compared to healthy people (around 120 days). Patients in DOLPHIN were treated over 20 weeks covering more than approximately two lifespans of red blood cells. This model has been developed by applying the lifespan concept to large clinical trial data using a population approach, first in patients who did not receive any previous ESA. In the maintenance setting, when patients receiving epoetin alfa/beta or darbepoetin alfa can be switched to C.E.R.A., a decrease in Hb is observed because the loss of red blood cells produced by the interruption of the previous ESA is not immediately compensated by sufficient production induced by C.E.R.A..10, 11 The maintenance setting is particularly relevant for the use of C.E.R.A. in paediatric patients as its administration is currently restricted after Hb stabilisation by another ESA in this specific population. To account for the Hb loss subsequent to the switch from a previous ESA to C.E.R.A., the term S _ESA has been added, as described in the equation above. This additional term is only accounted for during the lifespan following the treatment switch to C.E.R.A. The initial condition of the model is given by the Hb value at the time of the switch from the previous ESA to C.E.R.A., Hb(0) = Hb_sw. In this model, the endogenous Hb production is represented by Hb₀/LS and the C.E.R.A. effect is proportional to the endogenous production and added to it. S _max, SC₅₀, LS and Hb₀ were the estimated PK/PD model parameters in the initial analysis on adult phase III studies.11 This model was applied to the updated PK/PD dataset without re‐estimation of PK/PD parameters to see how the phase III model described the paediatric data, also called Bayesian feedback. Indeed, it was assumed that once differences in C.E.R.A. pharmacokinetics between adult and paediatric patients were accounted for, the exposure‐response relationship would remain the same in both populations, and so a complete re‐estimation of model parameters was not required. The validity of this assumption was checked by comparing the distribution of drug‐dependent PK/PD parameters S _max and SC₅₀ in paediatric and adult patient populations. Random effects of PK/PD parameters and their correlations were re‐estimated. Historical covariates (C‐reactive protein and ESA dose), age and body weight were explored to guide a re‐evaluation of covariate effects, as necessary. The variability in the pharmacodynamics of C.E.R.A. is huge, as shown with the inter‐subject variability associated with S _max (142% CV) and SC₅₀ (559% CV) in the previous analysis based on adult phase III studies.11 It was important to re‐evaluate both random effects and impact of covariates based on a larger population including adult phase II studies and paediatric data. Inter‐individual variability was modelled assuming a lognormal distribution as described for the PK analysis.

2.3. Qualification of the modelling and simulation framework

To qualify the PK/PD model, a modelling and simulation framework was built for the DOLPHIN study. PK and PK/PD models were implemented along with the DOLPHIN study design, notably including dose‐adjustment rules. Simulations for model qualification were performed by sampling on DOLPHIN information: empirical Bayes estimates of PK and PK/PD parameters, observed baseline characteristics, ie, body weight, previous ESA dose, Hb at switch from previous ESA to C.E.R.A. and observed C.E.R.A. starting dose; they also accounted for residual variability. Model qualification was performed using posterior predictive checks, assessing the ability of the model to simulate observed clinical endpoints in the DOLPHIN study (mean change in Hb, occurrence of Hb > 12 g dL⁻¹ during the evaluation period and C.E.R.A. dose at the end of the evaluation period). The evaluation period was from 16 to 20 weeks after the start of C.E.R.A. treatment. For each metric listed above, the observed value in DOLPHIN was compared to the 95% prediction interval derived from simulations based on 200 replicates. If the observed value was included within the 95% prediction interval, the model was considered qualified. Results were stratified by study group.

