Bevacizumab dosing strategy in paediatric cancer patients based on population pharmacokinetic analysis with external validation.

AIM: The aim of the present study was to evaluate the pharmacokinetics of bevacizumab and various dosing strategies for this agent in paediatric patients.
METHODS: Data were collected from 232 paediatric patients (1971 concentrations) in five studies, with a wide range of age (0.5-21 years), body weight (BWT; 5.9-125 kg), and regimens (5-15 mg kg(-1) biweekly or triweekly). Data from 152 patients (1427 concentrations) and 80 patients (544 concentrations) were used for model building and external validation, respectively. Steady-state exposure was simulated under BWT-based, body surface area (BSA)-based, ideal body weight (IBW)-based, and tier-based doses. NONMEM and R were used for analyses.
RESULTS: Typical estimates of clearance, central volume of distribution (V1), and median half-life were 9.04 ml h(-1) , 2851 ml, and 19.6 days, respectively. Clearance decreased with increasing albumin. Clearance and V1 increased with BWT and were higher in male patients. Clearance and V1 were lower in children with primary central nervous system (CNS) tumours than in children with sarcomas, resulting in 49% higher trough (C min) and 29% higher peak (Cmax) concentrations. BWT-adjusted clearance and V1 remained unchanged across ages. Paediatric C min was similar to adult C min under all dosing strategies. Paediatric Cmax exceeded adult Cmax under tier-based doses.
CONCLUSIONS: BWT-adjusted pharmacokinetic parameter estimates in paediatric patients were similar to those in adults, and similar across ages. Bevacizumab exposure was higher in children with primary CNS tumours than in children with sarcomas. BSA-based, IBW-based, and tier-based doses offered no substantial advantage over the BWT-based dose currently used in adults for bevacizumab. Given the similarity in pharmacokinetics among many monoclonal antibodies, this may help to develop practical paediatric dosing guidelines for other therapeutic antibodies.

What is Already Known About this Subject

Bevacizumab pharmacokinetics and dosing guidelines have not been comprehensively investigated in paediatric patients.

Multiple strategies are currently used for dosing therapeutic antibodies in children.

Given the similarity in pharmacokinetics among many monoclonal antibodies, developing appropriate and practical paediatric dosing guidelines for bevacizumab may inform other therapeutic antibodies.

What this Study Adds

Bevacizumab pharmacokinetics is similar between paediatric and adult patients and remains unchanged across ages in children.

Bevacizumab exposure was higher in children with primary CNS tumours than in children with sarcomas.

BSA‐based, IBW‐based, and tier‐based doses offered no substantial advantage over the BWT‐based dose that is currently used for bevacizumab in adults.

Introduction

Bevacizumab (Avastin®, Genentech Inc., South San Francisco, CA, USA) is a humanized monoclonal immunoglobulin G (IgG) 1 antibody that specifically binds to, and neutralizes the biological activity of, vascular endothelial growth factor A (VEGF‐A), a key isoform of VEGF involved in angiogenesis, and a well‐characterized pro‐angiogenic factor 1. Bevacizumab causes inhibition of tumour angiogenesis by blocking VEGF‐A from binding to its receptors and leads to tumour growth inhibition. Bevacizumab in combination with standard therapy has received marketing authorization for use in the treatment of various cancers, including metastatic colorectal cancer 2, 3, non‐small‐cell lung cancer 4, breast cancer 5, renal cell carcinoma 6, cervical cancer 7, and ovarian cancer 8.

Appropriate and practical dosing guidelines of monoclonal antibody drugs (mAbs) in paediatric cancer patients are still not clearly defined. Currently, there are mainly two types of dosing strategies for mAbs in children: tier‐based (a fixed dose for the approved age or body size range) and body size based (linear dose scaling by body size) 9. For body size‐based dosing, total body weight (BWT) is currently the most widely used body size metric. Body surface area (BSA) was proposed to be a more satisfactory index of drug requirements than BWT or age, particularly during infancy and childhood 10. Ideal body weight (IBW) has also been used for dosing paediatric patients 11.

Population pharmacokinetic (PK) modelling is a powerful tool for determining the most appropriate and practical dosing strategies. The population PK of bevacizumab was previously characterized in adults 12, and the model was updated (Supplementary Table S1). In adult cancer patients, clearance (CL) and central volume of distribution (V1) increased with BWT, decreased with albumin, and were lower in females. In addition, CL decreased with total protein, and V1 increased with tumour burden. However, bevacizumab PK and dosing guidelines have not been comprehensively evaluated in paediatric cancer patients, especially very young patients under 3 years of age. Only two previous studies evaluated bevacizumab PK in, 10 and 27 patients between the ages of 7 years and 21 years, respectively 13, 14. The limited data on bevacizumab PK to inform dosing guidelines in paediatric cancer patients have mainly been derived from the many challenges in conducting paediatric studies, including limited access to the population of interest, low consent rates, etcetera.

