Pharmacokinetic Model Based Sensitivity Analysis to Lower Recruitment Burden for Young Children Requiring Intravenous Immunoglobulin G Replacement

ABSTRACT

To support a post‐marketing requirement for pharmacokinetic (PK)‐focused assessments in patients ages 2–16 years, a model‐informed drug development approach was used to overcome enrollment barriers in recruiting pediatric subjects with primary immune deficiency (PID) disorders under Age 6 in a Phase 4 pediatric study. Models (1) characterized total immunoglobulin G (IgG) PK of Immune Globulin Intravenous [Human], 10% Liquid [IVIG] (BIVIGAM) in children and adolescents with PID; (2) quantified the impact of age and body weight; and (3) compared simulated exposure of IVIG between pediatric and adult subjects. Models were developed using pooled adult and pediatric data from 2 Phase 3/4 studies in 79 subjects (1243 IgG levels) with 3, 9, 13, and 54 subjects 2 to < 6 years, 6 to < 12 years, 12–16 years, and > 16 years, respectively. Serum IgG PK of IVIG following intravenous infusion was characterized using a 2‐compartment PK model with body weight on total IgG clearance and volumes of distribution. Model‐based clearance values when estimating allometric exponents were comparable across age‐group categories. Simulations predicted trough IgG levels for a virtual population of subjects for recommended IVIG 10% dosages of 300–800 mg/kg. Fixed and estimated allometric scaling allowed conservative extrapolation with simulations showing ≥ 90% of subjects would achieve trough levels ≥ 5 g/L (minimum recommended level) for a mid‐range dose of 500 mg/kg. Modeling and simulation were integral in confirming achievement of clinically acceptable trough IgG levels (~7 g/L) to support supplemental PK, efficacy, and dosing recommendations for patients ≥ 2 years of age.Trail Registration: NCT00538915 and NCT03164967

Study Highlights

• What is the current knowledge on the topic?

  • ○
    Immune Globulin Intravenous [Human], 10% Liquid [IVIG] (BIVIGAM) is currently approved in the US for treatment of patients 2 years old with primary immunodeficiency.
• What question did this study address?

  • ○
    To support a post‐marketing requirement, model‐informed drug development (MIDD) was leveraged to demonstrate comparable exposure between pediatric and adult subjects, overcoming practical difficulties enrolling a sample of very young children.
• What does this study add to our knowledge?

  • ○
    A pooled analysis allowed full characterization of BIVIGAM PK for all 79 subjects across two approval studies, including 25 pediatric subjects ≤ 16 years of age. Allometry‐based simulation can serve as a sensitivity analysis to support extrapolation of established dosing in adults to achieve clinically acceptable IgG levels in pediatric patients ≥ 2 years of age.
• How might this change drug discovery, development, and/or therapeutics?

  • ○
    Given a collective knowledge of IVIG PK, familiarity with plasma‐derived therapeutics for PID, and tailored weight‐based IVIG 10% dosing, this MIDD approach adds further support as prior knowledge to justify a lower burden of PK study sample sizes in very young children.

1. Introduction

Primary immune deficiency (PID) diseases, now referred to as inborn errors of immunity (IEI) [1, 2], are a group of rare, heterogeneous genetic disorders that affect the immune system and are diagnosed in approximately one in 2000 children in the United States (US) [3], and which can predispose them to mild to serious complications including recurrent infections, allergy, autoimmunity, and malignancy [4]. Although PID/IEI are rare, their cumulative prevalence constitutes a substantial public health burden [1]. Immunoglobulin (IG) replacement is an integral therapy in managing 75% of these disorders [2].

IG replacement therapy has been a standard of care for patients with PID for 7 decades and is available in similarly effective intravenous (IV) and subcutaneous formulations [5]. The benefits of treatment with IG, following increased antibody levels, include prevention of severe bacterial and viral infections [6, 7, 8] and less frequent and shorter hospitalizations [9] for children with PID. Indications of IVIG 10% use include, but are not limited to, the humoral immune defect in common variable immunodeficiency, X‐linked agammaglobulinemia, congenital agammaglobulinemia, Wiskott–Aldrich syndrome, and severe combined immunodeficiencies [10].

Immune Globulin Intravenous [Human], 10% Liquid [IVIG] (BIVIGAM) is a formulation currently approved in the US for treatment of adults and pediatric patients at least 2 years of age with PID [10] based on two sequential clinical studies [11, 12]. A pivotal Phase 3 clinical study [11] supported the initial approval of IVIG 10% in 2012.

