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. Key steps in using mechanistic mathematical models to interpret data often include: (i) identifiability analysis; (ii) parameter estimation; and (iii) model prediction. We present a computationally efficient workflow that addresses these steps in a general likelihood-based framework. We first summarise the theoretical background of our workflow for efficient parameter identifiability, parameter estimation, and predictive confidence set construction. A central aspect of the workflow is using profile likelihood to construct profile-wise prediction intervals that propagate confidence sets for model parameters forward to predictions in a way that explicitly isolates how different parameter combinations affect model predictions. We also show how to combine these prediction confidence sets to give an overall prediction confidence set that accounts for all parameters and approximates the full likelihood-based prediction confidence set well. We demonstrate practical aspects of the workflow via three case studies focusing on ordinary differential equation (ODE) mechanistic models with both Gaussian and non-Gaussian noise models. While the three case studies focus on ODE-based models, the workflow applies to other classes of mathematical models, such as partial differential equations and simulation-based stochastic models. We provide open-source software on GitHub to replicate the case studies