Five dedicated paediatric clinical studies have been conducted and included evaluation of bevacizumab PK (Table 1): a Phase I study AVF2771s (NCT00085111) 13 and four Phase II studies AVF4117s (NCT00667342) 14, AVF3842s (NCT00381797) 15, BO20924 (NCT00643565), and BO25041 (NCT01390948). These allowed for the opportunity to investigate bevacizumab PK in paediatric cancer patients over a wide range of age, body size, cancer types, and dosing regimens. The objectives of the current analysis were to develop a robust population PK model in paediatric cancer patients and develop the most appropriate and practical dosing strategy.

Table 1

Summary of studies and patient characteristics

	Model building population	External validation population
	N = 152	N = 80
PK samples*	1427 (1592)	544 (554)
Study	1. AVF2771s††: Refractory sarcomas	1. BO25041: Primary CNS tumours
	2. AVF3842s: Primary CNS tumours	2. BO20924 (remaining data): Metastatic soft‐tissue sarcoma
	3. AVF4117s: Newly diagnosed osteosarcoma
	4. BO20924 (interim data): Metastatic soft‐tissue sarcoma
Dosing regimen †	Q2W: 5, 10, 15 mg kg–1 Q3W: 7.5, 15 mg kg–1	Q2W: 10 mg kg–1 Q3W: 7.5 mg kg–1
Infants ‡	7	2
Age < 3 years §	9	3
Age ¶ (year)	n = 152	n = 80
	10.8 (44.1)	10.4 (42.0)
	10.8 [0.5–21.0]	11.0 [1.4–17.6]
BSA ¶ (m2)	n = 142	n = 80
	1.26 (35.1)	1.24 (31.9)
	1.30 [0.32–2.39]	1.28 [0.50–2.05]
Body weight ¶ (kg)	n = 152	n = 80
	43.6 (52.5)	40.3 (46.6)
	43.8 [5.94–125.0]	40.0 [11.8–82.3]
Albumin ¶ (g l–1)	n = 98	n = 80
	38.8 (13.9)	38.7 (15.0)
	39.0 [24.0–52.0]	39.0 [23.0–51.0]
Total protein ¶ (g l–1)	n = 99	n = 32
	69.3 (10.7)	67.3 (10.5)
	70.0 [51.0–87.0]	67.0 [56.0–82.0]
Gender F:M **	70 (46.1%): 82 (53.9%)	30 (37.5%): 50 (62.5%)

BSA, body surface area; CNS, central nervous system; CV, coefficient of variation; N, total number of patients in this study; n, number of patients with available information about this variable; PK, pharmacokinetic; Q2W, once every 2 weeks; Q3W, once every 3 weeks.

Displayed as number of PK samples included in the analysis (total number of PK samples collected).

bevacizumab was given via an intravenous infusion over 30–90 minutes.

Infants are defined as children between 0 and 2 years of age, according to the Food and Drug Administration guidance 28.

Number of patients below 3 years of age.

Displayed as: number of patients with available data; mean (CV%); median [minimum – maximum].

F (female):M (male), displayed as number of patients (percentage).

bevacizumab was given as single‐agent escalating dose in AVF2771s and in combination with chemotherapy in all other studies.

Methods

Patients

Patients with at least one PK sample were included in the analysis. Serum bevacizumab concentrations were determined at Genentech, Inc. using an enzyme‐linked immunosorbent assay that used recombinant human VEGF for capture and a goat antibody to human IgG conjugated to horseradish peroxidase for detection. The lowest limit of quantification (LLOQ) was 78 ng ml–1 in serum 13. Concentrations below the LLOQ were omitted.

The clinically relevant covariates tested included those related to demographics, biochemical tests, concomitant medications, and pathophysiological factors (Table 1). The missing value was imputed as the median for continuous covariates or the most frequent value for categorical covariates derived with available data for each gender.

Population PK modelling

A population PK model was developed using data (Table 1) from studies AVF2771s, AVF3842s, AVF4117s, and BO20924 (interim data). Nonlinear mixed‐effects modelling was performed using NONMEM (version 7.2; ICON Development Solutions, Ellicott City, MD, USA) 16 using the FOCE (first‐order conditional estimation method) method of estimation with interaction, Perl‐speaks‐NONMEM (version 3.5.3; Uppsala University, Uppsala, Sweden) 17 and R 3.0.3 18. Several models were tested to select the optimal base model. The base model included a power function of body size (e.g. BWT) on all PK parameters:

where BWT  = baseline BWT of patient i; P  = typical PK parameters of patients with BWT ; P  = typical value of PK parameters for patients with a BWT of 70 kg; θ  = exponent for the PK parameter P.

