ArticlePLoS computational biology2023
Profile-Wise Analysis: A profile likelihood-based workflow for identifiability analysis, estimation, and prediction with mechanistic mathematical models.
Article in PLoS computational biology, 2023. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 21 papers.
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21 citing papers in PubMed.
- Individual-Eye Pharmacokinetics of Intravitreal Ranibizumab: Linking Ocular Geometry to Drug Retention Using MRI and Modeling.Investigative ophthalmology & visual science · 2026Article
- Multiscale modeling of T cell exhaustion: A mathematical framework integrating continuous dynamics with spatial heterogeneity.PLoS computational biology · 2026Article
- Does Timing Matter? Exploring the Effects of Measurement Error on Models.Bulletin of mathematical biology · 2026Article
- In silico modeling of anterior foregut endoderm differentiation towards lung epithelial progenitors.NPJ systems biology and applications · 2026Article
- Modelling ion channels with a view towards identifiability.Bulletin of mathematical biology · 2025Article
- Scalable inference and identifiability of kinetic parameters for transcriptional bursting from single cell data.Bioinformatics (Oxford, England) · 2025Article
- Assessing parameter identifiability of a hemodynamics PDE model using spectral surrogates and dimension reduction.PLoS computational biology · 2025Article
- Analysing the Structural Identifiability and Observability of Mechanistic Models of Tumour Growth.Bioengineering (Basel, Switzerland) · 2025Article
- Beyond RECIST: mathematical modeling and Bayesian inference reveal the importance of immune parameters in metastatic breast cancer.bioRxiv : the preprint server for biology · 2025Article
- In silico modeling of directed differentiation of induced pluripotent stem cells to definitive endoderm.PLoS computational biology · 2025Article
- Conformal prediction for uncertainty quantification in dynamic biological systems.PLoS computational biology · 2025Article
- Incorporating spatial diffusion into models of bursty stochastic transcription.Journal of the Royal Society, Interface · 2025Article
- Employing Observability Rank Conditions for Taking into Account Experimental Information a priori.Bulletin of mathematical biology · 2025Article
- Efficient data collection for establishing practical identifiability via active learning.Computational and structural biotechnology journal · 2025Article
- Celebrating a body of work.PLoS computational biology · 2024Article
- Structured methods for parameter inference and uncertainty quantification for mechanistic models in the life sciences.Royal Society open science · 2024Article
- Making Predictions Using Poorly Identified Mathematical Models.Bulletin of mathematical biology · 2024Article
- Structural and practical identifiability of contrast transport models for DCE-MRI.PLoS computational biology · 2024Article
- Informing policy via dynamic models: Cholera in Haiti.PLoS computational biology · 2024Article
- In silico model development and optimization of in vitro lung cell population growth.PloS one · 2024Article
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2 authors.
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Abstract
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.
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