A subsequent Phase 4 study was conducted to satisfy Pediatric Research Equity Act Post‐Marketing Requirement (PREA PMR) and post‐marketing US Food and Drug Administration (FDA) requirements for a dedicated pharmacokinetic (PK)‐focused assessment in pediatric patients ages 2–16 years [13, 14]. This Phase 4 study established the efficacy and safety of IVIG 10% [12] supported by a model‐informed drug development (MIDD) approach. A pooled PK modeling and simulation analysis was used to analyze total IG levels collected across the Phase 3 and Phase 4 studies to support the approval of a supplemental biologics license application (sBLA) with labeling for pediatrics ≥ 2 years of age [14].

This MIDD approach was leveraged to overcome enrollment barriers in recruiting pediatric subjects with PID, most notably for those under 6 years of age, and to fulfill the required PK assessment [15]. With enrollment of less than the planned 6 subjects in the youngest patient category, in addition to a noncompartmental (NCA) PK analysis utilizing only Phase 4 data [16], total IVIG 10% levels collected across both studies were combined in a model‐based analysis. Reported from the Phase 3 study, total IG PK parameters for 21 subjects (Ages 18–75) were determined using levels collected from a dedicated PK frequent sampling arm [11]. Trough levels were available from the remaining 42 subjects, which consisted of 9 pediatric subjects (5 in the 12 to ≤ 16 age group and 4 in the 6 to < 12 years age group) and included in a modeling analysis, which an NCA cannot leverage. This MIDD approach increased the number of patients contributing IG levels, improving the estimation of factors affecting drug exposure, notably by including the trough levels assessed in an additional 9 pediatric subjects [17]. The models built using pooled IVIG 10% pediatric and adult data were used to conduct virtual simulations to support the universality of labeling dosing recommendations for pediatrics with the application of allometry evaluated as a sensitivity analysis.

Accordingly, this study aimed to characterize total IgG PKs of IVIG 10% in children and adolescents with PID using a MIDD approach, to quantify the impact of age or body weight on the PKs of IVIG 10%, and to compare simulated exposure of IVIG 10% (trough exposures) between pediatric and adult subjects to support supplemental PK and efficacy. This study hypothesized that for children aged > 2 years, infusion of IVIG 10% at 300–800 mg/kg every 3 or 4 weeks would effectively attain recommended trough levels (≥ 5 g/L) [18].

2. Methods

2.1. Analysis Data Set and Sampling Schedules

A population PK model for IG was developed using pooled adult and pediatric data from two clinical studies that included 79 evaluable subjects (Phase 3 Study Nabi‐7101 [NCT00538915; n = 63] and Phase 4 Study 994 [NCT03164967; n = 16]) with 3, 9, 13, and 54 subjects in age groups of 2 to < 6 years, 6 to < 12 years, 12 to 16 years, and > 16 years, respectively (Table S1). Details of the inclusion and exclusion criteria and study design have been published previously [11, 12].

IVIG 10% was administered at the current labeled dose consistent with clinical practice of 300–800 mg/kg on 3‐ or 4‐week cycles for approximately 1 year in the Phase 3 study [11] and 5 months in the Phase 4 study [12]. The guidance for IVIG dosing initiation for PID is typically 400–600 mg/kg every 3–4 weeks [19]. The EMA recommends that the starting dose for IVIG replacement therapy is 400–800 mg/kg every 3–4 weeks with a target trough level of 5–6 g/L [18]. Given that there is no universal IgG level which can prevent infection [15], subsequent dose and interval adjustments are individualized based on trough IgG concentration monitoring in tandem with the patient's clinical response (i.e., infection frequency). The patients enrolled in these studies were not treatment‐naïve as the inclusion criterion required stable dosing for at least 3 months prior to study entry and the requirement of having maintained an IgG trough level of at least 5 g/L. Patients entered the trial receiving the same dose as their historically established prescription reflective of their baseline therapeutic requirements with protocol‐directed dosing adjustments designed to maintain a 5 g/L trough level. Details regarding the study population, dose regimens, and PK sampling scheme are provided in Table S1. Serum concentrations of total IgG were determined using validated tests. Subjects were considered for population PK modeling if they had received at least 1 dose of IVIG 10%, along with ≥ 2 measurable IgG concentration observations with associated sampling time and dosing information. Data from both studies were pooled.

