Handling within-subject/between-occasion variability in longitudinal data: Common Challenges and Practical Solutions
Paolo Denti
University of Cape Town, Cape Town, South Africa
One of the main features of nonlinear mixed-effects models (NLME), and arguably the most powerful one, is their ability to separate different layers of variability in the data, thus teasing out the deterministic signal (fixed effects) from the separate strata of stochastic noise (random effects). The stochastic variability can be broken down into random effects on the parameters of the structural model (i.e. ETAs in NONMEM jargon) and the residual ones on each observation (i.e. EPSILON). Often, ETA random effects are used to quantify between-subject variability, relegating within-subject variations to residual unexplained variability (RUV).
However, within-subject variability (WSV) may arise from factors (such as physiological changes or environmental influences) that affect the value of the structural parameters. These can be modelled as such, as opposed to simply lumping them with the RUV, thus extracting more information from the data.
The within-subject change in parameters over time is sometimes gradual (e.g. due to relatively slow weight and body composition changes), and other times more independent between different defined periods (e.g. random variability in rate of gastric emptying between different dose intakes). Most commonly, WSV for model parameters is characterized based on an assumption of independence between defined “occasions” and is referred to as of between occasion variability (BOV).
The importance of including BOV in population PK/PD analyses - and the consequences of not doing so - has been highlighted before [1]–[3] Despite this, use of BOV in population PK/PD models remains relatively uncommon and often sub-optimally implemented. This is probably because implementation of BOV adds complexity and is therefore sometimes ignored, but it can be extremely relevant, depending on the purpose of the model. Finally, correctly coding BOV in the dataset and model is often trickier than one would think.
In this tutorial we will explore how between-occasion variability can be implemented in population PK/PD models.
The definition of what constitutes an “occasion” for different PK/PD parameters will be discussed. In PK data, each single dosing interval may be considered as having its own occasion-specific parameter value for absorption, while disposition parameters tend to change more slowly and gradually, so discretisation of the experiment time into occasions is not straightforward. An option is to consider that only “visits” that are days/weeks may constitute an occasion for parameters such as clearance and volume. When studying drugs that are dosed repeatedly within a maintenance regimen, a pre-dose sample is often collected. Its concentration depends on the dosing history and the PK parameters in the day(s) before the PK visit. This is particularly tricky in outpatient PK studies, where one often has to rely on self-reports. Despite the paucity of information contained in single pre-dose samples, these can be considered as belonging to a separate PK occasion, thus absorbing some of the consequences of poor information.
The definition of BOV for PD models and their parameters is also not straightforward. It is implementable for rapid direct effect perhaps, whereby the experiment time can be separated for single doses or visit, and also on top of BOV in PK. In other scenarios with continuous monitoring of subjects for extended periods of time, more complex methodologies may need to be employed allowing continuous time changes [4].
The implementation of these concepts in the dataset and the model code will be discussed, highlighting practical challenges such as handling time-varying variable with “dummy records”, and addressing the coding of BOV when dealing with a large number of repeated doses, especially for drugs with a long terminal half-life.
The tutorial will also elucidate the consequences of ignoring BOV using some real-world examples, showing incorrect attribution of variability between different parameters, or inflated residual unexplained variability, as previously reported [1], [2]. Moreover, and more importantly, ignoring BOV may cause inaccurate and unstable estimates of fixed effects, or prevent the correct identification of a covariate effect or even the structural model.
Finally, the tutorial will discuss the importance of correctly accounting for WSV in scenarios such as TDM and model-informed dose adjustments [5][6]. In this case, properly accounting for within-subject variability ensures more accurate estimation of the individual parameters, leading to better understanding of individual-specific dynamics, thus advising more robustly on the optimal dose. Inclusion of BOV is also essential when assessing bioequivalence, and when performing clinical trials simulations.
By the end of this tutorial, participants should have a comprehensive understanding of WSV and its importance in NLME modelling, plus a smorgasbord of practical strategies on the implementation of BOV.
[1] M. O. Karlsson and L. B. Sheiner, “The importance of modeling interoccasion variability in population pharmacokinetic analyses,” J. Pharmacokinet. Biopharm., vol. 21, no. 6, pp. 735–750, Dec. 1993, doi: 10.1007/BF01113502.
[2] S. Koehne-Voss, A. Gautier, and G. Graham, “The impact of unmodelled interoccasion variability in bioavailability and absorption on parameter estimates in population pharmacokinetic analysis,” in PAGE 24 (2015), 2015, p. Abstract 3555. Available: https://www.page-meeting.org/?abstract=3555
[3] R. L. Lalonde, D. Ouellet, E. K. Kimanani, D. Potvin, L. M. Vaughan, and M. R. Hill, “Comparison of different methods to evaluate population dose-response and relative potency: Importance of interoccasion variability,” J. Pharmacokinet. Biopharm., vol. 27, no. 1, pp. 67–83, 1999, doi: 10.1023/A:1020682729226.
[4] C. Deng, E. L. Plan, and M. O. Karlsson, “Approaches for modeling within subject variability in pharmacometric count data analysis: dynamic inter-occasion variability and stochastic differential equations,” J. Pharmacokinet. Pharmacodyn., vol. 43, no. 3, pp. 305–314, 2016, doi: 10.1007/s10928-016-9473-1.
[5] J. A. Abrantes, S. Jönsson, M. O. Karlsson, and E. I. Nielsen, “Handling interoccasion variability in model‐based dose individualization using therapeutic drug monitoring data,” Br. J. Clin. Pharmacol., vol. 85, no. 6, pp. 1326–1336, Jun. 2019, doi: 10.1111/bcp.13901.
[6] L. Keutzer and U. S. H. Simonsson, “Individualized Dosing With High Inter-Occasion Variability Is Correctly Handled With Model-Informed Precision Dosing—Using Rifampicin as an Example,” Front. Pharmacol., vol. 11, no. May, pp. 1–15, May 2020, doi: 10.3389/fphar.2020.00794.