The base model was evaluated using either theoretical (0.75 for CLs; 1 for volumes of distribution) 19 or fitted values of exponent θ . The nonlinearity of the PK was assessed using the Michaelis–Menten model.

The quality of fit was evaluated using a standard model discrimination process including statistical criteria [i.e. minimum of objective function value (OFV)], adequate estimation of the parameters (e.g. relative standard error < 50%), and graphical representations of goodness‐of‐fit. The final model was established in a stepwise manner by forward addition followed by backward elimination, with a significance level of P < 0.05 and P < 0.001 (OFV decrease of 3.84 and 10.83 for one degree of freedom), respectively.

The effect of n covariates on PK parameters was coded using a multiplicative model:

where θ is the typical value of the parameter for patients with a set of covariates i, θ is the typical value of the PK parameter for patients having the covariate values equal to the median of the covariate for all patients, and Effect through Effect are multiplicative factors of the effects for covariate 1 through n, for the set of covariates i.

The multiplicative factor was defined using the power function for continuous covariates:

and defined as follows for categorical covariates:

where Effect is the multiplicative factor of the covariate effect for covariate i, Cov is the covariate value, Cov reference value is the median of the covariate for all patients and ln(θ ) is the exponent of the power function to be estimated. ln(θ ) was used to avoid bounds during the calculation by NONMEM.

Model evaluation and sensitivity analysis

The population PK models were evaluated using diagnostic plots 20, 21, visual predictive check (VPC) 21, 22, prediction‐corrected VPC (pcVPC) 23, bootstrapping 24 and shrinkage assessment 25. VPC, pcVPC, and bootstrapping were all performed using 1000 replicates based on the final model. The relative impact of each covariate included in the final model alone on PK parameters and exposure was explored. Exposure, including steady‐state trough (Cmin) and peak (Cmax) concentrations, was computed given a dose of bevacizumab of 10 mg kg–1 once every two weeks (Q2W) using the final model.

External validation

After the final model was built, data from study BO25041 and the remaining data from BO20924 (Table 1) became available and subsequently were used to validate the model externally. Predicted concentrations (CPRED) for the validation population were obtained using post hoc Bayesian forecasting by fixing the parameters in the structural and variance models to the final estimates. Prediction errors (PE) were calculated for each concentration as PE = (COBS − CPRED)/CPRED, where COBS denotes observed concentrations. pcVPC was used to compare the 95% prediction interval (PI) and COBS.

Predicted PK parameters (PPRED) for each patient were obtained based on individual covariate values using the equations in the final model without considering observed concentrations. Post hoc estimates of PK parameters (PEST) were obtained based on observed concentrations and the final model. PE were calculated as (PEST − PPRED)/PPRED.

Evaluation of dosing strategies

Bevacizumab steady‐state Cmin and Cmax in paediatric patients were simulated under the four most widely discussed dosing strategies: BWT‐, BSA‐, IBW‐, and tier‐based doses, which were compared to Cmin and Cmax simulated in adult patients receiving 10 mg kg–1 Q2W. The IBW of each patient was calculated by multiplying the square of the height (m2) by body mass index (BMI), which was determined using the 50th percentile of the gender‐specific BMI‐for‐age growth charts published by the Center for Disease Control and Prevention 26. The paediatric doses (Q2W) used in the simulation were determined so that the simulated paediatric steady‐state area under the curve (AUC) matched the simulated adult steady‐state AUC. The final doses used in the simulation were 10 mg kg–1 for the BWT‐based dose, 398 mg m–2 for the BSA‐based dose, 11 mg kg–1 for the IBW‐based dose, and as follows for the tier‐based dose: 180 mg for <15 kg; 360 mg for 15 – 40 kg; 640 mg for >40 kg. The 90% PI was generated by simulating 1000 times using the base model of paediatric and adult patients (Supplementary Table S1). The individual Cmin and Cmax of the 152 paediatric patients were also simulated using the individual post hoc PK parameter estimates. In order to compare to the bevacizumab maximum tolerated dose (MTD) of 15 mg kg–1 previously determined in adults 27, the BSA‐, IBW‐, and tier‐based doses of each individual paediatric patient were converted to mg kg–1 dose by dividing the actual dose by BWT.