The clinical studies were conducted in accordance with the revised Declaration of Helsinki (2013), International Conference on Harmonization E6/Good Clinical Practice Guidelines for the conduct of Clinical Trial Investigations (1996), and in compliance with the requirements of the clinical trial regulatory guidelines and regulations. All sites were activated following institutional review board approval. Written informed consent was obtained from participants' parent/legal guardian.

Assembly of the population PK modeling datasets was performed using SAS (Version 9.4). Simulation datasets were generated using R (Version 4.0.2 or above).

2.2. Population PK Model Development

Modeling and simulation analyses were carried out according to the US Guidance for Industry: Population PKs [20], the US Guidance for Industry: Exposure‐Response Relationships [21], and the European Union Guidance on Reporting the Results of Population PK Analyses [22].

The population PK modeling for IVIG 10% was conducted using the first‐order conditional estimation with interaction method (FOCEI) with nonlinear mixed effects modeling software (Nonlinear Mixed Effects Modeling [NONMEM], version 7.4.3; ICON Development Solutions, Hanover, Maryland, US) [23]. Xpose, Pearl‐speaks‐NONMEM (PsN; Department of Pharmacy, Uppsala University, Uppsala, Sweden) were used for model diagnostics and to facilitate a variety of NONMEM tasks, such as covariate testing [24].

R software (version 4.0.3) (R Core Team, Vienna, Austria) was also used for graphical analyses, model diagnostics, and statistical summaries.

The development of population PK models used the pooled total IgG data to establish the structural model (based on exploratory graphical evaluations) and stochastic (both interindividual variability [IIV] and residual unexplained variability) characteristics. While the historical literature demonstrates IVIG PK are multicompartment, both one‐ and two‐compartment structural models were tested. Models were evaluated using standard diagnostics and goodness‐of‐fit (GOF) criteria. Final model candidates were qualified using sampling importance resampling and prediction‐corrected visual predictive checks (pcVPCs) for stability and predictability, respectively [25, 26]. The individual pretreatment baseline total IgG for each subject closest to the start of on‐study treatment was used to initialize both the central and peripheral compartments assuming pre‐dose steady‐state distribution, with baseline body weight as a covariate. Baseline body weight was included a priori based on allometric principles. The estimated allometry model used a shared exponent for clearance (CL) and intercompartmental clearance (Q) and a separate shared exponent for central volume (Vc) and peripheral volume parameters (Vp). Fixed‐allometry standard exponents were applied to CL and Vc.

A covariate analysis was performed to establish the impact of any potential covariates in addition to body weight on PK, along with a stepwise covariate selection approach [27]. Age, age group, race, and ethnicity on CL, Vc, and Vp were screened, but none of these covariates were significant.

Following completion of covariate testing, alternative variance–covariance structures for variance–covariance matrix (Ω) were evaluated, including partial and full block structures. Such a structure was deemed suitable if it provided a statistically significant (p < 0.001) improvement in the model objective function and if it improved model stability as measured by the condition number and/or a successful covariance step. The model that resulted from this step of the model‐building process was considered the final model.

2.3. Simulations

Simulations were conducted to derive PK exposures (e.g., trough serum IgG concentration and area under the serum concentration‐time curve at steady state (AUCss)) for total IgG after IVIG 10% administration in three pediatric age groups (2 to < 6 years, 6 to < 12 years, and 12–16 years) for comparison with adults. Virtual pediatric and adult populations (N = 1000 subjects per age category) were generated to conduct the simulations. Body weight was resampled from the NHANES database to capture a representative distribution for pediatric subjects aged 2 to 16 years as well as for the adult population. Stochastic simulations using the final population PK model for IVIG 10%, without accounting for uncertainty around the PK parameters, were conducted to generate IgG concentration‐time profiles for both 3‐ and 4‐week dosing intervals for three body weight‐based doses: 300, 500, and 800 mg/kg. The proportion of subjects achieving various trough thresholds of 5, 7, and 10 g/L for these three representative doses across the anticipated therapeutic range was calculated.

3. Results

3.1. Study Population and Dataset

The PK analysis dataset comprised 1437 measurable PK observations from 81 subjects. Two subjects were excluded due to missing dosing or sampling date/time information. A total of 23 PK observations were excluded due to inaccurate sampling or dosing information, and 171 PK observations were excluded as pretreatment/screening baseline total IgG serum samples. The resulting population PK analysis set contained 79 evaluable subjects and 1243 modeled PK observation records. The count of evaluable total IgG samples summarized by age group is presented in Table 1.

TABLE 1.

Modeling analysis dataset makeup: Sample sizes and covariate statistics by age category.