2.4. Simulations

A similar modelling and simulation framework built to qualify the final PK and PK/PD models was used to perform clinical trial simulations with IV or SC C.E.R.A.. The starting doses were resampled from observed starting IV C.E.R.A. doses from patients enrolled in group 2 of the DOLPHIN study (n = 47; one subject removed due to lack of Hb information leading to unreliable empirical Bayes estimates of PK/PD parameters) for both IV and SC simulations to ease the comparison between both routes of administration. For each route of administration (IV and SC), 200 replicates with 47 patients each were simulated. Dose adjustments used for the simulations were implemented following dose adjustment rules practised in DOLPHIN. In these simulations, dose adjustments were scheduled for 4, 8, 12, 16 and 20 weeks after treatment start. The maximum C.E.R.A. dose allowed in the SC simulations was set to 1000 μg every 4 weeks. This ceiling was defined based on the observed maximum IV C.E.R.A. dose in the DOLPHIN study (675 μg every 4 weeks), the likelihood that SC dosing of C.E.R.A. might require higher unit doses than IV dosing due to low bioavailability and the observed maximum C.E.R.A. dose given in adults recorded in the analysis dataset (1500 μg every 4 weeks). To account for potentially higher bioavailability in paediatric patients, in absence of clinical data on C.E.R.A. administered SC to paediatric patients, three simulation scenarios were performed assuming similar bioavailability between adult and paediatric patients, and 30% or 50% higher bioavailability in paediatric patients than in adults.

2.5. Comparison of simulations with real‐world data

Simulation results were challenged by comparing with real‐world data on C.E.R.A. doses and Hb levels obtained from paediatric patients treated with IV (n = 32) and SC (n = 126) C.E.R.A. in the International Pediatric Dialysis Network (IPDN) database (http://www.pedpd.org).20

2.6. Software

Population PK and PK/PD analyses were performed using nonlinear mixed effect modelling. The population PK analysis was performed in NONMEM (NONlinear Mixed Effects Modeling)21 version 7.3.0, while the present PK/PD analysis was performed using Phoenix NLME (nonlinear mixed effect) 1.3 (build 6.4.0.768) with the QRPEM (quasi‐random parametric expectation maximisation) algorithm.

PK and PK/PD model qualifications were performed in Perl speaks NONMEM (PsN)22 version 4.2.0 and in Pharsight® Trial Simulator™ version 2.2.2, respectively. PK/PD simulations were performed in Pharsight® Trial Simulator™ version 2.2.2. Exploratory data analyses and post‐processing of modelling and simulation outputs were performed using R® version 3.2.3.

The data that support the findings of this study are available from the corresponding author upon reasonable request. Part of data that support the findings of this study are available from the IPDN registry, these are aggregated data available from the authors upon permission of the IPDN registry.

3. RESULTS

Demographic and treatment characteristics of evaluable paediatric patients for the analyses are provided in Table S1.

The updated PK model for C.E.R.A. adequately described the paediatric patient C.E.R.A. concentrations. As already determined in adults (historical PK model), C.E.R.A. clearance (CL) increased with body weight, and the volume of distribution (V) increased with body weight and age. The respective expressions of clearance (L day⁻¹) and volume of distribution (L) were:

$$\mathrm{CL}=0.738·{\left(\frac{\mathrm{BW}}{67.5}\right)}^{0.761}$$

$$V=3.46·{\left(\frac{\mathrm{BW}}{67.5}\right)}^{0.612}·{\left(\frac{\mathrm{age}}{18}\right)}^{0.232}$$

where BW = individual body weight value.

After accounting for those effects, there was no remaining bias in random effects of PK parameters, suggesting that age and body weight fully explained differences in PK between adult and paediatric populations. The parameter estimates of the final PK model are shown in Table 2. A covariance term between CL and V was added to the initially developed model, and correlation between both parameters was estimated at 0.68. The random effects on Ka were not needed given the reparameterization of Ka (Ka = Kh + Ke); random effects were tested on Kh but did not provide any improvement and were not kept in the final model. The consistency of relationships between PK parameters and age and body weight ranges across adult and paediatric populations is shown in Figure 1. The model was successfully qualified using visual predictive checks in adult and paediatric patients receiving IV C.E.R.A. as shown in Figure S1 where prediction intervals (shaded area) of the simulated median and of the 5th and 95th percentiles of simulated data included corresponding observed values (lines). Typical PK simulations were performed at different dose levels reached in adult and paediatric patients at the end of the evaluation period and provided comparable C.E.R.A. exposure levels in both populations (Figure S2).

