# A new method for a priori practical identifiability

## TL;DR

This paper introduces a new method for analyzing identifiability in biomedical models by relaxing the assumption that all derivatives of measured variables are available.

## Contribution

The paper introduces (ν1,...,νm)-identifiability and new algorithms to assess it without requiring all derivatives.

## Key findings

- The new method allows for identifiability analysis with limited derivative information.
- In some models, assuming only up to third-order derivatives reduces identifiable parameters significantly.
- Previously assumed identifiability requires at least 20 derivatives of all signals in some models.

## Abstract

Background and objective: Practical identifiability analysis, i.e., ascertaining whether a model property can be determined from given data, is central to model-based data analysis in biomedicine. The main approaches used today all require that coverage of the parameter space be exhaustive, which is usually impossible. An alternative could be using structural identifiability methods, since they do not need such coverage. However, current structural methods are unsuited for practical identifiability analysis, since they assume that all higher-order derivatives of the measured variables are available. Herein, we provide new definitions and methods that allow for this assumption to be relaxed. Methods and results: We introduce the concept of (ν1,...,νm)-identifiability, which differs from previous definitions in that it assumes that only the first νi derivatives of the measurement signal yi are available. This new type of identifiability can be determined using our new algorithms, as is demonstrated by applications to various published biomedical models. Our methods allow for identifiability of not only parameters, but of any model property, i.e., observability. These new results provide further strengthening of conclusions made in previous analysis of these models. For the first time, we can quantify the impact of the assumption that all derivatives are available in specific examples. If one, e.g., assumes that only up to third order derivatives, instead of all derivatives, are available, the number of identifiable parameters drops from 17 to 1 for a Drosophila model, and from 21 to 6 for an NF-κB model. In both models, the previously obtained identifiability is present only if at least 20 derivatives of all measurement signals are available. Conclusion: Our results demonstrate that the assumption regarding availability of derivatives made in traditional structural identifiability analysis requires a big overestimation regarding the number of parameters that can be estimated. Our new methods and algorithms allow for this assumption to be relaxed, bringing structural identifiability methodology one step closer to practical identifiability analysis.