Quantitative model diagrams (QMD): a new perspective in model evaluation

Aims: To facilitate model communication and evaluation through intuitive visual representation of their structure, parameter values and uncertainty.

Methods: An open source R package (R 3.2.4) was developed for the translation of model structure from NONMEM output and scaling of parameters into diagrams, using the package DiagrammeR [1] for plotting. QMD were generated by scaling the compartment size to the distribution volume and arrow width to the corresponding clearance or rate constant. When available, parameter uncertainty or between subject variability (BSV) could be visualized using color-coded compartments and arrows.

Results: Diagrams for the standard NONMEM model library (ADVAN 1–4 and 11–12) have been fully automated. A differential equation parser has been implemented to require minimal or no user input. To illustrate the use of QMD in Pharmacometrics, three example models of various complexities were selected, including a 3-compartment model with first order absorption [2] (Figure 1), a mechanistic model [3] and a physiologically-based pharmacokinetic model [4].

Figure 1: QMD of a 3-compartment model with first order absorption [2]. BSV is represented by the color code, bioavailability by the pie chart, volumes by the surface area of compartments and clearances by arrow width. The interactive tooltip displays arrow and compartment information. 

Conclusion: QMD effectively summarized the information on model structure, compartment volume, clearance and rate constant, along with their uncertainty or BSV within a single intuitive graph. Informative representation of pharmacometric models was demonstrated to be applicable for a range of model structure and complexity and may improve model communication within and outside of the pharmacometric community.



[1] R. Iannone et al. Create Graph Diagrams and Flowcharts Using R. CRAN. 2016; [v0.8.2].

[2] S. Fanta et al. Developmental pharmacokinetics of ciclosporin – a population pharmacokinetic study in paediatric renal transplant candidates. BJCP. 2007;64(6):772–84.

[3] E. Hénin et al. A Mechanism-Based Approach for Absorption Modeling: The Gastro-Intestinal Transit Time (GITT) Model. AAPSJ. 2012;14(2):155–63.


[4] S. Björkman. Prediction of drug disposition in infants and children by means of physiologically based pharmacokinetic (PBPK) modelling: theophylline and midazolam as model drugs. BJCP. 2004;59(6):691–704.