	2 to < 6 years (N = 3)	6 to < 12 years (N = 9)	12 to ≤ 16 years (N = 13)	> 16 years (N = 54)
Number of evaluable total IgG samples	29	94	144	976
Age (years)	4.3 (1.2) 5.0 [3.0, 5.0]	8.2 (2.0) 7.0 [6.0, 11.0]	13.8 (1.6) 14.0 [12.0, 16.0]	46.1 (16.6) 48.0 [17.0, 75.0]
Sex
Male	3 (100%)	9 (100%)	11 (84.6%)	24 (44.4%)
Female	0 (0%)	0 (0%)	2 (15.4%)	30 (55.6%)
Baseline body weight (kg)	17.4 (1.11) 17.2 [16.4, 18.6]	35.0 (11.2) 31.7 [19.7, 54.9]	59.3 (24.4) 54.0 [33.1, 120]	75.4 (20.9) 72.0 [43.4, 135]
Baseline total IgG (g/L)	7.95 (2.05) 7.61 [6.09, 10.10]	8.26 (1.68) 8.25 [4.59, 10.80]	9.46 (1.88) 10.10 [6.06, 11.60]	10.40 (2.81) 10.20 [6.13, 22.50]
Dose (mg/kg)	670 (386) 538 [368, 1100]	447 (128) 418 [273, 707]	504 (187) 462 [265, 897]	505 (145) 468 [295, 1030]

Note: Numeric columns are formatted as mean (SD) and median [range]; dose values are calculated as mg/kg doses derived from administered amounts and body weight; per protocol, trough‐guided dose adjustments may result in values outside the nominal 300–800 mg/kg range.

Abbreviations: IgG, immunoglobulin G; N, number of subjects with available information; SD, standard deviation.

Key covariates (baseline body weight, total IgG concentrations, and dosage) to visualize the makeup of the PK population by age are shown in Table 1. The pooled study dataset (studies Nabi‐7101 and 994) increased the number of pediatric subjects (≤ 16 years of age) contributing PK data from 16 to 25 individuals, although only three subjects were in the 2 to < 6 years group, all from Study 994. The IVIG 10% dose ranged from 265 to 1100 mg/kg across studies and dosing regimens.

3.2. Population PK Analysis

3.2.1. Exploratory PK Analysis

Exploratory graphical evaluations used the pooled total IgG data to establish the structural model of IGIV 10%. Figure 1 displays total IgG levels versus time plots stratified by 3‐ and 4‐week cycle and study since most recent dose on a logarithmic scale, with the locally weighted smoother indicating biexponential disposition.

FIGURE 1.

Total IgG concentrations versus time with LOESS on a logarithmic scale stratified by cycle and study. Red lines represent the LOESS, and gray lines represent individual subject data. Study stratification is denoted on the z‐axis. Study 994 and N7101 (also known as Nabi‐7101) are study identifiers. IgG, immunoglobulin G; LOESS, locally weighted scatterplot smoothing.

3.2.2. Population PK Model Development

Structural models including one‐ and two‐compartment disposition models with first‐order elimination were evaluated based on exploratory analyses and goodness‐of‐fit diagnostics. Model selection was guided by objective function value (OFV), diagnostic plots, and parameter precision. Body weight was included using allometric scaling normalized to 70 kg. In the estimated‐allometry model, a shared exponent was applied to CL and Q, and a separate shared exponent was applied to Vc and Vp (NONMEM control stream in Listing S1). In the reported fixed‐allometry sensitivity model, standard exponents were applied to the central compartment. The two‐compartment model demonstrated superior fit based on improved GOF plots (Figure S1). Residual diagnostics showed no significant trends for either model. However, both models exhibited misspecifications at extreme concentration ranges, as evident in the observation versus population prediction (PRED) plots. The two‐compartment model better characterized the PK data and serves as a robust foundation for further model development as base model, despite minor prediction errors at concentration extremes.

