Profile-Wise Analysis: A profile likelihood-based workflow for identifiability analysis, estimation, and prediction...

Area of Science:

• Computational Biology
• Mathematical Modeling
• Data Interpretation

Background:

• Mechanistic mathematical models are crucial for scientific discovery and decision-making.
• Integrating experimental data with models is vital for advancing biological understanding.
• Key challenges include model identifiability, parameter estimation, and prediction.

Purpose of the Study:

• To present a systematic and computationally efficient workflow, Profile-Wise Analysis (PWA), for interpreting data using mechanistic mathematical models.
• To unify identifiability analysis, parameter estimation, and model prediction within a single framework.
• To leverage recent advancements in profile-wise prediction intervals for enhanced model analysis.

Main Methods:

• Developed and implemented the Profile-Wise Analysis (PWA) workflow.
• Utilized profile-wise prediction intervals to link parameter confidence sets to model predictions.
• Extended profile-wise prediction intervals for two-dimensional parameters and combined confidence sets for overall prediction accuracy.
• Demonstrated the workflow using ordinary differential equation (ODE) models with Gaussian and non-Gaussian noise.

Main Results:

• PWA provides a unified approach to key steps in mechanistic model-based data interpretation.
• Profile-wise methods effectively propagate parameter uncertainty to predictions.
• The workflow demonstrated good approximation of full likelihood-based prediction confidence sets.
• Case studies showcased practical application for ODE models.

Conclusions:

• Profile-Wise Analysis (PWA) offers a robust and efficient method for mechanistic model-based data interpretation.
• The workflow is applicable to various mathematical models, including ODEs, PDEs, and stochastic models.
• Open-source software is available to facilitate the application and replication of the PWA workflow.