Mixture Modeling as a Data Imputation Method
Purpose:. To demonstrate the use of mixture modeling in population PK analysis to predict drug concentrations for a subset of subjects with missing data for a key categorical covariate.
Methods: Drug X is mainly metabolized by the polymorphic enzyme CYP2D6 and consequently the extent of metabolism is genotype dependent. A population PK model was developed for Drug X with the goal of predicting steady-state concentrations for a subsequent PK/PD analysis of the clinical effects. A core PK model was developed using only those subjects with known CYP2D6 genotype. To estimate the steady-state exposure for subjects with missing genotype, a mixture model was developed. Subjects with known genotypes were assigned to Population 1 and their genotypes were not estimated. The mixture model assigned the subjects with unknown genotype to one of the 4 populations defined by the subjects with known genotype (that is, poor (PM), intermediate (IM), extensive (EM), and ultra-extensive metabolizer (UM)). Population PK modeling was performed using NONMEM® Version 6. Goodness of fit for the core and mixture models was assessed by examination of the following data and figures: the outcome (convergence and covariance); the agreement in scatterplots of population and individual predicted versus measured observations for each classification group; and the scatterplots of weighted residuals versus population and individual predicted observations.
Results: The core model fit the data well; the model converged with 3.3 significant digits and a successful covariance step (standard errors less than 33%). Goodness-of-fit plots show that the model is without bias. The mixture model minimized successfully with 2.5 significant digits. The R matrix for the mixture model was algorithmically singular, and standard errors were obtained from the S matrix. The plots of population predicted versus measured concentrations show that the model provided unbiased predictions for the subjects of unknown genotype classified by the mixture procedure. Scatterplots of weighted residuals versus population and individual predicted concentrations show no trends. Standard errors for the core parameters were less than 20%. This model was considered fit-for-purpose in predicting concentrations for subjects with missing genotype.
Conclusions: Mixture models have been used previously to explain interindividual heterogeneity as arising from the mixing of unknown subpopulations. This case study illustrates the novel and successful use of a mixture model to obtain predicted drug concentrations for a subset of subjects with a missing key categorical covariate.
American Conference on Pharmacometrics (ACoP), San Diego, California, April 2011
By S. Willavize, Jill Fiedler-Kelly, W. Hanley, L. Mahnke, Y. Hang, J. Z. Peng, Luann Phillips