Table 2 summarizes parameter estimates for the two‐compartment models with both estimated and fixed allometric exponents. While both estimated and fixed approaches describe the data well, the estimated‐allometry model was preferred based on a statistically significant drop in objective function value (ΔOFV = −50.398; p < 0.05 with the addition of the two estimated parameters). Despite this both fixed and estimated allometric exponent models were qualified to conduct simulations. IVIG PKs were well described by a 2‐compartment disposition model with linear CL (0.0969 L/day), volume of distribution for both central (Vc; 3.25 L) and peripheral (Vp; 4.55 L) compartments, and intercompartmental clearance (Q; 0.432 L/day) based on the estimated exponent model. The IIV was estimated for CL, Vc, and Vp parameters with coefficients of variation of 23.7%, 17.7%, and 312%, respectively, with shrinkage estimates below 30%. Body weight was included a priori as a structural covariate on clearance and volume parameters with both exponents estimated to describe the current dataset. The estimated effects of baseline body weight on CL and Vc were 0.939 and 0.528, respectively. Results were similar for the fixed allometric exponents model (Table 2).

TABLE 2.

Model with estimated and fixed allometric exponents parameter estimates.

Parameters	Estimate	%RSE	95% CI	Shrinkage (%)
Estimated allometry model
CL (L/day)	0.0969	3.13	0.0910, 0.1030	—
Vc (L)	3.25	2.59	3.08, 3.41	—
Vp (L)	4.55	21.3	2.65, 6.45	—
Q (L/day)	0.432	9.63	0.3504, 0.5136	—
Allometric clearance (−)	0.939	6.69	0.815, 1.06	—
Allometric volume (−)	0.528	11.3	0.411, 0.645	—
Random effects (%CV)
IIV on CL	23.7	9.12	19.1, 27.7	7.10
IIV on Vc	17.7	12.4	12.7, 21.6	21.4
IIV on Vp	312	35.4	143, 607	28.8
Residual error
Proportional error (SDTM.PC) (−)	0.119	2.43	0.113, 0.124	5.80
Proportional error (SDTM.LB) (−)	0.0808	5.71	0.0717, 0.0898	9.20
Fixed allometry model
CL (L/day)	0.0979	3.16	0.0917, 0.1039	—
Vc (L)	3.36	3.29	3.15, 3.58	—
Vp (L)	3.62	19.8	2.22, 5.03	—
Q (L/day)	0.4872	14.9	0.3456, 0.6312	—
Allometric clearance (fixed)	0.75	—	—	—
Allometric volume (fixed)	1.0	—	—	—
Random effects (%CV)
IIV on CL	25.2	9.25	20.2, 29.4	5.40
IIV on Vc	24.6	11.2	18.5, 29.6	15.1
IIV on Vp	216	28.9	111, 366	29.4
Residual error
Proportional error (SDTM.PC) (−)	0.119	2.43	0.113, 0.124	6.10
Proportional error (SDTM.LB) (−)	0.0820	5.58	0.0730, 0.0909	9.70

Note: Residual error was estimated separately for IgG results from SDTM.PC and SDTM.LB.

Abbreviations: CI, confidence interval; CL, clearance; CV, coefficient of variation; IgG, immunoglobulin G; IIV, interindividual variability; Q, intercompartmental clearance; RSE, relative standard error; SDTM.LB, study data tabulation model clinical laboratory; SDTM.PC, study data tabulation model pharmacokinetic concentrations; Vc, central volume of distribution; Vp, peripheral volume of distribution.

All structural model parameter estimates were associated with relative standard errors ≤ 21% indicating acceptable precision. The interindividual variability (IIV) for Vp was high, likely due to all the data being modeled at steady state. The η‐shrinkage for the final/base model was acceptable for all parameters (< 30%). The ε‐shrinkage was low (< 10%).

Prediction corrected VPCs for the population PK models are displayed stratified overall and by adults versus pediatrics for the estimated allometric exponents model (Figure 2A,B) and for the fixed allometric exponents model (Figure 2C,D). The final population PK model was able to predict the observed median and the 5th and 95th percentiles of the observed total IgG concentrations with good accuracy. The median concentration was fully captured throughout the profile. Two subjects from the Phase 4 study as representative individual fits for estimated and fixed models are shown in Figure S2A,B.

FIGURE 2.

Prediction‐corrected visual predictive check of the population PK model. (A) Estimated allometric exponents–overall. (B) Estimated allometric exponents stratified by age group. (C) Fixed allometric exponents–overall. (D) Fixed allometric exponents stratified by age group. Black circles represent observed data. Solid black line represents the median (50th percentile) of the observed data. The dotted and dashed black lines represent the 5th and 95th percentiles of the observed data, respectively. The blue line represents the median (50th percentile) of the simulated data, and the shaded blue region is the 95% CI for that median. The lower red line and shaded region represent the 5th percentile of the simulated data and the 95% CI for that value, respectively. The upper red line and shaded region represent the 95th percentile of the simulated data and the 95% CI for that value, respectively. CI, confidence interval; IgG, immunoglobulin G; PK, pharmacokinetic.

