Summary:
Data from clinical study of Pharmathen were analyzed and three different population pharmacokinetic models (pop- PK) were developed. It was an open label, balanced, randomized, single-dose, three-treatment, three-sequence, three-period, three-way crossover, pilot Bioequivalence Study of Tacrolimus in 12 healthy, adult, subjects under fasting conditions. All products were prolonged release, with reference products Envarsus tablets prolonged release 4 and 1 mg and Advagraf hard capsules prolonged release 5 mg. The test product is a tacrolimus prolonged release tablet 5 mg. Three models were developed, one for each product, since they had different formulation and were given once, with a rinsing interval of 22 days.
To begin with, data and results from other papers were studied and used as guidance. Firstly, observations were separated per product. Later, for each product, the structural model, the error model, the interindividual variability and interoccasion variability were defined. Furthermore, models were tested for correlations and covariates between parameters. Tools used for the screening process and the general validation of the model were, the value of the objective function -2LL and Likelihood Ratio Test (LRT), the information criterions AIC and BIC, the goodness of fit plots, the VPC and the bootstrap.
Concerning the structural model, a variety of options was provided by the library of Monolix, such as the type of administration, the existence of time delay, the order of absorption and the type of distribution and elimination. In addition, double absorption models were taken under consideration due to the multiple peaks displayed in the data. Oral type of administration was selected. To investigate whether there is delay in the absorption, three things were observed: a) data b) deviation in the OBS vs PRED plot in log scale for the first hours (indicates delay) c) values of -2LL before and after the addition of delay in the structural model (decline greater than 3.84 points in the value of -2LL indicates there is time delay). To determine the number of compartments, similar procedures followed with the addition of the observation of the relative standard error estimates % of the parameters. High values show, that the addition of an extra compartment made difficult the estimation of the parameters and therefore made the model with more compartments inappropriate. Two and three compartment model was chosen, since one compartment was inadequate.
About type of absorption, zero and first order of absorption were tested with variant combinations. The type of absorption that caused decline of -2LL/AIC/BIC, improvement of VPC and goodness of fit plots was selected. Same method was applied to determine the type of elimination, linear or Michaelis Menten.
As error model, the proportional was preferred in all cases. Because, when using combined model the parameter of the constant model was extremely low. The interindividual variability was defined for all parameters and followed lognormal distribution except for the parameter F1 (fraction of absorption) at double absorption models which followed logit normal distribution.
Correlation was found between some parameters. Unfortunately, the input of covariates was not possible, either because they didn’t have statistical significance or because the ones that were significant didn’t have natural meaning and increased the RSE% of the parameters.
Covariates and correlations were detected through the observation of correlation between random effect plots and individual parameters vs covariates plots. Also, they were detected via the number of p-value at Pearson correlation test or the T-test.
Interoccasion variability wasn’t added to the model since the subjects were given one dose of 5 mg from each formulation with an interval of 22 days. All models were internally validated with VPC and bootstrap.
The results are presented below.
Test product: Two compartment model, with double absorption and linear elimination. The two absorptions are simultaneous and both have time delay. The first absorption is first order with ka1=0.42 h-1, has a (time delay) Tlag=0.39 hours and fraction of absorption F1=0.42 of the total drug. Second absorption is zero order with duration Tk02= 0.87 h, has a Tlag2=Tlag1+diffTlag2= 1.33 h and absorbs 1-F1 of the total drug. Correlation was found between CL-Q-V2. The interindividual variability of clearance (CL) is 56%, of the volume (V1) is 32.6%, of the intercompartmental clearance (Q) is 48.4% and of the volume (V2) is 48.1%. Parameters are highly correlated with correlation coefficients ≈ 0.97 and uncertainty lesser than 5%. Residual variability was found 8.1%.
Advagraf: Two compartment model, with lag time Τlag=0.35 h, first order of absorption ka=0.39 h-1, linear elimination and correlation between Q-V2-CL. Interindividual variability of clearance in central compartment was (CL) 50.7%, of the intercompartmental clearance (Q) 66.4%, of the volume (V1) 55.4% and of volume (V2) 47.6%. Residual variability was estimated 9.76%. Parameters Q-V2, V2-CL, Q-CL are correlated with correlation coefficient close to 0.93 each and uncertainty lesser than 5%.
Envarsus: Two compartment model, with double absorption and linear elimination. The absorptions are simultaneous, are zero order and have time delay. One of them starts earlier with Tlag1= 0.32 h, has fraction of absorption F1=0.56 and duration Tk01= 3.2 h. The second one starts at Tlag2= Tlag1 + diffTlag2 =2 h, has fraction of absorption 1-F1 and duration Tk02= 1.06 h. Furthermore, correlation between V2 and CL was found, with correlation coefficient 0.96 and uncertainty 2.6 %. Interindividual variability of clearance was (CL) 58.1%, of volume (V1) 73.9 %, of intercompartmental clearance (Q) 73.8 % and of volume (V2) 55.6%. Residual variability was estimated 8.99 %
To conclude, comparison with bibliography showed there is a great range in the value of parameters. In certain studies the results were similar and in others different. The size of the sample and the health status of the population had great impact in the conclusions that are drawn for each study. Positive was the fact that for studies with similar structure with this one the results were similar. Finally, the parameter values displayed big variation within each product.
