Building Effective Visualizations to Assess and Communicate Fit for Pharmacometric Models with Covariates (VACHETTE)
Jos Lommerse (1), Anna Largajolli (1), Nele Plock (1), S.Y. Amy Cheung (1), Jeffrey R. Sachs (2)
(1) Certara, Princeton, NJ, USA, (2) Merck & Co., Inc., Rahway, NJ, USA
Introduction
With the increase in application of pharmacometrics as part of model-informed drug discovery and development (MIDD) decisions, one essential ingredient is effective communication and visualization of the captured quantitative evidence in pharmacometrics (PMx) models and data to all stakeholders including the project teams and regulators. A previously published method (V2ACHER [1]) yielded an intuitive, clear visual overlay of data for certain GNLS, GLM, and NLME models, allowing an integrated display (in a single plot) of model predictions and data from different groups (i.e. across covariate-value-defined subgroups). V2ACHER is applicable to static models (non-ordinary-differential-equation-based) and requires explicit use of relationships of covariates and parameters resulting from the model. A method is needed to enable similarly effective visualizations for non-static models with one or more covariates (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 observations relevant to the model. It defines a series of transformations to align multiple query curves to a single (user-selected) reference curve. (The “curves” here are model-simulated results for covariate sets of interest, e.g., {older, male, 71 kg}, {younger, female, 55 kg}., with one covariate combination selected as a reference). 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 as input: these are simulations from the user’s model. The method first automatically identifies characteristic landmarks (e.g., minimum/maximum, inflection points, asymptotes) via Savitzky-Golay filtering and equilibrium search, and these are used to split each curve into segments. Then, the method maps 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 VACHETTE transformation is a two-step process of a) x-scaling and b) y-scaling. Finally, the mappings between segments are applied to observations, relocating them to the corresponding position relative to the reference curve position (transforming both dependent and independent observation values, using the mapping corresponding the segment they are in). Like V2ACHER, the transformation preserves the remaining random effects between data (for subjects with covariate value sets corresponding to one of the curves) and their respective model curves so that the visualization is a fair and consistent representation of how the model integrates the data across all covariate values. The resulting visualization elucidates observations’ covariate-corrected positions relative to the reference curve (by preserving the distance to their corresponding query curve). Also, as for V2ACHER, a visual predictive check (VPC) [2] can be applied to VACHETTE transformed data to enhance the diagnostic performance (“VACHETTE-VPC”). VACHETTE scaling was applied to multiple types of pharmacometrics models to demonstrate its flexibility in visualizing non-static models with covariates. To demonstrate its equivalence to V2ACHER, a VACHETTE transformation was also carried out for a direct-response model.
Results
For a range of model types (with observations), VACHETTE automated the generation of a single visualization which can be easily understood by modelers and non-modelers. Overlays of transformed query and original reference data preserved the key visual features of the original data points. Consistent with the VACHETTE visualization, VACHETTE-VPC results in a single plot which is useful to evaluate model fit, providing results more easily interpreted than pcVPC. VACHETTE transformation of the direct-response model gave results consistent with V2ACHER, demonstrating VACHETTE to be a visual generalization of V2ACHER.
Conclusion
The new “VACHETTE” visualization method extends the desired key features of V2ACHER, enabling it for non-static models and automating it for both static and non-static models. Adding to already existing methods of model visualization, this new family of visualization methods enables easier and more effective evaluation and communication of PMx results critical to informing key decisions. A VACHETTE R package will be available in 2023.
References:
[1] Lommerse J, et al. CPT Pharmacometrics Syst Pharmacol. 2021;10(9):1092-1106.
[2] Karlsson MO, Holford N. [www.page-meeting.org/?abstract=1434]