The final model was utilized to obtain individual post hoc estimates of CL and Vc parameters; units for CL were converted to per kg, which are used frequently in the presentation of IgG products and previously for IVIG 10% [17]. Summary statistics by age group are shown for the estimated allometric exponents model and the fixed allometric exponents model in Table 3.

TABLE 3.

Post hoc pharmacokinetic parameters estimated by model with estimated and fixed allometric exponents by age group.

Age group	CL (dL/day/kg)		Vc (dL/kg)
	Mean	CV(%)	Mean	CV(%)
Estimated allometric exponents
2 to < 6 years	0.0149	6.7	0.88	17.05
6 to < 12 years	0.0146	15.8	0.63	19.05
12 to ≤ 16 years	0.0137	21.2	0.53	20.75
> 16 years	0.0145	24.8	0.46	17.39
Fixed allometric exponents
2 to < 6 years	0.0185	22.2	0.58	24.14
6 to < 12 years	0.0165	27.9	0.53	15.09
12 to ≤ 16 years	0.0143	24.5	0.50	18.00
> 16 years	0.0147	25.2	0.47	17.02

Abbreviations: CL, clearance; CV, coefficient of variation; SD, standard deviation; Vc, central volume of distribution.

3.2.3. Dosing Interval Simulations by Age Group

Boxplots for simulated trough IgG levels for 3‐week and 4‐week cycles are shown in Figure 3. Using 3 IgG trough thresholds of 5, 7, and 10 g/L that were selected as the minimum target level prior to dose individualization, the putative average therapeutic target, and the level achieved for the subjects in this study, respectively, the proportion of subjects above steady‐state total IgG thresholds by dose level and age group by fixed allometry are summarized in Table 4. Simulations performed for every 4‐week dosing cycle for both model types (Figure 3) suggested 90% of subjects would achieve ≥ 5 g/L trough levels (minimum recommended level) for a mid‐range dose of 500 mg/kg every 4 weeks.

FIGURE 3.

Boxplots for simulated total trough IgG concentration following 3‐ and 4‐week cycles of IVIG 10%. (A) 3‐week cycle estimated (left panel) and fixed (right panel) allometric exponents models. (B) 4‐week cycle estimated (left panel) and fixed (right panel) allometric exponents models. The box starts in the first (25%) and ends in the third quartile (75%) of trough concentration in each age group. The solid line in each box represents the median of trough concentration in each age group. The dots represent the subjects with trough concentration more than 1.5 × IQR from the closest edge of the box. IgG, immunoglobulin G; IQR, interquartile range; IVIG 10%, immune globulin intravenous [human], 10% liquid.

TABLE 4.

Trough concentration simulation summary: Proportion of subjects above steady‐state total IgG thresholds by dose level and age group–fixed and estimated allometry.

Age group (years)	Dose (mg/kg)	Proportion (%) of subjects above the total IgG trough level						Mean total IgG concentration (g/L)
		≥ 5 g/L		≥ 7 g/L		≥ 10 g/L
		3 Weeks	4 Weeks	3 Weeks	4 Weeks	3 Weeks	4 Weeks	3 Weeks	4 Weeks
Fixed allometry model
> 16	300	92.3	75.7	71.4	41.8	31.6	14.1	11.1	9.5
	500	99.7	97.5	97.9	86.4	83.5	59.5	18.5	15.8
	800	100	99.9	99.9	98.9	99.3	91.0	29.8	25.5
12–16	300	91.8	72.1	68.2	37.6	25.0	8.4	10.4	8.8
	500	99.6	96.4	97.4	84.8	82.6	51.0	17.2	14.5
	800	100	99.7	100	98.0	97.7	90.5	27.6	23.7
6 to < 12	300	85.6	62.8	52.3	29.1	14.5	5.6	9.0	7.8
	500	99.3	94.7	92.8	78.6	68.0	42.6	14.9	13.1
	800	100	99.6	100	97.5	96.4	84.5	23.8	20.8
2 to < 6	300	74.3	54.5	34.6	18.7	5.80	2.60	7.5	6.8
	500	98.7	89.5	89.4	68.6	54.2	31.9	12.7	11.0
	800	100	98.9	99.4	93.5	94.9	76.5	20.1	17.7
Estimated allometry model
> 16	300	92.9	74.9	70.4	42.6	28.0	12.9	10.9	9.43
	500	99.8	97.4	98.7	87.1	82.8	60.0	18.3	15.7
	800	100	99.9	99.9	99.2	99.5	91.4	29.4	25.2
12–16	300	95.0	77.3	72.8	42.6	29.3	10.3	10.8	9.27
	500	100	98.3	98.6	89.4	87.1	58.3	17.9	15.2
	800	100	99.9	100	98.8	98.7	93.6	28.7	24.8
6 to < 12	300	95.0	81.4	71.2	45.6	27.9	12.3	10.3	9.04
	500	100	98.9	98.5	91.6	84.6	62.2	17.1	15.1
	800	100	99.9	100	99.6	99.5	95.7	27.3	24.1
2 to < 6	300	94.2	84.0	70.3	48.8	25.1	11.9	9.75	8.84
	500	100	99.1	99.3	91.3	86.8	64.3	16.5	14.4
	800	100	99.9	100	99.6	99.5	95.4	26.1	23.1

