Bridging studies: handling covariates models using the Prior approach
Anna Chan Kwong (1), Elisa Calvier (3), David Fabre (3), Gilles Tuffal (3), Florence Gattacceca (1), Sonia Khier (2)
(1) Aix Marseille Univ, INSERM, CNRS, CRCM SMARTc, F-13005 Marseille, France, (2) University of Montpellier, (3) SANOFI Montpellier
The PRIOR function in NONMEM stabilizes model estimates toward prior estimates by adding a penalty function on the objective function [1,2]: it enables the modelling of sparse data. However, covariate inclusion using this function requires further exploration.
We propose two strategies to handle covariates when modelling sparse data using the PRIOR function in NONMEM: first, to test the significance of a covariate already identified in the previous dataset (from which the prior parameters were estimated), second, to identify the covariates of the sparse dataset. We illustrate these approaches with the case example of a subcutaneously administered antibody.
Two datasets were used for the analysis:
- Dataset A (previous data): rich data from two clinical trials (36 healthy volunteers, 546 samples; 18 patients, 154 samples)
- Dataset B (new data): sparse data from one clinical trial (216 patients, 1171 samples)
Population pharmacokinetic (PopPK) analysis was run with NONMEM® version 7.4.1. Covariate inclusion was performed with the Stepwise Covariate Modelling (SCM) tool implemented in Perl Speaks NONMEM (PSN)® (forward inclusion: α=0.05, backward deletion: α=0.001). Age, weight, creatinine clearance, Glomerular Filtration Rate (GFR) and sex were tested as potential covariates.
Model A was built on dataset A.
Model AB was built on the pool of datasets A and B, to be used as a reference.
Dataset B was analysed using model A as prior in the PRIOR function, with two strategies for handling covariates:
- Assessment of the significance of the covariate included in the previous model. Model A without covariate and Model A with covariate were both fitted on dataset B with informative PRIOR on all parameters. The two models were compared using the Likelihood Ratio Test (α=0.001). The sum of the weights of the prior estimates of each model was normalized to 1 in order to get comparable objective function values.
- Search for new covariates. Model A without covariate was fitted on dataset B with informative PRIOR only on the parameters that needed to be stabilized. This model was then used as a base for SCM on the parameters estimated without prior information.
Covariates that were found statistically significant using strategies 1 and 2 (on dataset B) were compared to those of Model AB (on dataset A and B)
Model A and Model AB were monocompartmental with a first order absorption and a linear elimination, with interindividual variability estimated on all parameters (and a correlation between clearance and volume interindividual variability). Model A included the effect of age on clearance. Model AB included the effect of age, GFR and weight on clearance, and the effect of weight on volume. The relationship between clearance and age in Model AB was described by a piece-wise linear function (“hockey-stick”).
The results of the two strategies to handle covariates on dataset B are presented below:
- Assessment of the significance of the covariate included in the previous model. A drop of 7 points in objective function was found between Model A with or without covariate fitted on dataset B with informative PRIOR on all parameters, meaning that the covariate of Model A was not significant on dataset B.
- Search for new covariates. As dataset B alone was sufficiently informative to estimate clearance and volume and their interindividual variability, the covariate search was done on these parameters. Informative PRIOR were implemented only on the absorption rate constant. The following covariates were included: GFR and weight on clearance, and weight on volume.
With both strategies, the covariate age that was included on clearance in both Model A and AB was not found to be statistically significant. This could be explained by the large difference in age distribution between Datasets A and B (median [range] of 36 [19-77] and 68 [44-85] respectively) together with an impact of age on clearance only across the “young” subjects, assessed by the piece-wise relation between age and clearance in Model AB.
Except for this covariate, the second strategy found the same covariates as Model AB.
In this case example, the significant covariates found by the two strategies on the sparse dataset using the PRIOR function were consistent with those of the model of reference.
To generalize our results, this approach should be performed on simulations and challenged on other molecules and on datasets of different sizes.
 Per O. Gisleskog, Mats O. Karlsson, et Stuart L. Beal. « Use of Prior Information to Stabilize a Population Data Analysis ». Journal of Pharmacokinetics and Pharmacodynamics 29, n? 5-6 (1 décembre 2002): 473-505. https://doi.org/10.1023/A:1022972420004.
 Robert J. Bauer (ICON): NONMEM 7.4: Workshop for Advanced Methods