Results

A total of 2146 bevacizumab serum concentrations from 232 patients were collected and underwent bioanalysis. Of these, 138 concentrations were below the LLOQ (prestudy samples) and 37 were outliers (mainly due to human errors in recording time and dose). Information about studies and patient characteristics is summarized in Table 1. All patient characteristics were similar between children with primary central nervous system (CNS) tumours (AVF3842s and BO25041) and children with sarcomas (AVF2771s, AVF4117s, and BO20924). The percentage of children with primary CNS tumours with albumin below normal level (35 g l–1) appeared lower than that of children with sarcomas: 8% vs. 24%. Noticeably, nine infants (as defined by the US Food and Drug Administration guidance 28) were included in the analysis. Albumin and total protein levels in paediatric patients were comparable to those in adults.

Out of the 232 paediatric patients, data from 152 patients (1427 concentrations) were used for model building. The optimal base model was a linear two‐compartment model with theoretical exponents fixed at 0.75 for CL and inter‐compartment clearance (Q), and estimated for V1 and peripheral volume of distribution (V2), full‐block inter‐individual variability (IIV) on CL, V1, and V2 with combined additive and proportional residual error. The Michaelis–Menten model did not significantly (P > 0.05) improve the model fitting based on the range of available concentrations (0.4 – 741 μg ml–1). The estimates of typical bevacizumab CL, V1, Q, V2, and median terminal half‐life values were 3.05 ml day–1 kg–1, 40.0 ml kg–1, 9.34 ml day–1 kg–1, 34.6 ml kg–1, and 19.6 days, respectively, in paediatric cancer patients, similar to values in adults of 3.00 ml day–1 kg–1, 39.1 ml kg–1, 7.57 ml day–1 kg–1, 40.7 ml kg–1 and 20 days, respectively (Supplementary Table S1). The correlation between V1 and albumin was not significant in the final model. After taking into account BWT, CL and V1 still decreased with increasing albumin, and were higher in male patients (Supplementary Figure S1), but were no longer correlated with age (Figure 1).

Figure 1

Weight‐adjusted pharmacokinetic (PK) parameters. (A) Clearance and (B) central volume of distribution obtained from the bevacizumab base model across age. LOESS, locally weighted scatterplot smoothing

Bevacizumab CL and V1 in children with primary CNS tumours (n = 76) were significantly (P < 0.0001) lower than in children with sarcomas (n = 76). This effect was first indicated by the difference in CL and V1 across the four studies (Supplementary Figure S1). Models with all possible combinations of study effect on CL and V1 were compared one by one. In the resulting final model, CL and V1 in AVF2771s, AVF4117s, and AVF3842s (various sarcomas) were not statistically significantly different from each other, but were statistically significantly different from those in AVF3842s (primary CNS tumours).

Parameter estimates of the final model are summarized in Table 2. Bevacizumab CL and V1 for a paediatric patient i were described as follows:

Table 2

Parameter estimates of the final model in paediatric cancer patients

Parameters	Estimates	RSE (%)	95% CI	Bootstrapping median	Bootstrapping 95% CI	Shrinkage (%)
CL (ml h–1)	9.90	4.1	[9.10, 10.7]	9.90	[9.16, 10.7]
V1 (ml)	2850	3.0	[2683, 3017]	2850	[2701, 3005]
Q (ml h–1)	28.0	10.4	[22.3, 33.8]	28.2	[23.0, 35.4]
V2 (ml)	2564	5.8	[2274, 2854]	2569	[2294, 2852]
BWT on CL	0.75	Fixed		0.75	Fixed
Male on CL	1.11	4.1	[1.02, 1.20]	1.11	[1.02, 1.20]
ALBU on CL	−0.300	50.6	[−0.597, −0.00227]	−0.302	[−0.600, 0.0366]
Primary CNS tumour on CL	0.725	4.3	[0.666, 0.789]	0.725	[0.667, 0.784]
BWT on V1	0.701*	3.9*	[0.647, 0.755]*	0.701	Fixed
Male on V1	1.14	3.5	[1.07,1.22]	1.14	[1.07, 1.22]
Primary CNS tumour on V1	0.854	3.7	[0.793, 0.919]	0.853	[0.795, 0.918]
BWT on Q	0.75	Fixed		0.75	Fixed
BWT on V2	0.766*	14.4*	[0.550, 0.982]*	0.766	Fixed
Prop. error (%)	13.9	6.9	[11.9, 15.7]	13.9	[12.0, 15.5]	10.4
Add. error (μg ml–1)	3.06	25.1	[0.406,4.30]	3.09	[1.43, 4.50]	10.4
IIV CL (%)	21.4	7.4	[18.0, 24.3]	21.1	[18.2, 24.2]	10.4
IIV V1 (%)	17.6	9.2	[14.0, 20.5]	17.3	[14.2, 20.4]	14.3
IIV V2 (%)	58.0	13.3	[40.1, 71.6]	57.3	[41.8, 71.4]	18.1
Var. IIVs CL and V1	0.0248	17.6	[0.0162, 0.0334]	0.0244	[0.0162, 0.0328]
Var. IIVs CL and V2	0.0228	75.2	[−0.0108, 0.0563]	0.0216	[−0.0160, 0.0547]
Var. IIVs V1 and V2	0.0248	51.0	[−6.56 × 10−6, 0.0496]	0.0249	[0.000875, 0.0499]

