Pediatric Pharmacometrics
The use of model informed drug development (MIDD) approaches in pediatric drug development is highly recommended due to:
- Practical and ethical limitations in data collection.
- Ability to quantify the effects of growth and maturation by leveraging data from literature and older patients.
Pediatric Age Terminology
The terminology used around pediatric age is commonly inconsistent. Relating age to last menstrual period is done because most women know when their last period began but not when ovulation occurred. As long as menstrual dates are remembered accurately, this method of estimating the date of delivery is reliable (Figure 1; Table 1) [1].
| Term | Abbreviation | Comment |
|---|---|---|
| Gestational (or “menstrual”) age | GA | Used when describing the age of a neonate. A 28-week, 5-day neonate is considered a 28-week neonate. |
| Postnatal (or “chronologial”) age | PNA | Time since birth |
| Postmenstrual age | PMA | Applied from 0–1 years of chronological age. A 33-week, 1-day GA infant who is 10 weeks, 5 days PNA would have a PMA of 43 weeks, 6 days. |
| Corrected (or “adjusted”) [gestational] age | CGA | Time since expected date of delivery (see Equation 1). Used to describe children up to 3 years of age who were born preterm. |
| Conceptional age | Time between conception and birth. Very accurate for in-vitro fertilization. Should not be used. |
Methods of determining GA should be clearly stated so that the variability inherent in these estimations can be considered when outcomes are interpreted. The convention for calculating GA when the date of conception is known is to add 2 weeks to the conceptional age. CGA is PNA reduced by the number of weeks born before 40 weeks of gestation (Equation 1).
\[ \text{Corrected gestational age}_\text{weeks} = \text{PNA}_\text{weeks} - (40 - \text{GA}_\text{weeks}) \tag{1}\]
Age Classification of Pediatric Patients
Any classification of the pediatric population into age groups is to some extent arbitrary, but a classification such as the one below provides a basis for thinking about study design in pediatric patients (Table 2). The identification of which ages to study should be medicinal product-specific and justified. Dividing the pediatric population into many age groups might needlessly increase the number of patients required. Sometimes, it may be more appropriate to collect data over broad age ranges and examine the effect of age as a continuous covariate.
The study design and statistical plans should prospectively take into account changing numbers of patients within a given age group.
| Group | Age | Comment |
|---|---|---|
| Preterm neonates | birth–27 days (CGA, Equation 1) | < 39 weeks gestation |
| Term neonates | birth–27 days (CGA, Equation 1) | 39–41 weeks gestation |
| Infants | 28 days–23 months | |
| Children | 2–11 years | Often divided into 2–5 years, and 6–11 years. |
| Adolescents | 12–17 years | PK often similar to adults. |
| Adults | ≥ 18 years | Acts as reference. |
Pediatric PK studies
Relative bioavailability comparisons of pediatric and adult formulations should typically be performed in adults. PK studies in the pediatric population are generally conducted in patients with the disease.
For drugs with linear PK in adults, a single-dose in pediatric patients may be sufficient for dose selection. Sparse sampling in multidose clinical studies could confirm these findings. However, steady-state studies are necessary if adults exhibit dose- or time-dependent PK or PD.
Pediatric dosing is typically based on mg/kg body weight, up to the maximum adult dose. Although surface area-guided dosing might be preferred, measuring the height or length, especially in infants and young children, is often prone to errors. For medications with a narrow therapeutic window, such as those used in oncology, surface area-guided dosing may be necessary.
PK extrapolation
Whether PK extrapolation is feasible or not, is ultimately a clinical question. If an indication can be assumed to behave similarly in adult and pediatric populations, PK extrapolation (“bridging”) can be used. However, there could be cases in which a dedicated pediatric study is warranted (e.g., safety concerns or clinical presentation of the disease).
The relevant PK metric(s) linked to efficacy and safety and the exposure-response relationship should first be established in adults. In pediatric patients, we want to start with a clinically relevant dose. Pediatric PK should then be comparable to that of adults.
The plan is to predict exposure in a pediatric age group (Table 2), collect data, refine predictions for the next younger group, and repeat. Extrapolation generally includes a population PK model and exposure-response models. These models may be independent of adult models if there are adequate data or they may be developed in combination with adult data.
Allometric scaling for PK
A previously developed adult PK model can be extrapolated to pediatric patients using allometry, which relates volume of distribution and clearance to body size. Researchers have studied and applied this theory across various animal species and human subjects using a wide range of compounds [2]. Volume of distribution scales proportionally with body size (Code 1), while clearance scales less proportionally (Code 2). It has proven robust and reliable, except in some targeted therapies and large molecule biologics. Allometric scaling should not be used on rate constants.
Step 1: Refit the Final Adult Data with Allometric Exponents
Scale each volume parameter, including central volume and peripheral volumes.
V1 = THETA(1) * EXP(ETA(1))
V1 = V1 * (WT / 70)**1 ; Allometric scaling
V2 = THETA(2) * EXP(ETA(2))
V2 = V2 * (WT / 70)**1 ; Allometric scalingScale each clearance parameter, including total clearance (CL) and inter-compartmental clearance values such as Q.
CL = THETA(1) * EXP(ETA(1))
CL = CL * (WT / 70)**0.75 ; Allometric scaling
Q = THETA(2) * EXP(ETA(2))
Q = Q * (WT / 70)**0.75 ; Allometric scalingFix exponents if you don’t have pediatric PK data. Fix AND estimate them if you have pediatric PK data. Do a sensitivity analysis: How do the exposure predictions change?
The new model should give slightly different estimates for the volume and clearance parameters, but the diagnostics should be quite similar.