Table 2.

Parameter estimates of the adult/paediatric pharmacokinetic model

Parameter	Unit	Estimate	SE	RSE (%)	Variability (%)	Shrinkage (%)
Fixed effects
CL	L day−1	0.738	0.0231	3
V	L	3.46	0.143	4
Ka – Ke	day−1	0.198	0.0616	31
F		0.326	0.0200	6
Random effects (variance)
CL		0.202	0.0317	16	45	7
V		0.135	0.0242	18	37	16
Covariance CL – V		0.111	0.0274	25	Correlation 0.68
Inter‐occasion variability (variance)
CL		0.0160	0.00344	22	13
Covariate effects
Body weight on CL		0.761	0.0665	9
Body weight on V		0.612	0.0686	11
Age on V		0.232	0.0383	17
Residual variability (variance)
Proportional		0.146	0.00736	5	38
Additive		0.911	0.117	13

Note. To ensure that Ka was higher than Ke, Ka was modelled as Ka = Kh + Ke, the estimated parameter was thus Kh corresponding to Ka – Ke as reported in the table.

Abbreviations: CL, clearance; F, bioavailability; Ka, first‐order rate constant of absorption; Ke, first‐order rate constant of elimination; RSE, relative standard error; SE, standard error; V, volume of distribution.

Figure 1.

Parameter (individual empirical Bayes estimate)‐covariate relationships as predicted by the pharmacokinetic model. Open circles indicate data from paediatric patients and hatched circles indicate data from adult patients. The black lines describe the prediction from the pharmacokinetic model

Parameter estimates in the PK/PD model following re‐estimation of random effects and re‐evaluation of covariate effects are shown in Table 3. There was no difference in the C.E.R.A.‐specific PK/PD parameters S _max (maximum increase in Hb production rate after switch to C.E.R.A., relative to production rate in the absence of any ESA treatment) and SC₅₀ (C.E.R.A. concentration at which 50% of S _max is achieved) between paediatric and adult patients (Figure 2). The non‐C.E.R.A.‐specific parameters, Hb concentration in the absence of ESA treatment (Hb₀) and apparent red blood cell lifespan tended to be lower in paediatric patients. Age and body weight could both impact the system‐specific parameters, LS and Hb₀, and were tested on both parameters. The currently reported model, with a body weight effect on Hb₀, offered the best fit to the data. The respective expressions of SC₅₀ (ng mL⁻¹) and Hb₀ (g dL⁻¹) are:

$${\mathrm{SC}}_{50}=0.898·{\left(\frac{\mathrm{ESA}}{6000}\right)}^{0.389}$$

where ESA = individual dose of the previous epoetin before switching to C.E.R.A.. Darbepoetin doses were converted into epoetin equivalent doses.

$${\mathrm{Hb}}_0=9.3·{\left(\frac{\mathrm{BW}}{67.5}\right)}^{0.144}$$

where BW = individual body weight value.

Table 3.

Parameter estimates of the adult/paediatric pharmacokinetic/pharmacodynamic model

Parameter	Unit	Estimate	SE	RSE (%)	Variability (%)	Shrinkage (%)
Fixed effects
S max		0.425 fixed
SC50	ng mL−1	0.898 fixed
LS	day	61.3 fixed
Hb0	g dL−1	9.3 fixed
Random effects (variance)
S max		2.03	0.130	6.4	142	15
SC50		4.95	0.343	6.9	222	16
LS		0.283	0.0200	7.1	53	16
Hb0		0.0596	0.00425	7.1	24	25
Covariate effects
ESA dose on SC50		0.389	0.0234	6.0
Body weight on Hb0		0.144	0.0102	7.1
Residual variability (standard deviation)
Additive	g dL−1	0.583	0.00116	0.2

Abbreviations: C.E.R.A., continuous erythropoietin receptor activator; ESA, erythropoiesis‐stimulating agent; Hb, haemoglobin; Hb₀, Hb concentration in absence of any ESA treatment; LS, apparent lifespan of red blood cells; RSE, relative standard error; SC₅₀, C.E.R.A. concentration at which 50% of S _max is achieved; SE, standard error; S _max, maximum increase in Hb production rate after switch to C.E.R.A., relative to production rate in absence of any ESA treatment.