Add, additive; ALBU, baseline albumin; BWT, body weight; CI, confidence interval; CL, clearance (ml h–1); CNS, central nervous system; IIV, inter‐individual variability; Prop, proportional; Q, inter‐compartment clearance; RSE, relative standard error; Var., variance; V1, central volume of distribution; V2, peripheral volume of distribution;

value estimated for the base model.

Goodness‐of‐fit plots showed good agreement between predicted and observed bevacizumab concentrations, with no apparent bias in residual (Supplementary Figure S2). Shrinkage on all parameters and IIV was <20%. The pcVPC result (Figure 2) showed that the 2.5th, 50th, and 97.5th percentiles of observed concentrations were within the predicted 95% confidence interval (CI) of these percentiles, suggesting accurate model fitting across a wide range of dosing regimens and time courses. Bootstrapping resulted in median parameter estimates and 95% CIs similar to the estimates from the original dataset, indicating that the final model provided good precision for parameter estimation.

Figure 2

(A) Prediction‐corrected visual predictive check for the serum concentration–time profiles of bevacizumab using the final model in paediatric cancer patients. (B) Section of (A) before day 35 after dose administration, where the majority (94%) of the data points lay. CI, confidence interval; Pred, population prediction

The impact of the variation for a single covariate included in the final model on CL and V1 (data not shown) and steady‐state exposure (Cmin and Cmax) were demonstrated by comparing the simulated CL, V1, and exposure of patients with extreme covariate values (5th and 95th percentiles) to a typical patient with a median covariate value (Figure 3). Among all covariates, BWT had the strongest impact on CL and V1. With BWT <24.1 kg, CL and V1 were reduced to less than 50% of the typical value. Primary CNS tumours had the second strongest impact on CL and V1. In children with primary CNS tumours, CL and V1 were 27% and 15% lower than the typical value, respectively. The gender effect on CL and V1 was less than 25%. The IIV area mostly covered ±50% variation of the individual CL and V1 values.

Figure 3

Impact of the variation for a single covariate included in the final model on steady‐state bevacizumab exposure in paediatric cancer patients. (A) Trough concentration (Cmin) and (B) peak concentration (Cmax). Red vertical lines represent the ‘base’, defined as the exposure of a typical patient – i.e. a 44‐kg female paediatric patient with an albumin level of 39 g l–1 and sarcomas. The dark blue‐shaded curve at the bottom, with a value at each end, shows the 5th to 95th percentile exposure range across the entire population. Each light blue‐shaded bar represents the influence of a single covariate on the steady‐state exposure after repeated bevacizumab doses of 10 mg kg–1 once every two weeks. The label at left end of the bar represents the covariate being evaluated. The upper and lower values for each covariate capture 90% of the plausible range in the population. The length of each bar describes the potential impact of that particular covariate on bevacizumab steady‐state exposure, with the percentage value in the parentheses at each end representing the percentage change in exposure from the ‘base’. The most influential covariate is at the bottom of the plot for each exposure metric, except for the body weight effect stratified by age group, which is displayed on the top. CI, confidence interval; Cmax, peak concentration; Cmin, trough concentration

Primary CNS tumours had an almost equally strong impact as BWT on bevacizumab steady‐state Cmin (Figure 3). Cmin and Cmax in children with primary CNS tumours were 49% and 29% higher than in children with sarcomas, respectively. Variations of exposure in paediatric cancer patients due to albumin and gender effect were less than 31% and 12%, respectively.

Out of the 232 paediatric patients, data from 80 patients (544 concentrations) were used for external validation (Table 1). Only 5.1% of prediction‐corrected observations fell outside the 95% PI, which was very close to the 2.5th and 97.5th percentiles of observed concentrations (Figure 4). Mean PE for concentrations, CL, and V1 were 3.54%, −1.84%, and −0.06%, respectively. No bias in PE was observed over time and across predicted values. In spite of the substantial difference in exposure between primary CNS tumours (Figure 4a) and sarcomas (Figure 4b), the model could predict both very well.

