Fitting dynamic models with forcing functions: application to continuous glucose monitoring in insulin therapy

The artificial pancreas is an emerging technology to treat type 1 diabetes (T1D). It has the potential to revolutionize diabetes care and improve quality of life. The system requires extensive testing, however, to ensure that it is both effective and safe. Clinical studies are resource demanding and so a principle aim is to develop an in silico population of subjects with T1D on which to conduct pre-clinical testing. This paper aims to reliably characterize the relationship between blood glucose and glucose measured by subcutaneous sensor as a major step towards this goal. Blood-and sensor-glucose are related through a dynamic model, specified in terms of differential equations. Such models can present special challenges for statistical inference, however. In this paper we make use of the BUGS software, which can accommodate a limited class of dynamic models, and it is in this context that we discuss such challenges. For example, we show how dynamic models involving forcing functions can be accommodated. To account for fluctuations away from the dynamic model that are apparent in the observed data, we assume an autoregressive structure for the residual error model. This leads to some identifiability issues but gives very good predictions of virtual data. Our approach is pragmatic and we propose a method to mitigate the consequences of such identifiability issues.