Usman Arshad, Estelle Chasseloup, Rikard Nordgren and Mats O. Karlsson
Dept of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden. Department I of Pharmacology, University Hospital Cologne, Germany.
Objective: The underlying basic assumption of interindividual variability being unimodally distributed in nonlinear mixed effects models does not hold when the studied population exhibits multimodal parameter distributions (e.g. fast or slow metabolizers). Multimodal distributions can either be described by a covariate or with the implementation of mixture models which allow the identification of parameters specific to a subpopulation. Despite their utility to describe data arising from a population with underlying heterogeneity, there are limitations in assessing mixture models, since the common assessment tools do not account for the multimodality in parameter distributions. Visual predictive checks (VPCs) are a standard simulation based diagnostics tools, but these are not yet adapted for the mixture models. The aim of this project was to design VPCs accounting for multimodal parameter distributions and thereby allow (i) the diagnosis of the mixture component aspects of the model, and (ii) more powerful assessment of other model components by reducing between-subpopulation variability from the graphs.
Methods: Analysis with mixture models provides two individual-level metrics of subpopulation association (i) the probability for an individual to belong to subpopulation1, and (ii) the most likely subpopulation for an individual to belong to. The former metric is in the NONMEM program termed PMIX and can be retrieved from the *.phm file which is a standard output of models with mixture components. The latter metric is retrievable as the MIXEST variable and can be output to standard table files. Naturally, MIXEST can also be easily calculated from the PMIX information. VPCs are based on a comparison of simulated and observed data statistics. In order to retrieve individual PMIX and MIXEST information for simulated data, an evaluation (or estimation) step is necessary.
Mixture model specific VPCs were developed based on the output from PsN and implemented in Xpose/R. The mixture-specific VPCs were developed and assessed using both simulated data. For illustration, the approaches were also applied to an irinotecan mixture model2 demonstrating 30% lower clearance of irinotecan metabolite (SN-38) in individuals with UGT1A1 homo/hetero vs wild-type genotype. The irinotecan/SN-38 model was applied to an external data set3 and diagnostics were generated.
Results: Two types of mixture model specific VPCs were developed and implemented. The first type splits the observed and simulated data according to the MIXEST assignment. Thus the most likely subpopulation for each real or simulated individual is estimated and directing the VPC panel to which the data is allocated. As the individual subpopulation allocation frequency can differ between real and simulation data, and because such an allocation difference can be a sign of model misspecification, these numbers are included in the graphical display. A shortcoming of the MIXEST-based allocation strategy is that there is a tendency for subjects to be allocated to the dominating subpopulation (similar to the shrinkage phenomenon in individual, empirical Bayes, parameter estimation). This shortcoming can be avoided through the second type of VPC which splits observed and simulated data according to the PMIX value. VPCs with segregated subpopulations were helpful in identifying model misspecifications in case of irinotecan mixture model which were not evident with standard normal VPCs previously. It was evidenced that the model was over-predictive for fast metabolizers while under-predictive in case of slow metabolizers.
Conclusions: A graphical and statistical comparison of observations and predictions derived from the multimodal distributions in mixture models is presented. Partitioning of observed and predicted data between subpopulations can be done in two ways depending upon the underlying information (MIXEST or PMIX). These approaches can be a useful diagnostic tool for the development and evaluation of mixture models in future.
References:
[1]. Carlsson KC, Savic RM, Hooker AC, and Karlsson MO. Modeling Subpopulations with the $MIXTURE Subroutine in NONMEM: Finding the Individual Probability of Belonging to a Subpopulation for the Use in Model Analysis and Improved Decision Making. AAPS J. 2009; 11(1): 148–154.
[2]. Jiménez BJ and Ruixo JJP. Influencia de los polimorfismos genéticos en UGT1A1, UGT1A7 y UGT1A9 sobre la farmacocinética de irinotecán, SN-38 y SN-38G. Farm Hosp. 2013; 37(2): 111-27.
[3]. Xie R, Mathijssen RH, Sparreboom A, Verweij J and Karlsson MO. Clinical pharmacokinetics of irinotecan and its metabolites in relation with diarrhea. Clin Pharmacol Ther. 2002; 72(3): 265-75.
Reference: PAGE 27 (2018) Abstr 8600 [www.page-meeting.org/?abstract=8600]
Poster: Methodology - Model Evaluation