Population pharmacokinetics model validation using Kinetica
Xiaofeng Wang and Siu-Kei Tin
InnaPhase Corporation, Philadelphia, PA, USA
Purpose: To investigate the algorithms of population modeling and validation implemented in Kinetica applied to both rich data and sparse data.
Method description: Datasets for both modeling and validation were generated using Matlab. The simulated data sets are split into two groups either manually or by randomization: one group, called the test group, is used to build the model; and the other, called the validation group, is used to validate the model. 500 datasets were simulated with 20% of inter-individual variability (normal distribution) and 20% of proportional residual error. The sampling times for rich data are 0.1, 0.5, 1, 3, and 5 for each subject. Sparse datasets were made with two sampling time between 0.1 to 8 hours. Both modeling and validation were performed on rich datasets and sparse datasets. In one case, 400 datasets were used to build the model, and the remaining 100 were used as validation datasets; in another case, 40 datasets were used to build the model, and the remaining 460 were used as validation datasets.
Two methods are implemented in Kinetica for model validation: Concentration method and parameter method. In the concentration method, parameter values for subjects belonging to the validation group were obtained using results from the test group (both parameter values and covariable equations) combined with the covariables information of the subjects in the validation group. Then, the concentration profiles of the individuals in the validation group, called Ci,j,pred, together with 95% confidence interval, were predicted. The validation was made through concentration deviation of predicted from observed values. They were presented as both individual concentration deviations and the mean square errors.
In the parameter method, results (both parameter values and covariable equations) obtained from the test group using EM algorithm were applied to Bayesian fit (E-step) on the validation datasets. The individual parameters obtained from this step (E-step) are called Pj,obs. If there are no covariable equations, the deviation of Pj,obs from population parameter (Ppred) obtained from EM on test group will serve as the criterion for model validation. If there are covariable equations, the predicted individual parameter value, called Pj,pred will be obtained from the covariable equations (obtained from the test group) combined with the covariable information of each subject in the validation group. Then, the deviation of Pj,obs from Pj,pred will serve as the criterion for model validation.
In either method, the results are displayed both in spreadsheet form and in graphical form for easy comparison and visualization.
Results: For both rich datasets and sparse datasets, the parameter values obtained from model building agreed with the true parameter values used to simulate the datasets. The frequency histograms for both parameters and residuals indicated clearly the expected normal distribution. Model validation using either parameter method or concentration method also demonstrated that the results from model building are correct within inter-individual and intra-individual variability, either for sparse data or rich data.
Conclusions: The population algorithm implemented in Kinetica appears to perform correctly with the simulated datasets, within statistical errors. However, to further validate the performance of the algorithm in Kinetica, more scenarios need to be investigated.