If your model already includes WT as a covariate, perhaps centered on the median WT instead of 70 kg, replace it with the standard allometric exponents Code 1, Code 2. Estimated exponents based on median WT can skew results when extrapolating beyond the observed range.
By converting to the standard WT of 70 kg and using standard exponent values, you leverage over 50 years of experience from other compounds when simulating outside adult data. Additionally, if AGE or WT is included elsewhere in the model, remove these covariates. They could cause problems with extrapolation after refitting the model with standard allometric exponents.
Maturation
In neonates the maturation level of eliminating organs influences the estimates and in adults the body composition will affect them. Data from pediatric development programs are often too limited to confirm whether allometric exponents differ from theoretical values. MSWP considers the use of fixed exponents both scientifically justified and practical when developing popPK models in children.
In lower ages (< 2 years) there are also maturation functions that come into play. For these pediatric patients it is important to include maturation function(s) to describe pediatric PK (Code 3).
CLR = THETA(1) * EXP(ETA(1))
CLR = CLR * (WT / 70)**0.75 ; Allometric scaling
TM_50 = 47.7
Hill = 3.4
CLR = CLR * PMA**Hill / (TM_50**Hill + PMA**Hill) ; MaturationThe maturation half-life (TM50) is fixed to the literature value of 47.7 weeks and the Hill-exponent to the value of 3.4 [3]. The distribution (mean, [min–max]) of PMA (weeks) in this study population was (518, [57–1652]). Assuming renal maturation time differs in pre-term infants, a separate TM50 value could be estimated for them if the current model poorly describes this subgroup.
This is due to high correlation between body weight and age in pediatric patients [4].
Step 2: Prepare a Data Set with Pediatric Simulation Subjects
Use either NHANES (US subjects 2–18 years), or a growth chart (e.g. WHO). The WHO data is preferred for non-US studies or for pediatric patients less than 2 years of age.
Because NHANES involves sampling individual subjects, there may be limited data in certain categories—especially for younger patients. Therefore, for younger patients—usually those under 2 years of age, but sometimes under 6—it’s better to use the CDC or WHO growth charts instead.
Create at least 250 simulation subjects in each age group of interest (Table 2). You can adjust these age groups based on the disease condition or target patient population.
The growth charts provide the distribution of WT for various ages and statures of children. To create a simulation subject:
- Generate a uniform distribution of ages in each age-group, with the desired number of subjects.
- Create 250 simulated male subjects and 250 female subjects in the same age-group (e.g., 12–18 years).
- For each of these 500 subjects, identify the mean and standard deviation for WT based on their specific AGE and SEX.
- Randomly sample a single WT using the mean and standard deviation from the growth chart.
This process creates a set of simulation subjects with WT, age group, and SEX.
Step 3: Simulate Exposures and Estimate Target Pediatric Doses
Randomly sample ETAs (in e.g. R) to calculate the individual PK-parameters for each simulation subject. The WT will be used in the calculation of the V- and CL-parameters. Then, using the individual PK-parameters, the appropriate dosing regimen is simulated using the adult clinical dose. The exposure for each pediatric age group is calculated and compared to the reference exposure for adults. Assuming dose-proportional PK, the optimal pediatric dose can be calculated:
\[ \text{Dose}_{\text{pediatric, optimal}} = \frac{\text{Dose}_{\text{adult, observed}}}{\text{AUC}_{\text{pediatric, simulated}}/\text{AUC}_{\text{adult, observed}}} \tag{2}\]
Adjust Dosepediatric,optimal to a feasible amount (Dosepediatric,adjusted). Rerun the simulations with the new dose and compare AUCpediatric,simulated to AUCadult,observed. It is expected that Dosepediatric,optimal will be different for each age group (Table 2).
How to present results from a PK extrapolation
The plot with all age groups receiving the adult clinical dose can be contrasted with a plot with age groups using Dosepediatric,adjusted. If you have pediatric data, you can overlay observed pediatric exposure with the simulated distributions to identify how well your model predicted the pediatric exposure.
The most relevant covariate influencing PK in pediatric patients is body weight accounting for size differences, and age (Figure 1) in the youngest pediatric patients to account for maturation of drug eliminating processes (see Code 3).
Relevant predefined exposure metrics should be presented graphically versus body weight and age on a continuous scale (Figure 3). If the drug is indicated to be used in the age range below one year, exposure vs body weight and age should be depicted in an additional separate figure focused on children 0–1 year of age.
Often plots that show the distribution of AUCpediatric,simulated along with the distribution of AUCadult,observed or simulated values from individual adult subjects using the final popPK model using box-plots can be useful (Figure 4). If different doses are proposed for bands of weight or/and age, exposure ranges predicted for the proposed doses for the subsets of the pediatric population should be visualized as box-plots (Figure 4). The reference range in the adult population (median and outer percentiles of observed or simulated data) should be given additionally (Figure 4). The same statistics should be presented numerically in tables.
PD extrapolation
Unlike PK, PD models are disease- and therapy-specific, making direct extrapolation challenging.
Response and PD models from adults may not apply to children. This is because children and adults have different physiology that PD-wise cannot be easily extrapolated. Children are not small adults (Figure 5).
Babies are still developing, which can be visualized in part the relationship between the size of their head and the lengths of their arms is changing as the babies grow and become adults (See video below).
Unless there’s clinical efficacy data in pediatric patients, be very cautious to extrapolate response or PD models from adults to pediatric patients.
Considerations include:
- Ontogeny of drug targets: Maturation of biological systems may alter response.
- Sensitivity adjustments: Use conservative parameters (e.g., lower EC50).
- Clinical caution: Without pediatric data, PD extrapolations are empirical.