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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| Published in: | Bulletin of mathematical biology Vol. 86; no. 1; p. 2 |
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| Main Authors: | , , , , , , |
| Format: | Journal Article |
| Language: | English |
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Springer US
01.01.2024
Springer Nature B.V |
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| ISSN: | 0092-8240, 1522-9602, 1522-9602 |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. 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. 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.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. |
| ArticleNumber | 2 |
| Author | Whittaker, Dominic G. Mirams, Gary R. Hill, Adam P. Windley, Monique J. Lei, Chon Lok Preston, Simon P. Shuttleworth, Joseph G. |
| Author_xml | – sequence: 1 givenname: Joseph G. orcidid: 0000-0003-4884-6526 surname: Shuttleworth fullname: Shuttleworth, Joseph G. organization: Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham – sequence: 2 givenname: Chon Lok orcidid: 0000-0003-0904-554X surname: Lei fullname: Lei, Chon Lok organization: Institute of Translational Medicine, Faculty of Health Sciences, University of Macau, Department of Biomedical Sciences, Faculty of Health Sciences, University of Macau – sequence: 3 givenname: Dominic G. orcidid: 0000-0002-2757-5491 surname: Whittaker fullname: Whittaker, Dominic G. organization: Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham, 4 Systems Modeling & Translational Biology – sequence: 4 givenname: Monique J. orcidid: 0000-0001-6829-3856 surname: Windley fullname: Windley, Monique J. organization: Computational Cardiology Laboratory, Victor Chang Cardiac Research Institute, School of Clinical Medicine, Faculty of Medicine and Health, University of New South Wales – sequence: 5 givenname: Adam P. orcidid: 0000-0002-6403-1282 surname: Hill fullname: Hill, Adam P. organization: Computational Cardiology Laboratory, Victor Chang Cardiac Research Institute, School of Clinical Medicine, Faculty of Medicine and Health, University of New South Wales – sequence: 6 givenname: Simon P. orcidid: 0000-0002-1910-4227 surname: Preston fullname: Preston, Simon P. organization: Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham – sequence: 7 givenname: Gary R. orcidid: 0000-0002-4569-4312 surname: Mirams fullname: Mirams, Gary R. email: gary.mirams@nottingham.ac.uk organization: Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/37999811$$D View this record in MEDLINE/PubMed |
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| CitedBy_id | crossref_primary_10_1016_j_bpj_2024_10_018 crossref_primary_10_12688_wellcomeopenres_23319_1 crossref_primary_10_1016_j_agsy_2024_104147 crossref_primary_10_12688_wellcomeopenres_23319_2 crossref_primary_10_1371_journal_pcbi_1013319 crossref_primary_10_1016_j_techfore_2025_124077 crossref_primary_10_1098_rsta_2024_0227 crossref_primary_10_1088_1478_3975_adda85 crossref_primary_10_1098_rsta_2024_0232 crossref_primary_10_1098_rsos_240733 crossref_primary_10_1098_rsta_2024_0211 |
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| ContentType | Journal Article |
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| Keywords | Uncertainty quantification Discrepancy Mathematical model Ion channel Experimental design Misspecification |
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| SubjectTerms | 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 |
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| Title | Empirical Quantification of Predictive Uncertainty Due to Model Discrepancy by Training with an Ensemble of Experimental Designs: An Application to Ion Channel Kinetics |
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