Identifiability and accuracy: a closer look at contemporary contributions and changes in these vital areas of mathematical modelling

Abstract

In the development of mathematical models we are plagued with two key concerns: is the model unique and accurate enough? Under the umbrella of the first question we will show whether the extent of the model structure in our data will shed light on all of the model’s parameters. Identifiability in model advancement helps us with the question ‘will a proposed experiment on a system enable us to determine values for the parameters of a model of that system?’ The model is assumed to be known and to reflect the response of the system to the experiment. Identifiability is not concerned with the precision with which the parameters can be estimated. A comprehensive review and demonstrations of the practical considerations regarding identifiability are presented. We further introduced new concepts which when omitted from consideration in the identifiability process can lead to serious misjudgement about the resolution of important aspect of the model under investigation, and its identifiability classification per se. On the second question we discuss current methods and their pitfalls in evaluating model adequacy. The concordance correlation coefficient (CCC) has been commonly used to assess agreement of continuous data, such as agreement of a new assay and a gold-standard assay, observed versus model predicted values, different methods, raters, and reproducibility. The main advantage of CCC is that it incorporates precision and accuracy simultaneously. There are four methods to compute CCC; two of them are extremely dependent on normality whereas the other two are more robust to non-normality. Therefore, datasets that departures from normality or are not independent may pose a significant problem when using CCC with the squared distance payoff function. It has been shown that CCC may indicate an increasing agreement as the marginal distribution becomes different, suggesting the agreement should be compared over a similar range.