Figure 2.

Individual empirical Bayes estimate values of pharmacokinetic/pharmacodynamic parameters in adult (n = 524) and paediatric (n = 63) patients. Hb₀, Hb concentration in absence of any ESA treatment; LS, apparent lifespan of red blood cells; SC₅₀, C.E.R.A. concentration at which 50% of S _max is achieved; S _max, maximum increase in Hb production rate after switch to C.E.R.A., relative to production rate in the absence of any ESA treatment

Table 4 demonstrates the qualification of the modelling and simulation framework, using posterior predictive checks, on three endpoints: mean change in Hb from baseline (primary clinical endpoint in the DOLPHIN study), occurrence of Hb > 12 g dL⁻¹ during the evaluation period and median C.E.R.A. doses at the end of the evaluation period in both dose groups.

Table 4.

Posterior predictive check of the pharmacokinetic/pharmacodynamic model in paediatric patients from the DOLPHIN study

Dose group	Simulations (metric [95% prediction interval])	Observations (metric [95% confidence interval])
	Primary endpoint: mean change in Hb between baseline and evaluation period a (g dL −1 )
Group 1	−0.66 [−1.21, −0.11]	−0.74 [−1.32, −0.16]
Group 2	0.07 [−0.22, 0.43]	−0.09 [−0.45, 0.26]
	Patients experiencing Hb > 12 g dL −1 at least once during the evaluation period (%)
Group 1	21 [5, 45]	16.7
Group 2	49 [36, 66]	36.1
	Median C.E.R.A. dose at the end of the evaluation period (μg)
Group 1	68 [36, 127]	64
Group 2	84 [60, 123]	120

Note. Group 1: once every 4 weeks using C.E.R.A. doses (in μg) of four times the previous weekly darbepoetin alfa dose (in μg) divided by 1.1, or four times the previous weekly epoetin dose (in IU) divided by 250.

Group 2: once every 4 weeks using C.E.R.A. doses (in μg) of four times the previous weekly darbepoetin alfa dose (in μg) divided by 0.55, or four times the previous weekly epoetin dose (in IU) divided by 125.

Abbreviations: C.E.R.A., continuous erythropoietin receptor activator; Hb, haemoglobin.

^aThe evaluation period occurred from 16 to 20 weeks after the start of C.E.R.A. treatment.

Model‐based simulations of Hb concentration over time in paediatric patients demonstrated good overlap between SC and IV administration after 4 weeks, assuming 30% or 50% higher bioavailability in paediatric compared with adult patients (Figure S3). A sensitivity analysis explored variants of SC simulations. One set of simulations tested the above‐mentioned three simulation scenarios, but based on 25 subjects (sampled from group 2 patients from DOLPHIN) instead of 47; this led to similar results (Table S2) but with larger prediction intervals. Another set of simulations, also based on 25 subjects whose nominal SC C.E.R.A. starting dose was adjusted upwards to compensate for the 32.6% bioavailability, led naturally to higher simulated doses and Hb levels (Table S3).