Figure 4

External validation for (A) primary CNS tumours and (B) sarcomas. About 95% of the prediction‐corrected observations fall between the 95% prediction interval boundaries, which are very close to the observed 2.5th and 97.5th percentiles. CNS, central nervous system; PI, prediction interval

Bevacizumab steady‐state Cmin in paediatric patients generally fell within the 90% PI of Cmin in adult patients under all dosing strategies (Figure 5), meaning that Cmin in less than 5% of paediatric patients fell below the lower boundary or above the upper boundary of the 90% PI of Cmin in adult patients. Cmin and Cmax in paediatric patients increased under the BWT‐based dose and decreased under the BSA‐based dose with increasing BWT. Under the BWT‐based dose, Cmax in approximately 33% of the paediatric patients fell below the lower boundary of the 90% PI of adult Cmax but did not exceed the upper boundary of the 90% PI of adult Cmax. Under the BSA‐based dose, Cmax in paediatric patients generally fell within the 90% PI of adult Cmax. Under the tier‐based dose, Cmax in approximately 12% of the paediatric patients exceeded the upper boundary of the 90% PI of adult Cmax. Cmin and Cmax in paediatric patients were similar between BWT‐ and IBW‐based doses. When converted to an equivalent mg kg–1 dose, IBW‐based doses appeared similar to BWT‐based doses, whereas BSA‐ and tier‐based doses increased with decreasing BWT and age (Supplementary Figure S3). The converted mg kg–1 doses corresponding to the BSA‐ and tier‐based doses in young patients exceeded the bevacizumab MTD of 15 mg kg–1 previously determined in adults 27.

Figure 5

Simulated steady‐state bevacizumab exposure in paediatric patients under BWT‐, BSA‐, IBW‐, and tier‐based doses. Equivalent doses (once every 2 weeks) were used: 10 mg kg–1 for the BWT‐based dose, 398 mg m–2 for the BSA‐based dose, and 11 mg kg–1 for the IBW‐based dose. The tier‐based dose in each BWT range was determined so that the steady‐state area under the curve (AUC) under these doses matched the adult steady‐state AUC: 180 mg for <15 kg, 360 mg for 15 – 40 kg, 640 mg for >40 kg. Only patients with a BWT below 80 kg are displayed. BSA, body surface area; BWT, total body weight; Cmax, peak concentration; Cmin, trough concentration; IBW, ideal body weight; PI, prediction interval

Discussion

The present analysis was a comprehensive evaluation of bevacizumab dosing strategies in paediatric cancer patients, including very young patients, by population PK modelling and simulations. We assembled a large paediatric PK population of 232 patients from five dedicated paediatric studies, with 12 patients under the age of 3 years. A robust population PK model was built and externally validated. We demonstrated that BSA‐, IBW‐, and tier‐based dosing strategies offered no substantial advantage over the BWT‐based dose that is currently used in adults for bevacizumab.

The population PK model developed was robust, as demonstrated by goodness‐of‐fit plots (Supplementary Figure S2), pcVPC (Figure 2), and external validation (Figure 4). In spite of the substantial difference in exposure between primary CNS tumours (Figure 4a) and sarcomas (Figure 4b), the model could predict both very well, confirming the robustness of the final model. Shrinkage was small for all PK parameters and IIV, suggesting that the PK data collected were sufficient to characterize the PK parameters and IIV.

Bevacizumab PK is similar between paediatric and adult cancer patients, as demonstrated by similar PK parameters after taking into account BWT. The median terminal half‐life of 19.6 days (range 9–78 days) in paediatric cancer patients is also similar to that in adults (20 days). The low IIV of 21.4% and 17.6% observed for CL and V1, respectively, in paediatric patients is typical for antibody drugs. Nonlinear PK was not observed in paediatric patients, similar to the observation in adults. Nonlinear PK and target‐mediated disposition was not observed, probably because the bevacizumab molar concentration is thousands of times higher than that of the target VEGF‐A 12, a soluble antigen 29.

There was a trend of unknown clinical significance toward lower CL and V1 in children with primary CNS tumours than in those with sarcomas: CL and V1 were 27% and 15% lower, respectively, resulting in a 49% higher Cmin and 29% higher Cmax at steady state (Figure 3). This trend could not be confirmed in adults because these two types of tumour are rare in adults. In addition, PK in adults with glioblastoma from the Avastin in Glioblastoma (AVAglio) trial (BO21990; NCT00943826) appeared similar to that in other types of solid tumour. However, this trend may not be clinically relevant, given that exposure in children with primary CNS tumours or sarcomas fell within the range of adult exposure (Figure 5). The number of children with primary CNS tumours (n = 76) and sarcomas (n = 76) in the model‐building dataset was equal, and patient characteristics were similar (Table 1), with albumin being slightly higher in children with primary CNS tumours. The underlying mechanism is unclear but we propose three hypotheses.

