A workflow for evaluating and optimizing the designs of paediatric studies
Moustafa M. A. Ibrahim (1), Emma Hansson (1), Andrew C. Hooker (1,2), Martin Bergstrand (1)
(1) Pharmetheus, (2) Uppsala University, Department of Pharmacy, Pharmacometrics Research Group, Uppsala, Sweden
Objectives: To develop a standardized in-silico workflow for efficiently designing paediatric PK studies, aligning with the FDA precision criteria for sample size justification [1].
Methods: The template workflow was developed for RStudio and Quarto using an example inspired by multiple real-life examples [2]. In this example, the drug was first studied in adults. The adult PK model was a two-compartment linear model with a first order absorption. Then we followed the following workflow structure:
Paediatric PK model: The paediatric PK model is assumed to be the same as the adult PK model with the inclusion of the respective allometric scaling and maturation functions:
- Weight on CL and Q.
- Weight on Vc and Vp.
- Post-menstrual age (PMA) on CL:
CL = Θ * (WT/median WT)β * PMAγ / (PMA50γ + PMAγ)
where Θ is the population CL, β is the exponent of weight effect, γ is the hill coefficient, which controls the steepness of PMA function and PMA50 is the PMA at 50% of the maturation function.
The values of the parameters governing these functions were obtained from literature, and to be latter estimated based on data from the future paediatric study. The model was implemented in mrgsolve [3]. The model implementation was validated by comparing mrgsolve population predictions with the population predictions from NONMEM.
Initial design: The proposed design for the paediatric study included age and weight-based dosing regimen, selected to achieve exposure within a target therapeutic window of 20-300 nmol/L. The initial proposed study design contained 5 age-based cohorts with N of subjects per cohort:
- < 3 years
- 3 - <6 years
- 6 - <9 years
- 9 - <12 years
- 12 - <18 years
PopED evaluation: The proposed design was implemented in PopED [4,5]. We evaluated the design in two ways:
1- All patients in each cohort were assumed to have the same covariates, using the expected median age and weight from NHANES database, per cohort.
2- Each patient was assigned an individual age and weight, sampled from NHANES database [6] to achieve a realistic covariate distribution.
FDA precision criteria: “The study must be prospectively powered to target a 95% CI within 60% and 140% of the geometric mean estimates of CL and Vc for the drug in each paediatric sub-group with at least 80% power” [1,7].
To compute the 95% CI for both apparent CL and Vc for all age groups, we used the results from PopED evaluation with 100 simulations from the covariates distribution and the corresponding fisher information matrix. To compute the power, we repeated the previous step 100 times to construct 100 confidence intervals. Subsequently, the power was calculated as the percentage of the 95% CI that fell within 60 and 140% of the geometric mean estimates.
Optimization: When unsatisfactory results are obtained, different design aspects (sampling schedule, age-cohorts, N of subjects per cohort etc.) can be re-considered to arrive at an optimised proposed design.
Stochastic simulation and estimation (SSE): To confirm PopED results for the proposed final design, we sampled 100 different data sets from the NHANES data and performed SSE using NONMEM. The results of the SSE were used to compute the 95% CI for both apparent CL and Vc, and to compute the power.
Results: PopED evaluations showed that the proposed dosing regimens achieved the target therapeutic window per patient, and that the proposed dosing schedule was sufficient to estimate the PK model. From the 1st evaluation in PopED, all fixed effects had a satisfactory RSE (<30%) except for PMA50 and γ. Although the second evaluation yielded improved RSE the computed 95% CI of the apparent CL remained wide for younger age groups (>140%).
N of subjects per cohort was iteratively evaluated, leading to the conclusion that N=9 was optimal, with at least N=6 subjects under the age of 6 months, to obtain satisfactory RSE (<30%) for all fixed effects including PMA50 and γ. The computed 95% CI of the apparent CL and Vc were similar for the PopED evaluation and the SSE. The power for the apparent CL was 89% and for the apparent Vc, 100%.
Conclusions: To meet the FDA criteria with the current design, N=9 subjects per cohort with at least N=6 under the age of 6 month were needed. However, when the drug is not intended for use in younger age groups (<2 year) and a maturation function is required, satisfactory RSE could be obtained using only the median age covariates per cohort: Otherwise, a full covariate distribution is needed. The computed 95% CI obtained from PopED were in good agreement with NONMEM. Lastly, we successfully developed and show-cased a workflow for optimizing and evaluating paediatric studies based on available PK models in adults, before access to paediatrics data.
References:
[1] Wang, Yaning, Pravin R. Jadhav, Mallika Lala, and Jogarao V. Gobburu. 2012. “Clarification on Precision Criteria to Derive Sample Size When Designing Pediatric Pharmacokinetic Studies.” The Journal of Clinical Pharmacology 52 (10): 1601–6.
[2] Montepiedra, Grace, Elin M. Svensson, Weng Kee Wong, and Andrew C. Hooker. 2023. “Optimizing the Design of a Pharmacokinetic Trial to Evaluate the Dosing Scheme of a Novel Tuberculosis Drug in Children Living with or Without HIV.” CPT: Pharmacometrics & Systems Pharmacology 13 (2): 270–80.
[3] Baron, Kyle T. 2022. “Mrgsolve: Simulate from ODE-Based Models.”
[4] Foracchia, Marco, Andrew Hooker, Paolo Vicini, and Alfredo Ruggeri. 2004. “Poped, a Software for Optimal Experiment Design in Population Kinetics.” Computer Methods and Programs in Biomedicine 74 (1): 29–46.
[5] Nyberg, Joakim, Sebastian Ueckert, Eric A. Strömberg, Stefanie Hennig, Mats O. Karlsson, and Andrew C. Hooker. 2012. “PopED: An Extended, Parallelized, Nonlinear Mixed Effects Models Optimal Design Tool.” Computer Methods and Programs in Biomedicine 108 (2): 789–805.
[6] Centers for Disease Control and Prevention (CDC). National Center for Health Statistics (NCHS). National Health and Nutrition Examination Survey Data. 2017-2020. Available at: https://wwwn.cdc.gov/nchs/nhanes/continuousnhanes/default.aspx?cycle=2017-2020
[7] Draft Guidance - General Clinical Pharmacology Considerations for Pediatric Studies of Drugs, Including Biological Products Guidance for Industry, FDA-2013-D-1275, September 2022
