Identifiability and uncertainty for ordinary differential equation models with qualitative or semiquantitative data

The estimation of unknown parameters is a key step in the development of mechanistic dynamical models for biological processes. While quantitative measurements are typically used for model calibration, in many applications, only semiquantitative or qualitative observations are available, posing unique challenges for parameter estimation.

Specialized approaches have been developed to integrate such data, offering trade-offs in bias, flexibility, and computational efficiency. Most of these approaches involve a recording function that maps the quantitative model onto nonabsolute data; however, this introduces additional degrees of freedom that can contribute to non-identifiability. Reliable calibration therefore requires structural and practical identifiability analysis, alongside robust uncertainty quantification.

In this work, we provide an overview of available methods, critically examine them with respect to identifiability and uncertainty considerations, identify methodological gaps, outline strategies to improve computational efficiency, and advocate for the development of standardized benchmarking frameworks to support informed method selection and best practices.