# Analysing the Structural Identifiability and Observability of Mechanistic Models of Tumour Growth

## TL;DR

This paper analyzes whether parameters and states in tumor growth models can be reliably inferred from data, using 20 published models and an open-source tool.

## Contribution

The paper provides a systematic analysis of structural identifiability and observability for 20 tumor growth models, including those with interventions.

## Key findings

- Many tumor growth models are not structurally identifiable or observable under standard measurement setups.
- The identifiability and observability of models depend heavily on the choice of experimental design and measured variables.
- The paper provides computational implementations to reproduce the analysis and guide model selection.

## Abstract

Mechanistic cancer models can encapsulate beliefs about the main factors influencing tumour growth. In recent decades, many different types of dynamic models have been used for this purpose. The integration of a model’s differential equations yields a simulation of the behaviour of the system over time, thus enabling tumour progression to be predicted. A requisite for the reliability of these quantitative predictions is that the model is structurally identifiable and observable, i.e., that it is theoretically possible to infer the correct values of its parameters and state variables from time course data. In this paper, we show how to analyse these properties of tumour growth models using a well-established methodology, which we implemented previously in an open-source software tool. To this end, we provide an account of 20 published models described by ordinary differential equations, some of which incorporate the effect of interventions including chemotherapy, radiotherapy, and immunotherapy. For each model, we describe its equations and analyse their structural identifiability and observability, discussing how they are affected by the experimental design. We provide computational implementations of these models, which enable readily reproducing results. Our results inform about the possibility of inferring the parameters and state variables of a given model using a specific measurement setup, and, together with the corresponding methodology and implementation, they can be used as a blueprint for analysing other models not included here. Thus, this paper serves as a guide to select the most appropriate model for each application.