The precision of identified variables with respect to multivariable set size in glycaemic data from a virtual type 1 diabetic patient
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Prior research had been carried out to identify a large number of glycaemic variables in sparse, noisy data from a virtual diabetic patient. This paper investigates the precision of variables as an identification scheme introduces progressively more parameters into the variable set and as the quantity of data increases. Virtual data was simulated with a diabetic glycaemic meal model that contained six variable parameters. Data was sampled 6 times daily with noise. Increasing variable sets were identified for data subsets of increasing size. Norm-error of equivalent variable groups was compared before and after new parameter introductions. A Monte Carlo analysis was carried out to evaluate a population of results. Identifying new variables improved parameter estimates in all equivalent variable groups by 34 days in the mean population case. However, variability from data noise resulted in some cases never yielding sixparameter identification that improved upon results that relied on a-priori information. When parameters were introduced as variables too soon for the given data quality/quantity, reduced practical identifiability caused interference between these and other variables, diminishing their precision. However, when introduced too late the precision in the variable set was hindered by effects not fully described by the apriori guesses. Introducing the 3rd and 4th variables early in the data produced significant benefit in most cases. In contrast, the 5th and 6th parameters could not be introduced as early, improved precision by a lesser degree on average and in many cases never improved precision. The influence of noise on practical identifiability highlighted the need for similar analyses in-vivo so as to strategise parameter identification to gain the most information at the highest precision.