Eero Siivola (1,2), Sebastian Weber (1), Aki Vehtari (2)
(1)Statistical Methodology Group, Novartis Pharma AG, Basel, Switzerland; (2) Department of Computer Science, Aalto University, Espoo, Finland
Objectives
Pediatric drug development is lagged w.r.t. to the respective adult program. Knowledge about a safe and efficacious regimen is available for the adult population prior to initiating pediatric trials. Population pharmacokinetic (popPK) models account for between-subject variation and for population level effects. For the pediatric trials we can utilize the adult models to extrapolate in absence of data to the pediatric population to select the dose regimens. The extrapolation is often performed by applying allometric scaling which adjusts the physiologic parameters of a popPK model by a size measure to account for organ function variation with size like weight. In addition, or as alternative, PBPK modeling can be used to account for the ontogeny of enzymes involved in the drug’s PK. It is critical to either confirm the extrapolation assumptions or detect and quantify deviations using the very sparse data of pediatric trials. Commonly parametric modeling of the maturation effect is used, but these parametric forms are not derived from any first principles such that there is a risk of model misspecification. As a solution we propose the use of a data-driven non-parametric approach. We consider that extrapolation is performed using allometric scaling only while a maturation process in the pediatric population could be present which we would like to detect from the pediatric trial data.
Methodology
In practice maturation effects are functions of some age measure and are multiplied onto the individual clearance, for example, as a scaling factor less than unity implying a slower elimination of the drug. We suggest to use the non-parametric Gaussian Processes (GPs) to represent the maturation function [1]. Formally, the GP defines distributions of function values such that any finite combination of points follows a multivariate normal distribution with a covariance function that defines the properties including smoothness of the modelled functions.
We simulate a signal and a no-signal scenario. In both cases an adult model with allometric scaling of the clearance is used to choose weight-based dosing regimens for a simulated pediatric trial. The pediatric trial data is generated with allometric scaling only for the no-signal case and with presence of a maturation function in addition for the signal case. The pediatric trial is chosen to be realistically small with only 20 patients which are assumed to have age 0y – 5y with equally spaced ages and we measure only 10 pre-dose [WS1] measurements per patient. To ease the estimation we constrain the GP to be monotonically increasing and to vanish for large ages which assumes the adult model is correct in the domain of the adult data. The inference is done with Stan 2.18.1 [2].
Results
The results show that the GPs are able to detect maturation effects for the signal case and they do correctly assert the absence of a maturation function in case of the no-signal case. That is, in the signal case the GP correctly resembles the Hill function which was used to simulate the data while in the no-signal case the GP correctly reduces to 0 for the entire age-range. Furthermore, we evaluate the key design parameters of the pediatric trial sample size and the number of measurements per patient. Here we find that greater gains are made with more measurements per patients rather than increasing the number of patients.
Conclusions
The choice of the dosing regimen for pediatric trials is in most cases based on extrapolation applied to established popPK or PBPK models. We propose the use of constrained non-parametric Gaussian Process (GP) to detect deviations within the original extrapolation model given the new data. In a simulation study we confirmed that this approach can detect an unexpected maturation function of the clearance in a typical sparse data setting of pediatric trials. The advantage of using GPs as compared to parametric approaches is the lower risk of model misspecification and greater uncertainty in age ranges without data, which avoids over-confident conclusions in absence of data. The GP approach can thus serve as basis for detecting deviations from initial extrapolation assumptions and allow for correction of proposed dosing regimens as needed given the available data which warrants adequate treatment of the pediatric population.
References:
[1] Rasmussen, C. E. (2003). Gaussian processes in machine learning. In Summer School on Machine Learning(pp. 63-71). Springer, Berlin, Heidelberg.
[2] Stan Development Team. 2018. http://mc-stan.org.
Reference: PAGE 28 (2019) Abstr 8874 [www.page-meeting.org/?abstract=8874]
Poster: Methodology - New Modelling Approaches