Note: The proportion (%) of subjects above the total IgG trough level simulated including residual variability was calculated as (number of subjects above the threshold/1000) × 100.

Abbreviation: IgG, immunoglobulin G.

4. Discussion

IVIG 10% was first licensed for replacement therapy for PID in adults in 2012 based on the pivotal efficacy and safety study by Wasserman et al. [11]. Subsequently, in accordance with PREA PMR, a pediatric study was undertaken that demonstrated the efficacy and safety of IVIG 10% in children at least 2 years of age with PID; albeit this study only included three subjects aged 2 to < 6 years and six subjects 6 to < 12 years [12]. This is the first report to fully characterize the population PK profiles of IVIG 10% based on data from all 79 subjects who participated in these two clinical studies [11, 12], which formed the basis of the supplemental New Drug Application for IVIG 10%.

This pooled PK analysis set of 79 subjects contained a reasonable amount of pediatric data, with 13 subjects contributing data in the 12 to ≤ 16 years of age group and 9 subjects in the 6 to < 12 years of age group to support pediatric dosing recommendations. However, one limitation of this analysis is that only three subjects contributed data for the 2 to < 6 years of age group. This particular logistic barrier of difficulty in recruiting pediatric subjects is commonly observed in other studies [28, 29, 30, 31].

The precise estimation of PK parameters can be defined as a prospectively powered sample size to target a 95% confidence interval (CI) within 60% and 140% of the geometric mean estimates of for a given parameter in each pediatric sub‐group [32]. Estimates for pediatric sample sizes based on PK criteria can be calculated based parameter intersubject variability, which for total IgG CL can range up to ~35% [33], which would equate to a sample size of six to nine subjects. Given the practical constraints in recruiting very young pediatrics, model‐based simulation provides a powerful tool from which to extrapolate information from older pediatrics and leverage wide body of literature characterizing not only IVIG PK but also body size as a driving factor in its disposition. While common demographic covariates were screened for the potential to effect PK, as is most often case with for this category of plasma‐derived therapeutic, body weight was identified as the sole covariate affecting total IgG CL, and Vc parameters. Despite age and body weight correlations particularly notable for young subjects, age has not been identified as an independent predictor affecting exposure. Therefore, from a PK perspective, subgroup age category breakpoints (e.g., 2 to < 6, 6 to < 12 years, etc.) applied to the determination of IgG clearance and exposure under a weight‐based dosing paradigm are less meaningful.

Average baseline total IgG concentrations were lower in younger children, consistent with possible disease diagnosis or developmental differences; however, the range overlapped across pediatric age groups. Given stable dosing for at least 3 months prior to study entry was an inclusion criteria, baseline IgG was used solely to initialize model compartments. The contribution of intrinsic immunoglobulin production versus replacement therapy was not estimated given the lack of data from patients naïve to therapy.

The structural model for total IgG PKs after intravenous infusion of IVIG 10% was well described using a 2‐compartment model, consistent with other IVIGs administered by this route [33]. The principal model‐based results from this analysis aligned with the adult (N = 21) noncompartmental analysis results reported previously (mean total CL dL/kg/day = 0.02) [10]. The model‐based mean CL for adults (N = 54) was 0.0145 dL/kg/day for estimated and 0.0147 dL/kg/day for fixed allometric exponents. The sum of Vc and Vp was 7.8 L, which are reasonable estimates for a large molecule scaled to 70 kg and comparable to that reported in the literature for a range of IVIG products [33]. The estimated effects of baseline body weight for CL and Vc were 0.939 and 0.528, respectively. This is an interesting contrast to fixed allometric scaling where physiological principles dictate clearance scales less than proportionally to body size (fixed to 0.75) and volumes scale proportionally to body size (fixed to 1).

