Sebastian Ueckert (1), Svetlana Freiberga (1), Gunnar Yngman (1), Mats O. Karlsson (1)
(1) Department of Pharmaceutical Biosciences, Uppsala University, Sweden
Objectives: Understanding and explaining sources of variability in the data is a significant component of any analysis. Clinical trial data with its many levels of hierarchy, such as country, center, patient, visit, sample, and so on, is particularly complex. Fortunately, nonlinear mixed effect models (NLMEM) have proven to be well suited to handle this complexity, and they have become the quasi-standard for pharmacometric trial data analysis. However, it can be challenging in practice to understand the complex interactions of parameter variability, residual variability, covariates and the non-linear function. A parameter on the logit-scale with large estimated variability might still only contribute to a small fraction of the variability in the response and another one with a low BSV magnitude might translate to a significant driver of response variability.
The objective of this work was therefore to introduce a novel model visualization that allows attributing the different constituents of response variability dynamically.
Methods:
Derivation: Following the law of total variance, the model variability model was first split into residual unexplained variability (RUV) and between-subject variability (BSV). Using a general formula for the decomposition of variation [1], the BSV was then further decomposed by successively conditioning the remaining variability on groups of random effect parameters. The resulting exact but analytically intractable expression was approximated by considering a linearization of the NLMEM. From this approximation, the conditional variance expressions were derived analytically.
Implementation: The visualization method was implemented using NONMEM, PsN, and R. First, PsN is used to generate an augmented NONMEM control stream extracting the necessary derivative information for the linearization. R is then used to calculate the conditional variability expressions and plot each variability component as stacked ribbon versus the independent variable.
Evaluation: The visualization was evaluated by applying the method to a set of 31 published model and assessing the plausibility of the resulting plots.
Results: A novel model visualization to attribute different sources of variability was implemented and applied to a set of 31 models. In its current implementation, the method applies to all continues-type data models in NONMEM.
For a one-compartment model with first-order absorption for warfarin [2], as an example, the visualization shows how during the first couple of minutes variability is almost entirely driven by the BSV in absorption rate. This is followed by a phase where variability is dominated by the variability in distributional volume and, finally, a phase with a successive increase in the importance of clearance BSV. The additive RUV in this model shows as a factor with varying contribution, only 5% in the absorption phase and up to 25% in the terminal phase.
For models with a full random effect covariate model (FREM)[3], the approach allowed visualizing the impact of covariates at different time points. Furthermore, by varying the conditioning order, it was also possible to highlight different aspects of the variability composition, such as either the contribution from each parameter or from all PK and PD parameters together.
Conclusions: This new visualization provides insights into the importance of the many sources of variability in an NLMEM. The gained understanding can guide model building decisions and assist in communicating model assumptions to non-modelers.
References:
[1] Bowsher et al. Proceedings of the National Academy of Sciences 109.20 (2012): E1320-E1328.
[2] O’Reilly RA et al. Journal of Clinical Investigation 1963;42(10):1542-1551
[3] Karlsson PAGE 21 (2012) Abstr 2455 [www.page-meeting.org/?abstract=2455]
Reference: PAGE 27 (2018) Abstr 8659 [www.page-meeting.org/?abstract=8659]
Poster: Methodology - Covariate/Variability Models