PECAN, a Shiny application for calculating confidence and prediction intervals for pharmacokinetic and pharmacodynamic models
Anne Kümmel (1), Ahmad Abu Helwa (2), Andreas Krause (1)
(1) Department of Clinical Pharmacology, Actelion Pharmaceuticals Ltd., Allschwil, Switzerland (2) Australian Centre for Pharmacometrics and Sansom Institute, School of Pharmacy and Medical Sciences, University of South Australia, Australia
Objectives: Estimation accuracy for PK/PD or dose response models is typically reported as standard errors of the model parameters. However, for judging the uncertainty of predicted clinical outcomes, e.g., the clinical benefit of an untested dose, standard errors and confidence intervals around the regression fit are of higher relevance. PECAN, an R-based application with a Shiny interface, provides calculation and visualization of confidence and prediction intervals for PK and PK/PD models.
Methods: The PECAN interface enables data upload and model selection, parameter estimation and confidence calculation of the predictions. For parameter estimation, either non-linear least squares or maximum likelihood estimation (MLE) is used. For MLE, additive, proportional, a combination of additive and proportional and an exponential error model is applied. Confidence intervals are calculated using either the δ-method [1], by sampling from the parameter covariance matrix, by bootstrapping, or by Monte-Carlo-simulations [2, 3]. Compartmental PK models amongst others based on ADVAN-style implementation [4] and PK/PD models are included in the PECAN's model library. The PECAN interface visualizes the uploaded data. After parameter estimation, estimation results and diagnostic plots are shown. Finally, the model prediction, its confidence and prediction intervals and the data are overlaid enabling a visual check of the model fit and its uncertainty and variability.
Results: PECAN combines models for pharmacometric applications and different methods into a single user interface, generalizing the idea of confidence and prediction intervals. PECAN demonstrates how PK and PK/PD model uncertainty can be derived in a standard programming language such as R. At the same time, the implementation as a Shiny application provides easy access for a broad audience. The user can choose between different methods for estimation and confidence calculation and error models. The Shiny application can be accessed at https://carumcarvi.shinyapps.io/pecan/
Conclusions: Visualization of model fit, confidence and prediction intervals allows judgment about the overall uncertainty of PK and PK/PD models: the uncertainty around the fitted model curve in contrast to only the individual model parameter estimates. This allows a direct visual assessment of the predicted relevant clinical outcome, e.g., the expected response of a future dose or the PK profile.
References:
[1] Hosmer, D.W., S. Lemeshow, and M. S., Applied Survival Analysis: Modeling of Time-to-Event Data. 2011, John Wiley and Sons, Inc.
[4] Abuhelwa, A.Y., D.J. Foster, and R.N. Upton, ADVAN-style analytical solutions for common pharmacokinetic models. J Pharmacol Toxicol Methods 73 2015; 42-8.
[2] Bonate, P.L., Pharmacokinetic-pharmacodynamic modeling and simulation. 2011, New York: Springer.
[3] Lavielle, M., Mixed effects models for the population approach: Models, tasks, methods and tools. 2014: Chapman and Hall/CRC.
[4] Abuhelwa, A.Y., D.J. Foster, and R.N. Upton, ADVAN-style analytical solutions for common pharmacokinetic models. J Pharmacol Toxicol Methods 73 2015; 42-8.
