Background: All models are underpinned by assumptions. The validity of any inference drawn from a model depends on the appropriateness and likely impact of the underlying assumptions [1]. However, in the literature surrounding quantitative pharmacology models and pharmacometrics, assumptions inherent to model development and use are not routinely acknowledged, described, or evaluated. This casts doubt on the effective use of the model. The aim of this work is to develop a framework for evaluating assumptions intrinsic to a top-down or bottom-up pharmacometric model. Here, we limit the scope of the framework to model building and model use.
Defining assumptions: We categorise assumptions into two types: (a) implicit in which a theorem is being relied upon to form a framework of the modelling process (e.g. linearity between two variables if relationships were to be quantified using Pearson correlation); (b) explicit which arises from a gap in knowledge for which an imputation by the investigator will be required (e.g. application of a Michaelis-Menten model to describe a system response for which we have no prior knowledge other than the model seems to work).
A flowchart to evaluate assumptions: A flowchart was developed for systematic evaluation of assumptions. For each assumption, the impact, I (“significant”, “insignificant/irrelevant”, “unknown”), and the probability, P (“likely”, “unlikely/irrelevant”, “unknown”), were judged based on prior knowledge or the result of an additional bespoke study. In this work, both I and P are evaluated for their influence on: (a) an internal component of the model building, or (b) an external use of the model. The outcomes of the flowchart included, acknowledgment of the assumption with certain conditions, acknowledgment of the assumption as a limitation, or “no-go”.
Use of the flowchart: The flowchart was applied to two examples to illustrate its use: (a) a top-down model building process and (b) a bottom-up work based on a quantitative systems model. The top-down approach was based on a kinetic-pharmacodynamics (KPD) model for warfarin and the vitamin-K dependent coagulation proteins [2]. In this work we highlight an example of each of the implicit and explicit assumptions. For the bottom up approach we consider the development of an individualised warfarin dosing method based on a systems coagulation network model [3]. Here we illustrate two explicit assumptions, one internal and one external.
Discussion: A framework for evaluating assumptions underpinning pharmacometric models is proposed and its utility is demonstrated using both top-down and bottom-up modelling approaches. The next step of this work is to apply the framework to a series of other settings to assess its value in identifying and making inference from assumptions.
References:
- Marshall SF, Burghaus R, Cosson V, Cheung SY, Chenel M, DellaPasqua O, et al. Good Practices in Model-Informed Drug Discovery and Development: Practice, Application, and Documentation. CPT Pharmacometrics Syst Pharmacol. 2016;5(3):93-122.
- Ooi QX, Wright DF, Tait RC, Isbister GK, Duffull SB. A Joint Model for Vitamin K-Dependent Clotting Factors and Anticoagulation Proteins. Clin Pharmacokinet. 2017.
- Wajima T, Isbister GK, Duffull SB. A comprehensive model for the humoral coagulation network in humans. Clin Pharmacol Ther. 2009;86(3):290-8.