Effective Visualizations Reloaded – Visually Assess and Communicate Model Fit for Pmx Models with Covariates Using VACHETTE (an Extension of V2ACHER)
Objectives: Visualization of pharmacometric (PMx) models and data is often central to effectively informing drug discovery and development decisions. A previously published model visualization method (V2ACHER) [1] yields an intuitive, clear visual overlay of data for MBMA, NLME, and other models. V2ACHER is applicable to static models and requires explicit use of covariate relationships to parameters. A method is needed to enable similarly effective visualizations for non-static models (the majority of PMx models) and to automate the process.
Methods: VACHETTE starts with user-provided PMx model simulations accounting for covariate effects, together with associated observations. It defines a series of transformations to align model simulations (“curves”) for covariate sets of interest (e.g., {younger, male, 71 Kg}, {older, female, 55 Kg}). The user selects one curve (one covariate set) as a reference: the other curves (“query” curves) are aligned to it. Like V2ACHER, the transformation accounts for random effects and preserves remaining distances from data to their respective model curves (i.e., RUV), visualizing the model’s integration of the data across the covariate sets. In contrast to V2ACHER, VACHETTE only relies on the shape of modeled curves and does not require explicit knowledge or use of parameter properties or (estimated) values. VACHETTE takes the curves (the model simulations) as input. The method automatically identifies characteristic landmarks (e.g., minimum/maximum, inflection points, asymptotes) which are used to split each curve into segments. By mapping points on the query segment to a corresponding point on the reference segment, each query segment is transformed to align with the corresponding segment of the reference curve. The mappings between segments can now be applied to observations, relocating them to the corresponding position relative to the reference curve (transforming both dependent and independent observation values). The resulting visualization elucidates observations’ covariate-corrected positions relative to the reference curve (by preserving the distance to their corresponding query curve). To demonstrate its flexibility visualizing non-static models with covariates, VACHETTE was applied to a range of PMx model types (with observations). A direct-response model amenable to V2ACHER was included to demonstrate that, when both methods can be used, they are equivalent.
Results: For each model tested, VACHETTE automatically generated a single visualization easily understood by modelers and non-modelers. Overlays of query and reference data preserved the key visual features of the original data points (i.e., of the untransformed observations). VACHETTE transformation of the direct-response model gave results consistent with V2ACHER, demonstrating VACHETTE to be a generalization of V2ACHER.
Conclusions: The new visualization method (VACHETTE) extends the desired key features of V2ACHER, enabling it for non-static models and automating it for both static and non-static models. The broader set of PMx model visualizations enables easier and more effective evaluation and communication of PMx results critical to informing key decisions.
[1] doi:10.1002/psp4.12679
Author(s)
- Jeffrey R Sachs, Merck & Co., Inc., Rahway, NJ, USA (Presenting Author)
- Jos Lommerse, Certara, Princeton, NJ, USA (CoAuthor)
- Anna Largajolli, Certara, Princeton, NJ, USA (CoAuthor)
- Nele Plock, Certara, Princeton, NJ, USA (CoAuthor)
- S.Y. Amy Cheung , Certara, Princeton, NJ, USA (CoAuthor)