A 50% increase in bioavailability in paediatric compared with adult patients was considered to be the most likely scenario, based on the darbepoetin experience,23, 24 and this was confirmed by the real‐world data. Indeed, based on this scenario (ie, 50% increase in bioavailability in paediatric compared with adult patients), simulations of Hb levels and IV and SC C.E.R.A. doses using the conversion factor established by the DOLPHIN study were consistent with values obtained from IPDN registry data from 158 paediatric patients with a median age of 12.9 years (range 0.3‐26.9) (SC C.E.R.A., n = 126) or 14.8 years (range 1.5‐21.8) (IV C.E.R.A., n = 32) (Figure 3 and Table 5). Simulated mean Hb levels from the PK/PD model were 10.9 g dL⁻¹ (95% prediction interval 10.6, 11.2) for SC C.E.R.A. and 11.0 g dL⁻¹ (10.6‐11.3) for IV C.E.R.A. in paediatric patients, in agreement with those reported in the IPDN registry (10.8 g dL⁻¹ and 10.5 g dL⁻¹). Simulated median monthly IV and SC C.E.R.A. doses following stabilisation of Hb were 105 μg (95% prediction interval 72, 159) for SC C.E.R.A. and 84 μg (95% prediction interval 60, 123) for IV C.E.R.A., also in agreement with those reported in the IPDN registry (100 μg and 80.4 μg, respectively).

Figure 3.

Simulated outcomes and 95% prediction intervals in patients switched to IV or SC C.E.R.A. using the conversion factor established in the DOLPHIN study compared with median values from 32 patients treated with IV C.E.R.A. and from 126 patients treated with SC C.E.R.A. in the IPDN registry. Simulated outcomes for IV C.E.R.A. are also compared with the observed median in 36 paediatric patients with CKD switched from epoetin alfa/beta or darbepoetin alfa to IV C.E.R.A. in the DOLPHIN study

Table 5.

Simulations of mean Hb, mean change in Hb and dose distribution at the end of the evaluation period (week 20)

Scenarios	SC simulations	Observations from IPDN
Mean change in Hb from baseline (g dL −1 ) and 95% prediction interval
F	−0.26 [−1.03, 0.52]	NA
1.3F	−0.20 [−1.13, 0.63]
1.5F	−0.11 [−0.90, 0.70]
Mean Hb (g dL −1 ) and 95% prediction interval
F	10.8 [10.5, 11.1]	10.8
1.3F	10.9 [10.6, 11.2]
1.5F	10.9 [10.6, 11.2]
Median dose a (μg every 4 weeks) and 95% prediction interval
F	127 [94, 178]	100
1.3F	114 [82, 169]
1.5F	105 [72, 159]

Abbreviations: C.E.R.A., continuous erythropoietin receptor activator; F, assuming adult bioavailability; 1.3F and 1.5F,, assuming 30% and 50% increase in bioavailability, respectively, compared with adults; Hb, haemoglobin; IPDN, International Pediatric Dialysis Network; NA, not available; SC, subcutaneous.

^aC.E.R.A. doses are adjusted according to Hb levels.

4. DISCUSSION

The updated population PK model adequately described paediatric data. Parameter estimates were found to be consistent with those obtained using phase III data only (historical PK model),11 especially CL, which was estimated at 0.74 L day⁻¹ (vs 0.75 L day⁻¹). V and bioavailability of the SC route were slightly lower, ie, 3.5 L and 0.33, respectively, compared with phase III estimates (4.7 L and 0.39, respectively). Covariates in the model remained the same as in the historical PK model. Estimates of body weight effects on CL and V were 0.76 and 0.61, respectively. While the effect on CL matches the allometric value (0.75),25 the effect on V is lower than the allometric value (1.00), probably due to the age effect on V, age being highly correlated to body weight. In fact, the estimate of the effect of body weight on V was 0.85 in an alternative model that did not have the age effect. However, combining weight and age effects on V provided a better description of the data. Body weight and age effects fully explained the difference in C.E.R.A. pharmacokinetics between adult and paediatric patients. The PK model showed that the different dose levels reached in adult and paediatric patients at the end of the evaluation period provide comparable C.E.R.A. exposure levels (simulations in typical paediatric and adult patients shown in Figure S2) in both populations, indicating that the exposure‐response relationship is likely to be similar.

