Guenter Heimann, Inga Ludwig, Sebastian Weber, Thomas Dumortier
Biostatistics & Pharmacometrics, Novartis Pharma AG
Objectives:
Recruitment of patients into pediatric studies is difficult and slow, and traditional fully powered pivotal trials are prohibitive.
For indications and drugs where the disease progression in children is similar to that in adults, and where the pharmacology of the drug is similar to that in adults, one may fully extrapolate efficacy from adults to children. Often, however, there is not yet enough evidence to apply full extrapolation. In these cases one may want to apply a partial extrapolation approach, and one needs to collect some efficacy data in children to demonstrate that the adult and the children efficacy are similar.
In this talk, we use three real (but anonymized) examples were extrapolation was or is applied, to explain the principles behind our approach. In two of these examples, some aspects of the extrapolation were done in an ad-hoc manner. We propose a better approach, which we applied for the third example. One of the objectives of this better approach is that its operating characteristics improves with increasing sample size in the pediatric study.
Methods:
In principle, our extrapolation approach consists of three steps: (1) the adult data are used to develop a model which links exposure and baseline risk factors to clinical outcome or surrogate markers, (2) the model is then used to predict the clinical outcome of the pediatric study conditional on observed exposure and covariates, and (3) the predicted outcome is then compared to the observed outcome to validate the model. Successful validation serves as supportive evidence to justify partial or full extrapolation.
In order to validate the prediction, our proposal is to simulate (from the adult model) a predictive distribution for the outcome each of the n pediatric patient separately (conditional on the exposure and risk factors), and to calculate the percent of this distribution below the actual observation. If the adult model is adequately predicting the pediatric data, one obtains n approximately uniformly distributed “observations”. We use these n percentages and a Cramer von Mises test statistic to provide a confidence interval for the deviation from uniformity (see [1], [2], and [3]).
Note that the approach proposed here are closely related and applicable to VPCs and the normalized prediction distribution errors (NPDE) as discussed in [7] and earlier by [4] and [6]. In our case, each pediatric subject only contributes one observation and hence the issue of decorrelation does not apply.
Results:
The first example is from a transplantation program. A model to predict organ rejection in an individual as a function of exposure over time was developed [4] for the original adult submission. This model is a proportional hazards model with time dependent covariates. The corresponding pediatric study consisted of 21 children, some of which were censored. A popPK model was used to estimate the exposure over time. The adult model was used to simulated 1000 pediatric studies with 21 children, conditional on the estimated exposure over time, and the observed censoring times. For each of these simulated studies, the overall number of organ rejections was counted, to obtain a predictive distribution for the number of organ rejections in 21 children. The validation was done by comparing the overall number of observed organ rejections with this predictive distribution.
In the second example, the same principle was applied to a survival endpoint. Here a predictive distribution for the Kaplan Meier estimator was provided. And compared to the observed Kaplan Meier estimator.
We show that the validation approaches applied in these examples do not improve with increasing sample size of the pediatric study. The revised approach, however, does have a better operating characteristic with increasing sample size.
Conclusions:
Full or partial extrapolation is based on scientific and empirical evidence that the adult label can be applied to children as well. Our approach mimics this objective better than using adult data as historical information and/or to generate informative priors for a separate analysis of the pediatric data.
The adult model can be a simple or complex statistical model, Bayesian or frequentist, or a population pharmacodynamic model. It should contain all relevant baseline risk factors. This is important to be able to address differences in the baseline distribution between adults and children with regard to these risk factors.
References:
[1] Baringhaus, Ebener, and Henze.The limit distribution of weighted L2-goodness-of-fit statistics under fixed alternatives. Ann Inst Stat Math (2017) 69:969–995.
[2] Baringhaus and Henze. Cramér–von Mises distance – probabilistic interpretation confidence intervals and neighbourhood-of-model validation. Journal of Nonparametric Statistics, 29:2, 167-188.
[3] Baringhaus, Gaigall, and Thiele. Statistical inference for L2-distances to uniformity. Computational Statisitcs (2018) 33:1863–1896.
[4] Brendel, Comets, Laffont, Laveille, Mentré. Metrics for external model evaluation with an application to the population pharmacokinetics of gliclazide. Pharm Res. 2006;23 (9):2036–49.
[5] Dumortier, Looby, Luttringer, Heimann, Klupp, Junge, Witte, VanValen, and Stanski. Estimating the Contribution of Everolimus to Immunosuppressive Efficacy When Combined With Tacrolimus in Liver Transplantation: A Model-Based Approach. Clinical Pharmacology and Therapeutics (2015) 97411-418.
[6] Karlsson and Savic. Diagnosing model diagnostics. Clin Pharmacol Ther. 2007;82(1):17–20.
[7] Laffont Concordet. A new exact test for the evaluation of PK-PD models using random projections. Pharm Res (2011) 28:1948–1962.
Reference: PAGE 28 (2019) Abstr 9167 [www.page-meeting.org/?abstract=9167]
Poster: Methodology - New Modelling Approaches