Ka-Ho Hui, Tai-Ning Lam
School of Pharmacy, Faculty of Medicine, The Chinese University of Hong Kong
Objectives: It has been in doubt whether parameter estimates are reliable when fitting a mixture model to pharmacokinetic data using NONMEM. In the case that a pharmacokinetic (PK) parameter is being modeled with a combination of the mixture model and covariate model, it is arguable that it may be mathematically challenging to distinguish the discrete random effects from the covariate effects, particularly when the two types of effects act in the opposite directions. The current study aims at evaluating the estimation of parameter estimates, especially the covariate effect and the individual probabilities, using a simulation approach, by which true values are available for evaluation. Three objectives were set:
- Simulate PK datasets assuming the mixture model and the covariate effect, followed by parameter estimations;
- Identify factors associated with the biases in the estimations of covariate coefficient (CC), individual probabilities (IP) and other parameters; and
- Quantify any significant association identified.
Methods: The one-compartment model with first-order absorption, a single covariate effect on clearance (CL) and a mixture model of two subgroups with different typical values of clearance was applied. The following parameters were block-sampled and varied between simulated datasets: typical values of PK parameters, i.e., CL of the subgroups, volume of distribution (Vd) and absorption rate constant (ka), inter-individual variances of CL (CVCL), mixing proportion of the subgroups, residual variability, number of subjects, covariate effect and covariate skewness. Each virtual subject received a single dose and was sampled at 12 occasions. Parameters were estimated using FOCE+I in NONMEM with the same model. For each of CC, IP, and other parameters, the estimation errors were plotted against other parameters to identify the presence of probabilistic and/or systematic biases under different circumstances. In the case of significant findings, the results would be further quantified.
Results: 59,049 PK datasets were simulated and then subjected to parameter estimations. The median errors in the estimation of CC were mostly within ±1% and did not show apparent trend against various parameters investigated. The sizes of errors in the estimates of CC were found to be associated with (1) the change in objective function value after removing the mixture model per observation (dOFV/obs) (95% ranges of relative errors were estimated to be 28% and 13% for dOFV/obs of 0.01 and 0.1, respectively), (2) the estimated CVCL (13% and 33% for CV of 10% and 50%, respectively), and (3) the number of subjects in the dataset (47% and 11% for 20 and 300 subject, respectively). As to estimated IP, previous findings that (1) the IP of each subject classified to his estimated subgroup is overestimated, and that (2) IP is more reliable when dOFV/obs is large could be replicated.[1] In the current study, it could also be observed that IP tends to be more overestimated when estimated CC is larger than the estimated ratio of typical values of clearance between the two subgroups (fast/slow), RCL. When estimated CC is half of RCL, overestimation of IP could reach 9%; but when estimated CC is 1.5-fold of RCL, overestimation of IP could reach as high as 27%.
Conclusions: The current study revealed that the change in objective function value after removing the mixture model is highly associated with the estimation error of covariate effects. In fact, together with previous findings, the current study again demonstrated how indicative the change in objective function value is against the reliability of model parameter estimates. [1,2] The current results quantified the biases in the estimation of parameter estimates when fitting a mixture model with covariate effects in NONMEM and could be of value for reference in future attempts to develop similar models.
References:
[1] Ka-Ho Hui, Tai-Ning Lam. 2018. Evaluation of individual probability in mixture model in NONMEM, poster presented to the 9th American Conference on Pharmacometrics, San Diego, CA, The United States, 7-10 October 2018.
[2] Ka-Ho Hui, Tai-Ning Lam. 2016. Prediction of subject classification performance of mixture model in NONMEM, poster presented to the AAPS Annual Meeting and Exposition 2016, Denver, CO, The United States, 13-17 November 2016.
Reference: PAGE 28 (2019) Abstr 8884 [www.page-meeting.org/?abstract=8884]
Poster: Methodology - Model Evaluation