The first hypothesis involves inflammation and the possible formation of neutralizing anti‐therapeutic antibodies (ATA). Sarcomas in the present analysis included metastatic osteosarcomas, metastatic soft tissue sarcomas, and other refractory sarcomas. These sarcomas are highly inflammatory and may be associated with the formation of ATA, which can result in an increase in mAb CL. Co‐administration of immunosuppressants has been shown to decrease mAb CL 30, 31, and one of the mechanisms has been proposed to be downregulation of the immune response to mAbs and/or reticuloendothelial system‐mediated CL 29, 32, 33.

The second hypothesis concerns overall health status. Sarcomas are highly inflammatory and therefore may be associated with worse health status and therefore higher CL of mAbs. Inflammatory markers have been shown to correlate with some clinical variables known to have an important prognostic role (stage, histological subtype, and response to therapy) in soft‐tissue sarcoma patients 34, 35. The percentage of children with primary CNS tumours with albumin below the normal level (35 g l–1) appeared lower than in children with sarcomas: 8% vs. 24%, which supports this hypothesis. However, the significant difference in CL by cancer type still exists after accounting for the effect of albumin, suggesting that some unobserved prognostic factors may play a role 36, such as baseline tumour burden, which has been shown to have a statistically significant and clinically relevant impact on the PK of mAb 37. However, two factors made it impossible to test tumour burden as a covariate in this analysis. First, tumour response criteria were inconsistent across these studies, which were conducted across a time span of over 12 years. Several different versions of the Response Evaluation Criteria in Solid Tumors (RECIST) and other criteria (e.g. the Macdonald criteria for glioblastoma) were used. Second, the methods used to measure tumour burden, such as computed tomography scans and magnetic resonance imaging, were inconsistent across studies. However, tumour burden is an indicator of disease burden and health status, which could already be represented by albumin in the model. In addition, the inclusion of tumour burden in the model would limit the applicability of the model to future data owing to the continuous advancement in tumour response criteria and measurement methods.

The third hypothesis concerns concomitant medications. It is possible that children with primary CNS tumours received higher doses of steroids than children with sarcomas. However, a possible effect of steroids on bevacizumab PK has not been reported. Many bevacizumab studies have been conducted in adults, and there has been no observation of any impact of concomitant chemotherapeutic agents on its PK (unpublished data). Further research is warranted in this area. Other factors that showed a statistically significant impact on bevacizumab PK are similar between paediatric and adult cancer patients: CL and V1 increased with BWT and were lower in females, and CL decreased with albumin.

We demonstrated that CL and V1 change very little across ages in paediatric cancer patients after taking into account BWT (Figure 1), indicating that the potential change in PK across ages is mainly caused by the change in body size, and there may be no need to adjust the dose of bevacizumab by age if it is properly dosed by body size.

An important consideration in paediatric oncology drug development is to match the paediatric exposure with the adult exposure because the adult exposure has been well studied for efficacy and safety in relatively large populations. Our results support that the BWT‐based dose of bevacizumab is the most appropriate and practical dosing strategy for paediatric patients. First, our results demonstrated that BSA‐, IBW‐, and tier‐based doses offered no substantial advantage over the BWT‐based dose (Figure 5). The bevacizumab steady‐state Cmin in paediatric patients generally falls within the 90% PI of adult Cmin under all dosing strategies. Clinically meaningful underexposure under the BWT‐based dose seems unlikely because Cmin under the BWT‐based dose falls below the 90% PI of adult Cmin in only 4% of paediatric patients with a low BWT, and the magnitude of underexposure in this latter group is limited. Second, the BWT‐based dose may be associated with fewer safety concerns. Under the BWT‐based dose, Cmax is substantially (in 33% of the paediatric patients) below the lower boundary of the 90% PI of adult Cmax. However, under the tier‐based dose, Cmax (in 12% of the paediatric patients) exceeded the upper boundary of the 90% PI of adult Cmax. Furthermore, when converted to the mg kg–1 dose, the BSA‐ and tier‐based doses exceeded the bevacizumab MTD of 15 mg kg–1 previously determined in adults. Finally, from a practical perspective, BSA‐, IBW‐, and tier‐based doses all require the calculation of BSA and IBW using a certain formula, or a decision to be made on a fixed dose by age or body size range, which could add additional complexity, human errors, and inconsistency. For example, different formulas are available for calculating BSA 38, 39, 40, 41, drug preparation and administration may become more inconvenient, and risk of medication errors may occur 42.

