Paediatric trial design optimization using prior knowledge in combination with modelling & simulations
Elisa Borella (1), Sean Oosterholt (2), Paolo Magni (1), Oscar Della Pasqua (2)
(1) Dipartimento di Ingegneria Industriale e dell’Informazione, Università degli Studi di Pavia, Pavia, Italy (2) Clinical Pharmacology & Therapeutics Group, University College London, London, United Kingdom
Objectives:
Evidence of PK/PD relationships for a new compound requires data arising from well-designed and relatively large clinical trials. Lack of attention to such requirements usually yields PK and PD parameters estimates which are biased or show poor precision. However, this prerequisite is often not possible in case of paediatric and rare diseases, where the patient population is small. In these cases, it is strongly recommended using all the available data and knowledge to design informative trials and analyse the data[1-5].
Our investigation uses clinical trial simulations based on the PK and the non-inferiority trial conducted by the DEferiprone Evaluation in Paediatrics (DEEP)[6] consortium as a case study. The main scope of the DEEP consortium trial is to characterize the PK of deferasirox (DFX) and to establish the non-inferiority of deferiprone (DFP) relative to DFX in paediatric patients with rare anaemias. Here we evaluate to what extent the use of prior knowledge can support: 1) the analysis of sparse samples collected in a (very) limited number of children when Bayesian estimation methods are used; 2) the optimisation of study design, as defined by ED-optimality, and the choice of alternative designs; 3) the development of drug-disease models to predict long-term clinical response.
Methods:
A population PK model for DFX was developed using published data from several PK studies in adults[7-11]. Allometric scaling was then used to account for PK differences in children. Scaled values of PK model parameters were used as input for the simulation of concentration-time profiles in virtual patients with same demographic covariates of the DEEP-2 study population.
1) Evaluation of the performance of Bayesian estimation methods in analysing very sparse PK data
PK trials were simulated in R, extracting randomly each time a different subset of virtual patients and one virtual sample per subject at sampling time points defined in the original clinical study protocol. For each simulated trial, the population PK model was evaluated in NONMEM with FOCE method, using the sparse simulated data, and $PRIOR when priors are defined. Three different analyses were compared: population analysis without priors, with highly-informative or weakly-informative priors. For each analysis, this simulation-estimation procedure was repeated until 100 successful runs were obtained. Probability of successful convergence and ratios of the individual exposure-related parameter estimates (AUC, Cmax) to the ‘true’ values were used to compare the performances of each method. A sensitivity analysis on priors was also performed to evaluate how heavily the conclusions were weighted on prior beliefs. To this aim, several scenarios including conditions in which DFX PK differences in children were not fully accounted for by allometric scaling were considered.
2) Evaluation of the impact of optimized designs on the precision of exposure extrapolation
Assuming uncertainty in PK model parameters, optimized blood sampling time-windows were obtained using the ED-optimization method in PopED. Optimized PK trials were simulated in R, extracting each time a different subset of virtual patients, who had samples collected at various points according to the optimized sampling time-windows. For each simulated trial, the population PK model was evaluated in NONMEM with FOCE method and $PRIOR with weakly-informative priors, using the optimized simulated dataset and priors on PK model parameters. This simulation-estimation procedure was repeated until 100 successful runs were obtained. Precisions of individual exposure-related parameters estimates and convergence of the algorithm were compared for different n° of optimized samples per subject (from 1 to 4).
3) Evaluation of the impact of a model-based approach on the duration of a non-inferiority trial
Serum ferritin data retrieved from several published studies[12-23], involving both untreated and treated patients with DFX or DFP, were used to develop a PK/PD model for iron overload. Serum ferritin-time profiles in the virtual patients were simulated assuming similar mechanism of action in adults and children. Shorter trial durations with a sampling interval of one month were then tested. Non-inferiority trials were simulated for each scenario, extracting each time a different subset of virtual patients with their corresponding ferritin values. These data were used together with the PK/PD model to predict individual treatment response at 1 year. A comparison between the predicted serum ferritin values and the ‘true’ values was used to evaluate the predictive performance and positive predictive value for each scenario.
Results:
1) DFX PK was well described by a 2-compartment model with first order absorption and elimination. Allometric scaling was added on CL and Q with exponent 0.75, and on V1 and V2 with exponent 1. The use of priors consistently helps to obtain a successful convergence of the FOCE method, increasing the probability of successful convergence in case of sparse sampling from only 12% (no priors) to 56% and 75% for weakly- and highly-informative priors, respectively. Weakly-informative priors are more robust when there is uncertainty on the assumptions adopted in the model (e.g., scaling method).
2) It has been demonstrated that collecting only one sample per subject, even if these samples are randomly extracted from the optimized sampling time-windows, leads to a 60% chance of over/underestimating the exposure in children of more than 1.3 folds. Increasing the number of samples only from 1 to 3 shrinks this probability to less than 10%.
3) The developed PK/PD model for iron overload accurately describes the individual time-course of serum ferritin in patients undergoing life-long blood transfusions and chelation therapy. The model consists in a compartment representing the iron in excess in the body which is linked to the serum ferritin through an Emax model. The use of a model-based approach, using a PK/PD model developed starting from historical data, leads to predictive performances (e.g., positive predictive values) at 6 months that are not significantly different from those at 1 year, suggesting the possibility of shorter trial duration.
Conclusions:
The concept of prior knowledge is often highlighted in statistical research, but rarely evaluated in a systematic manner. We have used a concrete case to illustrate the implications of Bayesian principles in the context of pharmacometric analyses. Our investigation shows that Bayesian estimation methods allow integration of prior distributions as descriptors of both uncertainty and expected differences in parameter estimates, supporting the analysis of sparse samples when the population sample size is limited. Besides, we show how prior distribution can be used together with optimization and M&S techniques to inform decisions about the design of studies in small populations.
References:
[1] EMA Guideline on clinical trial in small populations, 2006 (http://www.ema.europa.eu/docs/en_GB/document_library/Scientific_guideline/2009/09/WC500003615.pdf)
[2] FDA Draft Guidance for Industry on Rare Pediatric Disease, 2014 (http://www.fda.gov/downloads/RegulatoryInformation/Guidances/UCM423325.pdf)
[3] FDA Report: Complex Issues in Developing Drugs and Biological Products for Rare Diseases and Accelerating the Development of Therapies for Pediatric Rare Diseases, 2014 (http://www.fda.gov/downloads/RegulatoryInformation/Legislation/SignificantAmendmentstotheFDCAct/FDASIA/UCM404104.pdf)
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[6] http://www.deepproject.eu/
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