The model‐based clearances resultant from estimating allometric exponents were similar across both pediatric (≤ 16 years) and adult (> 16 years) age group categories. Estimated body weight exponents on IgG PK parameters vary widely in the literature, but are often higher for clearance compared to volume of distribution [33]. And while estimation is the more common approach for models fit to total IgG levels due to the uncertainty in the most appropriate scaling approaches for non‐small molecule therapeutics [34], estimated exponents can be sensitive to smaller sample sizes. Therefore, to allay concerns, fixed allometry was applied as a type of sensitivity analysis. Forcing clearance to scale with body weight forces children to have higher dose requirements on a mg/kg basis when comparing to adults [35]. Thus, simulations were conducted with 2 qualified models, one with allometric exponents estimated from the current data and one fixed to standard estimates for body weight. This allowed for a conservative approach from which to extrapolate and adjudicate whether the recommended dosage of 300 to 800 mg/kg used for adults would lead to comparable predicted trough IgG levels. Simulations showed clinically acceptable IgG levels would be achieved and support expanding the adult dosing recommendations to pediatric patients ≥ 2 years of age.

In this analysis, both models performed well to characterize total IgG concentrations where the typical bulk of clinical data were trough samples collected either 3 or 4 weeks post‐dose, demonstrating acceptable stability and predictability. Simulations were used, even for the more conservative approach of fixing the effect of body weight on PK parameters, which forces the nature of the relationship to demonstrate that an average dosing amount of 500 mg/kg IVIG 10% provides adequate trough levels in the majority of subjects regardless of age.

Trough IgG levels monitoring is an important consideration when evaluating IG therapies and is often used as a putative therapeutic target. Higher IgG trough levels have been associated with lower rates of infection with IVIG administration [36]. The European Medicines Agency requires that trough levels are non‐inferior to those of IVIG and does not recommend an initial dose adjustment [37, 38]. Although there is utility in estimates for population PK parameters to guide evidence‐based decisions, IG replacement therapy must still be individually tailored [19, 39]; there is increasing evidence that the IG dose needed to prevent infection varies with each patient [40, 41]. Data suggest a wide range of steady‐state serum IgG levels required in patients with PID [42], and individual patients may have their own biological IgG trough level that is essential to prevent infection [41, 43]. Each patient's dose should be individualized, taking into consideration the IgG trough levels and the clinical response. This may be, in part, why no clear total IgG exposure‐response relationships in PID have been reported.

In conclusion, all pediatric subjects with PK data had consistent IgG trough levels that remained above target therapeutic range (i.e., > 5 g/L). Drug clearance was similar between each pediatric age group, and between adult and pediatric PID subjects based on adult PK data from the previously completed pivotal study [12]. No pediatric subject required dose adjustment due to low IgG levels or infection [11, 12], and the incidence of treatment emergent adverse events was balanced across age categories in the Phase 4 study occurring in 2 of 3 subjects in the 2 to < 6 years age group, 3 of 5 subjects in the 6 to < 12 years age group, and all 8 subjects in the 12 to 16 years age group. Given a collective knowledge of IVIG PK, familiarity with plasma‐derived therapeutics for PID, and weight‐based IVIG 10% dosing tailored on an individual basis, the MIDD approach adds further support as prior knowledge to justify a lower burden of PK study sample sizes in very young children.

Author Contributions

T.D. and S.M. wrote the manuscript. T.D., S.M., R.A. and A.D. designed the research. K.K. and I.M. performed the research. T.D., S.M., R.A., A.D., K.K., and I.M. analyzed the data.

Funding

This study was funded by ADMA Biologics.

Conflicts of Interest

T.D. and S.M. are employees and minor stockholders of Certara USA. R.A., A.D., and K.K. are employees and minor stockholders of ADMA Biologics Inc. I.M. is an employee and minor stockholder of IMMUNOe Research.

Supporting information

Table S1: Clinical studies included in analysis.

Figure S1: Goodness‐of‐fit plots for the 2‐compartment base model with estimated or fixed allometric exponents by treatment cycle.

Figure S2: Individual model fit diagnostics—representative individuals.

Listing S1: Example NONMEM Control Stream.

Data Availability Statement

Access to anonymized data supporting the findings of this study is available from the corresponding author upon reasonable request after acceptance of this manuscript for publication and accessible for 12 months.