Profile-Wise Analysis: A profile likelihood-based workflow for identifiability analysis, estimation, and prediction with mechanistic mathematical models.
Interpreting data using mechanistic mathematical models provides a foundation for discovery and decision-making in all areas of science and engineering. Developing mechanistic insight by combining mathematical models and experimental data is especially critical in mathematical biology as new data an...
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| Format: | Article |
| Language: | English |
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Public Library of Science (PLoS)
2023-09-01
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| Series: | PLoS Computational Biology |
| Online Access: | https://journals.plos.org/ploscompbiol/article/file?id=10.1371/journal.pcbi.1011515&type=printable |
| _version_ | 1797659647349358592 |
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| author | Matthew J Simpson Oliver J Maclaren |
| author_facet | Matthew J Simpson Oliver J Maclaren |
| author_sort | Matthew J Simpson |
| collection | DOAJ |
| description | Interpreting data using mechanistic mathematical models provides a foundation for discovery and decision-making in all areas of science and engineering. Developing mechanistic insight by combining mathematical models and experimental data is especially critical in mathematical biology as new data and new types of data are collected and reported. Key steps in using mechanistic mathematical models to interpret data include: (i) identifiability analysis; (ii) parameter estimation; and (iii) model prediction. Here we present a systematic, computationally-efficient workflow we call Profile-Wise Analysis (PWA) that addresses all three steps in a unified way. Recently-developed methods for constructing 'profile-wise' prediction intervals enable this workflow and provide the central linkage between different workflow components. These methods propagate profile-likelihood-based confidence sets for model parameters to predictions in a way that isolates how different parameter combinations affect model predictions. We show how to extend these profile-wise prediction intervals to two-dimensional interest parameters. We then demonstrate how to combine profile-wise prediction confidence sets to give an overall prediction confidence set that approximates the full likelihood-based prediction confidence set well. Our three case studies illustrate practical aspects of the workflow, focusing on ordinary differential equation (ODE) mechanistic models with both Gaussian and non-Gaussian noise models. While the case studies focus on ODE-based models, the workflow applies to other classes of mathematical models, including partial differential equations and simulation-based stochastic models. Open-source software on GitHub can be used to replicate the case studies. |
| first_indexed | 2024-03-11T18:17:10Z |
| format | Article |
| id | doaj.art-61e25b63844646879d2494fa93988960 |
| institution | Directory Open Access Journal |
| issn | 1553-734X 1553-7358 |
| language | English |
| last_indexed | 2024-03-11T18:17:10Z |
| publishDate | 2023-09-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS Computational Biology |
| spelling | doaj.art-61e25b63844646879d2494fa939889602023-10-16T05:31:37ZengPublic Library of Science (PLoS)PLoS Computational Biology1553-734X1553-73582023-09-01199e101151510.1371/journal.pcbi.1011515Profile-Wise Analysis: A profile likelihood-based workflow for identifiability analysis, estimation, and prediction with mechanistic mathematical models.Matthew J SimpsonOliver J MaclarenInterpreting data using mechanistic mathematical models provides a foundation for discovery and decision-making in all areas of science and engineering. Developing mechanistic insight by combining mathematical models and experimental data is especially critical in mathematical biology as new data and new types of data are collected and reported. Key steps in using mechanistic mathematical models to interpret data include: (i) identifiability analysis; (ii) parameter estimation; and (iii) model prediction. Here we present a systematic, computationally-efficient workflow we call Profile-Wise Analysis (PWA) that addresses all three steps in a unified way. Recently-developed methods for constructing 'profile-wise' prediction intervals enable this workflow and provide the central linkage between different workflow components. These methods propagate profile-likelihood-based confidence sets for model parameters to predictions in a way that isolates how different parameter combinations affect model predictions. We show how to extend these profile-wise prediction intervals to two-dimensional interest parameters. We then demonstrate how to combine profile-wise prediction confidence sets to give an overall prediction confidence set that approximates the full likelihood-based prediction confidence set well. Our three case studies illustrate practical aspects of the workflow, focusing on ordinary differential equation (ODE) mechanistic models with both Gaussian and non-Gaussian noise models. While the case studies focus on ODE-based models, the workflow applies to other classes of mathematical models, including partial differential equations and simulation-based stochastic models. Open-source software on GitHub can be used to replicate the case studies.https://journals.plos.org/ploscompbiol/article/file?id=10.1371/journal.pcbi.1011515&type=printable |
| spellingShingle | Matthew J Simpson Oliver J Maclaren Profile-Wise Analysis: A profile likelihood-based workflow for identifiability analysis, estimation, and prediction with mechanistic mathematical models. PLoS Computational Biology |
| title | Profile-Wise Analysis: A profile likelihood-based workflow for identifiability analysis, estimation, and prediction with mechanistic mathematical models. |
| title_full | Profile-Wise Analysis: A profile likelihood-based workflow for identifiability analysis, estimation, and prediction with mechanistic mathematical models. |
| title_fullStr | Profile-Wise Analysis: A profile likelihood-based workflow for identifiability analysis, estimation, and prediction with mechanistic mathematical models. |
| title_full_unstemmed | Profile-Wise Analysis: A profile likelihood-based workflow for identifiability analysis, estimation, and prediction with mechanistic mathematical models. |
| title_short | Profile-Wise Analysis: A profile likelihood-based workflow for identifiability analysis, estimation, and prediction with mechanistic mathematical models. |
| title_sort | profile wise analysis a profile likelihood based workflow for identifiability analysis estimation and prediction with mechanistic mathematical models |
| url | https://journals.plos.org/ploscompbiol/article/file?id=10.1371/journal.pcbi.1011515&type=printable |
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