Based on simulations, the bevacizumab dose can stay the same for children with primary CNS tumours and those with sarcomas, in spite of the difference in bevacizumab PK by tumour type. In children with all tumour types, the bevacizumab steady‐state Cmin falls within the 90% PI of adult Cmin under all dosing strategies, and Cmax does not exceed the upper boundary of the 90% PI of adult Cmax under BWT‐based, BSA‐based and IBW‐based doses.

In conclusion, a robust bevacizumab population PK model for paediatric cancer patients, which can be used for simulations, was developed and externally validated. Children with primary CNS tumours showed significantly lower CL and V1 and higher steady‐state exposure than children with sarcomas, but the same dose can be used in children with both tumour types. The BWT‐based bevacizumab dose currently used in adults is most appropriate and practical for paediatric cancer patients. Given the similarity in PK among many mAbs 29, this may help to develop the most appropriate and practical paediatric dosing guidelines for other therapeutic mAbs.

Competing Interest

All authors have completed the Unified Competing Interest form at www.icmje.org/coi_disclosure.pdf (available on request from the corresponding author) and declare: no support from any organization for the submitted work; no financial relationships with any organizations that might have an interest in the submitted work in the previous 3 years; no other relationships or activities that could appear to have influenced the submitted work. Kelong Han, Angelica Quartino, Jin Jin, and David E. Allison receive a salary from Genentech, Inc. and hold stocks of Roche Pharmaceuticals; in addition, Jin Jin also holds stock in Eli Lilly; Thomas Peyret, and Nathalie H. Gosselin receive a salary from Pharsight Consulting Services.

We thank all of the patients, investigators and members of AVF3842s, BO20924, BO25041, AVF4117s and AVF2771s who participated in these studies. We acknowledge the contribution of Julia C. Chisholm (The Royal Marsden NHS Foundation Trust, Surrey, UK), Birgit Geoerger (Institut Gustave Roussy, Villejuif, France), Odile Oberlin (Institut Gustave Roussy, Villejuif, France), Amadeo Azizi (Medical University of Vienna, Vienna, Austria), Adela Canete (Hospital La Fé, Valencia, Spain), Darren Hargrave (Great Osmond Street Hospital, London, UK), Marie Cécile Le Deley (Gustave Roussy, Villejuif, France), Gilles Vassal (Gustave Roussy, Villejuif, France), Frank Saran (The Royal Marsden Hospital, London, UK), Eric Bouffet (The Hospital for Sick Children, Toronto, Canada), Pascale Varlet (Hopital St Anne, Paris, France), Paul Morgan (Nottingham University Hospital, Nottingham, UK), Chris Jones (The Institute for Cancer Research, London, UK), Tim Jaspan (Nottingham University Hospital, Nottingham, UK), Geoffray McCowage (The Children's Hospital at Westmead, Sydney, Australia), Raphael Rousseau (Genentech Inc. South San Francisco, CA, USA), Sabine Fuerst-Recktenwald (F. Hoffmann‐La Roche Ltd., Basel, Switzerland) for the plan, design and implementation of these studies, interpretation of data, preparation of the manuscript, and their valuable insights.

Contributors

All authors contributed substantially to the conception and design of the analysis, drafting or revising the paper, as well as giving final approval for submission.

Figure 1. Correlation between weight‐adjusted pharmacokinetic (PK) parameters obtained from the bevacizumab base model and patient variables in paediatric cancer patients. The grey line represents the locally weighted scatterplot smoothing (LOESS); the dashed line represents the typical value. In the boxplots, the black dots and black lines represent the mean and median value in each group, respectively. ALBU, baseline albumin (g l–1); BWT, baseline body weight (kg); CL.KG, weight‐adjusted clearance (ml h–1); r, Pearson correlation coefficient; TPRO, baseline total protein (g l–1); V1.KG, weight‐adjusted central volume of distribution (ml)

Figure 2. Goodness‐of‐fit for the final bevacizumab population pharmacokinetic model in paediatric patients. Conc, concentration; IDENT, identity line; IPRED, individual predicted concentration; LOESS, locally weighted scatterplot smoothing; OBS, observed concentration; PRED, population predicted concentration

Figure 3. The BSA‐, IBW‐, and tier‐based dose for each individual paediatric patient, converted to mg kg–1 dose. BSA, body surface area; BWT, total body weight; IBW, ideal body weight; MTD, maximum tolerated dose previously determined in adults

Table 1. Model parameters of base and final adult population pharmacokinetic models in solid tumours

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