The PK/PD model developed with adult phase III data (historical PK/PD model) could be applied successfully to paediatric data. The large variability in individual PK/PD parameters already shown in the analysis in adults11 has been confirmed by this analysis, justifying the need for individual C.E.R.A. dose adjustment based on Hb levels. The effect of previous ESA dose on SC₅₀ has also been confirmed: the higher the ESA dose, the higher the C.E.R.A. exposure needed to produce a similar effect when switching to C.E.R.A.. The magnitude of the estimated effect is also consistent with the previous estimate. An effect of body weight on Hb before any ESA treatment, ie, Hb₀, was found to be consistent with generally lower Hb levels in the paediatric population. In a typical 9‐year‐old patient, with a body weight of 25 kg, representing the 6‐11 years age category, Hb₀ is expected to be 8.1 g dL⁻¹. This may explain why younger patients required higher doses relative to their starting dose compared to older patients10 to achieve the same target of Hb of 10–12 g dL⁻¹.

No difference in C.E.R.A.‐specific PK/PD parameters, ie, S _max and SC₅₀, in paediatric and adult patients was observed, confirming that the C.E.R.A. exposure‐response relationship is similar in both populations.

Both PK and PK/PD models have been qualified using predictive checks. Table 4 shows that the model was qualified according to the three metrics in both groups. With a target range of Hb of 10‐12 g dL⁻¹, the occurrence of Hb > 12 g dL⁻¹ is a relevant safety endpoint, as the risk of cardiovascular events increases when the Hb level exceeds this value. On account of the dose‐titration based on Hb levels, it was expected that the primary endpoint (mean change in Hb between the baseline and evaluation periods) and the occurrence of Hb > 12 g dL⁻¹ would be accurately predicted. The prediction of the median doses at the end of the evaluation period represented a suitable metric to further assess the model's predictive performance. Median doses at the end of the evaluation period were predicted with good precision with narrow 95% predictions intervals: (36, 127) μg and (60, 123) μg for groups 1 and 2, respectively. Those qualification results have to be contrasted by the wide overall range of observed doses in DOLPHIN: from 16 μg to 675 μg. This model qualification allowed exploratory simulations to support the use of C.E.R.A., notably when administered subcutaneously.

Future use of the model has to account for its limitations and extrapolations beyond the usual design of clinical trials in the CKD indication have to be carefully handled. Indeed, it is important to adequately characterize the switch from one ESA to the next, and while the empirical approach used here was appropriate, it may not apply to all situations. The use of real‐world data will certainly contribute to that effort with patient data recorded over several years and potentially covering different ESA treatments.

Simulations of clinical outcomes of C.E.R.A. when administered subcutaneously were conducted to support a paediatric phase II study design of the ongoing SKIPPER study (NH19708, NCT03552393). The simulations support the current dosing strategy of once every 4 weeks for the maintenance treatment of anaemia in paediatric patients with CKD using C.E.R.A. doses (in μg) of four times the previous weekly darbepoetin alfa dose (in μg) divided by 0.55, or four times the previous weekly epoetin dose (in IU) divided by 125. As in adults, it is expected that the same starting dose of C.E.R.A. can be used for IV and SC administration when switching from epoetin alfa/beta or darbepoetin alfa.

As the bioavailability of C.E.R.A. is likely to be higher in paediatric patients than in adults, in the absence of clinical data on C.E.R.A. administered SC to paediatric patients, several scenarios tested assumptions on bioavailability changes in paediatric patients, ie, no change, 30% or 50% increase. Darbepoetin alfa bioavailability has been reported to be 54% in paediatric patients compared with 37% in adult patients, a 46% increase consistent with the assumed 50% increase in bioavailability in paediatric patients in the simulations.23 Increased bioavailability in paediatric patients has also been reported for epoetin alfa/beta.26, 27 Simulations of Hb levels over time assuming 50% increase in bioavailability showed almost complete overlap compared with IV simulations. Comparing simulated data with real‐world data from the IPDN registries supports the results and the validity of our approach and served as an external validation of the modelling and simulation framework. Data and simulations indicated that the IV and SC dosing regimen for maintenance of Hb when switching from another ESA (4 μg every 4 weeks for each weekly dose of 125 IU epoetin alfa/beta or 0.55 μg darbepoetin alfa) is fully appropriate for paediatric patients. In clinical practice, ESA treatments are individualised by paediatricians and doses are adjusted upwards or downwards based on Hb levels in each patient to achieve Hb levels within the 10–12 g dL⁻¹ target range.

