Empirical Quantification of Predictive Uncertainty Due to Model Discrepancy by Training with an Ensemble of Experimental Designs: An Application to Ion Channel Kinetics

When using mathematical models to make quantitative predictions for clinical or industrial use, it is important that predictions come with a reliable estimate of their accuracy (uncertainty quantification). Because models of complex biological systems are always large simplifications, model discrepa...

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Bibliographic Details
Published in:Bulletin of mathematical biology Vol. 86; no. 1; p. 2
Main Authors: Shuttleworth, Joseph G., Lei, Chon Lok, Whittaker, Dominic G., Windley, Monique J., Hill, Adam P., Preston, Simon P., Mirams, Gary R.
Format: Journal Article
Language:English
Published: New York Springer US 01.01.2024
Springer Nature B.V
Subjects:
Cell Biology
Electrophysiology
Estimates
Industrial applications
Ion Channels
Kinetics
Life Sciences
Mathematical and Computational Biology
Mathematical Concepts
Mathematical models
Mathematics
Mathematics and Statistics
Models, Biological
Models, Theoretical
Original Article
Parameter estimation
Pharmacovigilance
Potassium channels
Predictions
Product safety
Random noise
Random variables
Uncertainty
Uncertainty quantification
Discrepancy
Mathematical model
Ion channel
Experimental design
Misspecification
ISSN:0092-8240, 1522-9602, 1522-9602
Online Access:Get full text
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Summary:When using mathematical models to make quantitative predictions for clinical or industrial use, it is important that predictions come with a reliable estimate of their accuracy (uncertainty quantification). Because models of complex biological systems are always large simplifications, model discrepancy arises—models fail to perfectly recapitulate the true data generating process. This presents a particular challenge for making accurate predictions, and especially for accurately quantifying uncertainty in these predictions. Experimentalists and modellers must choose which experimental procedures ( protocols ) are used to produce data used to train models. We propose to characterise uncertainty owing to model discrepancy with an ensemble of parameter sets, each of which results from training to data from a different protocol. The variability in predictions from this ensemble provides an empirical estimate of predictive uncertainty owing to model discrepancy, even for unseen protocols. We use the example of electrophysiology experiments that investigate the properties of hERG potassium channels. Here, ‘information-rich’ protocols allow mathematical models to be trained using numerous short experiments performed on the same cell. In this case, we simulate data with one model and fit it with a different (discrepant) one. For any individual experimental protocol, parameter estimates vary little under repeated samples from the assumed additive independent Gaussian noise model. Yet parameter sets arising from the same model applied to different experiments conflict—highlighting model discrepancy. Our methods will help select more suitable ion channel models for future studies, and will be widely applicable to a range of biological modelling problems.
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ISSN:0092-8240
1522-9602
1522-9602
DOI:10.1007/s11538-023-01224-6