The Union between Structural and Practical Identifiability Makes Strength in Reducing Oncological Model Complexity: A Case Study

Mathematical models are increasingly proposed to describe tumor's dynamic response to treatments with the aims of improving their efficacy. The most widely used are nonlinear ODE models, whose identification is often difficult due to experimental limitations. We focus on the issue of parameter estimation in model-based oncological studies. Given their complexity, many of these models are unidentifiable having an infinite number of parameter solutions. These equivalently describe experimental data but are associated with different dynamic evolution of unmeasurable variables. We propose a joint use of two different identifiability methodologies, structural identifiability and practical identifiability, which are traditionally regarded as disjoint. This new methodology provides the number of parameter solutions, the analytic relations between the unidentifiable parameters useful to reduce model complexity, a ranking between parameters revealing the most reliable estimates, and a way to disentangle the various causes of nonidentifiability. It is implementable by using available differential algebra software and statistical packages. This methodology can constitute a powerful tool for the oncologist to discover the behavior of inaccessible variables of clinical interest and to correctly address the experimental design. A complexmodel to study "in vivo" antitumor activity of interleukin-21 on tumor eradication in different cancers in mice is illustrated.