Modelling the influence of MDR1 polymorphism on digoxin pharmacokinetic parameters

Abstract

Objectives

Digoxin is a well-known probe for the activity of P-glycoprotein. The objective of this work was to apply different methods for covariate selection in non-linear mixed-effect models to study the relationship between the pharmacokinetic parameters of digoxin and the genotype for two major exons located on the multi-drug-resistance 1 (MDR1) gene coding for P-glycoprotein.

Methods

Thirty-two healthy volunteers were recruited in three pharmacokinetic drug interaction studies. The data after a single oral administration of digoxin alone were pooled. All subjects were genotyped for the MDR1 C3435T and G2677T/A genotypes. The concentration-time profile of digoxin was established using 12–16 blood samples taken between 15 min and 72 h after administration. We modelled the pharmacokinetics of digoxin using non-linear mixed-effect models. Parameter estimation was performed using the stochastic approximation EM method (SAEM). We used three methods to select the covariate model: selection from a full model using Wald tests, forward inclusion using the log-likelihood ratio test and model selection using the Bayesian Information Criterion.

Results

The three covariate inclusion methods led to the same final model. Carriers of two T alleles for the C3435T polymorphism in exon 26 of MDR1 had a lower apparent volume of distribution than carriers of a C allele. The only other covariate effect was a shorter absorption time-lag in women.

Conclusion

The apparent volume of distribution of digoxin is lower in TT subjects, probably reflecting differences in bioavailability. Non-linear mixed-effect models can be useful for detecting the influence of covariates on pharmacokinetic parameters.

Appendix

The SAEM algorithm is implemented in the MATLAB language in the software MONOLIX, available on the author’s website (http://www.math.u-psud.fr/~lavielle/monolix/logiciels.html). We used MONOLIX version 1.1.

The dataset was prepared in R as a two-dimensional array, with columns representing subject identification (ID), time and observed concentrations. A column representing the dose was also added (with the same value at all times and for all subjects). To code for the categorical covariates representing the genotypes of MDR1, we used dummy variables. For example, to code for the exon 26 polymorphism, we defined three dummy variables, one with value 1 for the subjects with CC genotype and 0 for the other two genotypes; one with value 1 for the subjects with CT genotype and 0 otherwise; one with value 1 for the subjects with TT genotype and 0 otherwise. Each dummy variable was entered as an additional column in the dataset. Exemples of datasets used with MONOLIX are included in the Zip file containing the program.

The following code was used to define the pharmacokinetic model (lines beginning with the symbol % are comments), using the explicit analytical equation:

The program MONOLIX is run from within MATLAB. A window opens in which the user specifies the dataset, the model function and the number of covariates to include in the analysis. In our analysis, the variance-covariance matrix was set to diagonal and the variance for parameters k_1,2 and k_2,1 was set to 0. The covariate model was also specified via the graphical interface as a linear combination of the dummy covariates defined above.

Version 1.1 of the software requires some tuning of the numerical procedure to ensure convergence of the Markov chain during the stochastic approximation step (see the user manual on the website). We used the following sequence of four stepsizes in the algorithm:

$$ {\left\{ {\matrix{ {a_{1} = 0}{{\rm{during}}\,K_{1} = 500\,{\rm{iterations}}} \cr {a_{2} = 0.5}{{\rm{during}}\,K_{2} = 100\,{\rm{iterations}}} \cr {a_{3} = 0.8}{{\rm{during}}\,K_{3} = 100\,{\rm{iterations}}} \cr {a_{4} = 1}{{\rm{during}}\,K_{4} = 2000\,{\rm{iterations}}} \cr } } \right.} $$

(6)

The output from MONOLIX consists of a series of graphs as well as a table of parameter estimates with their associated standard errors. Hypothesis testing opens a new window in which the two models compared are specified, and the corresponding criteria (AIC, BIC, log-likelihood) are shown after the fit of each model is performed. Empirical Bayes Estimates (EBE) of the individual parameters are obtained as the mean of the posterior distribution, and the standard errors on these parameters (the standard deviations of the posterior distribution) are also reported.