The ongoing SKIPPER study will evaluate C.E.R.A. administered subcutaneously to 40 paediatric patients with anaemia of CKD using the conversion factor established in the DOLPHIN study. In the clinical development of C.E.R.A., the Pediatric Study Plan (US Food and Drug Administration) and the Pediatric Investigation Plan (European Medicines Agency) were revised on the basis of these modelling and simulation data, as well as clinical efficacy and safety data gained since its approval more than 10 years ago. As a result of this optimisation, the design for study NH19708, which originally involved 150 patients and included an active control, could be changed to a single‐arm study enrolling 40 patients, thereby preventing unnecessary clinical trial exposure and related monitoring burden in children with anaemia of CKD and also providing paediatric patients with faster access to SC C.E.R.A..

COMPETING INTERESTS

P.C., A.W., G.S., S.M.R., B.R. and N.F. are employees of F. Hoffmann‐La Roche Ltd. M.E. is an employee of Genentech Inc. P.C. was an employee of Certara Consulting Services, Certara, Princeton, NJ, USA, and contractor to F. Hoffmann‐La Roche Ltd at the time of this work. P.C. and B.R. hold stocks in F. Hoffmann‐La Roche Ltd. F.S. has received consulting and speaker honoraria from F. Hoffmann‐La Roche Ltd. All authors received medical writing support funded by F. Hoffmann‐La Roche Ltd.

CONTRIBUTORS

P.C., B.R., S.M.R., C.S., F.S. and G.S. designed the research. P.C., F.S., S.M.R., C.S. and G.S. performed the research and analysed the data. P.C., B.R., G.S., A.W., N.F. and B.W. interpreted the data. P.C. wrote the manuscript. All authors reviewed the manuscript and approved the final version for submission.

Supporting information

Figure S1 Prediction‐corrected visual predictive check of the PK model in (A) adult and (B) paediatric patients receiving IV C.E.R.A.. C.E.R.A., continuous erythropoietin receptor activator; IV, intravenous; PK, pharmacokinetic

Figure S2 Typical PK simulations in patients in different age categories receiving C.E.R.A. for maintenance of Hb levels

Figure S3 Time course of simulated mean Hb concentrations in paediatric patients following IV or SC administration of C.E.R.A., based on equivalent bioavailability between adult and paediatric patients (A) and 30% (B) or 50% (C) higher bioavailability in paediatric patients. Horizontal dotted line: target range of Hb (10–12 g dL⁻¹). Vertical dotted line: end of evaluation period at 20 weeks. Darkest area represents overlap of 95% prediction intervals for IV and SC administration. C.E.R.A., continuous erythropoietin receptor activator; Hb, haemoglobin; IV, intravenous; SC, subcutaneous

Table S1 Baseline demographic and treatment characteristics of evaluable paediatric patients with chronic kidney disease on haemodialysis

Table S2 Simulations of mean change in Hb and dose distribution at the end of the evaluation period (week 20) based on 25 subjects

Table S3 Simulations of mean change in Hb and dose distribution at the end of the evaluation period (week 20) based on 25 subjects whose C.E.R.A. nominal SC starting dose was adjusted upwards to compensate for the 32.6% bioavailability (eg, SC starting dose = IV starting dose/0.326 for scenario F)

Chanu P, Schaefer F, Warady BA, et al. Model‐based approach for methoxy polyethylene glycol‐epoetin beta drug development in paediatric patients with anaemia of chronic kidney disease. Br J Clin Pharmacol. 2020;86:801–811. 10.1111/bcp.14186