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80     CHAPTER 5 Modeling the SMBG measurement error




                         and measurement conditions are stable, the characteristics of SMBG measurement
                         error can vary for different BG concentrations [13,14]. This is visible, for example,
                         in the scatter plots of SMBG error versus reference glucose reported by Freckmann
                         et al. for 43 different SMBG devices [2] (see Fig. 1AeCinRef.[2]).
                            To receive approval from regulatory agencies and enter the market, SMBG
                         devices must satisfy accuracy standards. For example, the International Organiza-
                         tion for Standardization (ISO) requires that at least 95% of differences in the low
                         glucose range and relative differences in the high glucose range (calculated by
                         comparing SMBG measurements with high-accuracy reference measurements) not
                         exceed a prefixed range. In particular, standard ISO 15197:2003 [15] requires that
                         when BG concentration is < 75 mg/dL at least 95% of readings deviate less than
                         15 mg/dL from the reference, whereas when BG concentration is  75 mg/dL at
                         least 95% of readings deviate less than 20% from the reference. The 2013 revision
                         of the standard, ISO 15197:2013 [16], imposes tighter accuracy requirements:
                         if BG < 100 mg/dL at least 95% of readings must deviate less than 15 mg/dL;
                         if BG   100 mg/dL at least 95% of readings must deviate less than 15%. A recent
                         FDA guidance imposes that SMBG measurements must deviate no more than 15%
                         from the reference BG values independently on BG, that is, a stricter requirement is
                         imposed in the low glucose range [17]. Many studies assessing the performance of
                         SMBG devices according to the accuracy standards can be found in the literature.
                         These studies show that not all the SMBG devices on the market meet the standard
                         accuracy requirements. For instance, only 1 of the 7 systems tested by Brazg et al.
                         [18] satisfies standard ISO 15197:2013.
                            The SMBG measurement error can negatively impact glycemic control,
                         especially in subjects with type 1 diabetes (T1D), who rely on SMBG measurements
                         for making treatment decisions, for example, insulin bolus calculation and hyper/hy-
                         poglycemia treatment. For example, an underestimation of BG concentration can
                         lead to a too-small insulin dose that may result in hyperglycemia, which, when
                         prolonged and frequently repeated in time, can lead to long-term complications
                         like cardiovascular diseases, neuropathy, nephropathy, and retinopathy. Conversely,
                         an overestimation of BG concentration can lead to a too large insulin dose that
                         exposes the patient to the risk of hypoglycemia, which can lead, in the short-term,
                         to risky conditions like seizure and coma, and even to death. Particularly important
                         is the SMBG accuracy in the low glucose range [19], where positively biased
                         glucose measurements would not allow the patient to detect dangerous hypoglyce-
                         mic events. Recently, it has also been shown that SMBG devices currently on the
                         market present variable performance in the range of hypoglycemia (in Ref. [20],
                         the mean absolute relative error in hypoglycemia ranged between 4.4% and 13.5%).



                         Why modeling the SMBG measurement error?

                         A model of the SMBG measurement error is a mathematical or statistical description
                         of the SMBG measurement error that allows on one hand to summarize the error
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