A new method for a priori practical identifiability

Abstract

AbstractBackground and objectivePractical identifiability analysis – to determine 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 the coverage of the parameter space be exhaustive, which is usually not possible. An attractive alternative could be to use structural identifiability methods, since they do not need such a parameter 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.MethodsThe new methods and definitions are valid for ordinary differential equations, and use a combination of differential algebra and modulus calculus, implemented in Maple.ResultsWe introduce the concept of (ν1,..., νm)-identifiability, which differs from previous definitions in that it assumes that only the first νiderivatives of the measurement signalyiare available. This new type of identifiability can be determined using our new algorithm, 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. Importantly, our analysis can for the first time 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 these models, the previously obtained identifiability is present only if at least 20 derivatives of all measurement signals are available.ConclusionsOur results demonstrate that the assumption regarding availability of derivatives done in traditional structural identifiability analysis causes a big overestimation regarding the number of parameters that can be estimated. Our new methods and algorithms allow for this assumption to be relaxed, which moves structural identifiability methodology one step closer to practical identifiability analysis.