Investigating Interoccasion Variability and Estimation Methods
Dana Bakir and Murray P. Ducharme
Université de Montreal
Objectives:
Interoccasion (IOV) variability, also known as the variability that accounts for the changes in individual pharmacokinetic (PK) parameters between study occasions, is critical to estimate in Population PK analyses (PPK) when replicate dosing observations are included in a dataset. Karlsson et al., 1993 [1] published the first method to estimate IOV. Its use, however, is not without difficulty, as it involves the fitting of three interindividual difference parameters (ETAs) for only two occasions on an individual basis (although not on a population basis). How IOV should be calculated and reported with this method is not always clear, in part due to these estimation difficulties. We decided to investigate other methods for characterizing IOV, or lack of agreement between occasions, and compare their estimations using multiple NLME algorithms available in NONMEM® [2] and ADAPT5® [3] in order to provide useful practical recommendations.
Methods:
Thirty (30) studies with 40 subjects each were simulated by an independent researcher with only two PK parameters displaying IOV using a 2-cpt PK linear model. The researcher fitting the various studies only knew that the IOV had to be coded on CL/F and Ka, but was completely blinded as to the values of the PK parameters, their interCV, their IOV, and their associated residual variability. Studies were simulated to have small to large values in each of these parameters.
All studies were fitted starting with the same initial priors. They were fitted using three different methods for allowing inter-occasion differences. Algorithms tested included NONMEM® FOCE, FOCEI, and MCISEM, as well as MLEM in ADAPT5®. Population and individual IOV, as well as individual and population parameters, their variability and residual variability results were compared between algorithms in terms of absolute bias and imprecision. Statistical significance was set a priori at p<0.05.
Results:
For all analyses, MLEM always converged the first time it was tried (30 of 30), while FOCE and FOCEI on average only converged the first time 8 out of 30 times. Convergence was therefore easier to attain overall with MLEM.
For all analyses, bias of the population results and imprecision of the individual results appeared better with MLEM than FOCE or FOCEI. There were no apparent differences between FOCE and FOCEI.
When coding IOV with Method #1 (Karlsson method), only 26 studies successfully converged using FOCE, FOCEI, despite numerous attempts. This method could not be coded within MLEM, as the method does not allow the fitting of a superfluous interCV. On the CL/F parameter:
- The number of studies with a |bias| of less than 20% for IOV calculated from the individual simulated and fitted were 12 (median |bias|=6.31%) for FOCE and 12 (median |bias|=7.70%) for FOCEI.
- No apparent difference was detected between FOCE and FOCEI performance, although convergence may have been slightly easier to achieve with FOCEI overall.
When coding IOV with Method #2 (simplification of Karlsson method), 30 studies successfully converged using FOCE, FOCEI and MLEM. On the CL/F parameter:
- The number of studies with a |bias| of less than 20% for IOV calculated from the individual simulated and fitted were 18 (median |bias|=4.94%) for FOCE, 16 (median |bias|=3.77%) for FOCEI and 20 (median |bias|=4.73%) for MLEM.
- No apparent difference could be detected among the 3 estimation methods
When coding IOV with Method #3 (alternative method looking at lack of agreement between occasions), 30 studies successfully converged using FOCE, FOCEI and MLEM. On the CL/F parameter:
- The number of studies with a |bias| of less than 20% for IOV calculated from the individual simulated and fitted were 16 (median |bias|=4.05%) for FOCE, 18 (median |bias|=7.15%) for FOCEI and 21 (median |bias|=6.60%) for MLEM.
Conclusions:
Our findings indicate that both IOV coding method and estimation algorithms impact the final fitted results and should be chosen carefully. For all IOV methods, the bias in the population mean parameters and the imprecision in the individual fitted results appeared to be better with MLEM than with FOCE and FOCEI. Currently, results from the MCISEM are not in line with MLEM for reasons that are unknown. When comparing FOCE, FOCEI and MLEM with the individual IOV, the recommendation would be to use MLEM with coding Method 2 and 3 due to its ease in convergence and success in estimating less than 20% bias of the simulated IOV results.
References:
[1] Karlsson M, Sheiner L: The Importance of Modeling Interoccasion Variability in Population Pharmacokinetic Analyses, Journal of Pharmacokinetics and Biopharmaceutics, 21(6): 735-750, 1993.
[2] D’argenio A, Schmutizky A, and Wang X. 2009. ADAPT User’s Guide: Pharmacokinetic/Pharmacodynamic Systems Analysis Software, Los Angeles: Biomedical Simulations Resource.
[3] Beal SL et al. 1989-2011. NONMEM Users Guides. Icon Development Solutions, Ellicott City, Maryland, USA.