Page 83 - Glucose Monitoring Devices

82 CHAPTER 5 Modeling the SMBG measurement error

Literature models of SMBG measurement error
Many studies assessed the accuracy and precision of SMBG devices, but only a few
studies attempted to model the SMBG measurement error [32e38,40]. All these
studies focused on modeling the SMBG measurement error distribution by one or
more probability density function (PDF) models and considered the SMBG mea-
surements as independently sampled from such a PDF model, that is, assuming
uncorrelation between consecutive SMBG measurements. Such uncorrelation
assumption is reasonable for SMBG samples because of the sparseness of these
measurements, typically collected 3e5 times per day (as opposed to continuous
glucose monitoring (CGM) measurements, whose quasicontinuous nature allows
descriptions of the measurement error autocorrelation by using first or second-
order autoregressive models [28e31]).
A first simple model of the SMBG measurement error distribution was proposed
in a work by Boyd and Bruns [32] and consisted in modeling the SMBG relative
rel
error, E , by a Gaussian distribution whose mean and SD describe the analytical
bias and imprecision of the glucose meter:
X R
rel
E ¼ wNðBias; SDÞ (5.1)
R
where X and R represent the SMBG measurement and the reference glucose value,
respectively. This model was used for several applications in the literature, because
it is simple and easy to apply. Boyd and Bruns used the Gaussian model of Eq. (5.1)
to simulate different levels of accuracy and precision in SMBG measurements and
assessed their impact on insulin dosing errors in patients who use a sliding scale for
correcting insulin boluses according to SMBG measurements [32]. The same model
was applied in other studies to assess the effect of SMBG analytical errors on insulin
dosing errors in intensive care unit patients on tight glycemic control [33e35] and in
the presence of carb-counting errors [36].
However, none of these studies validated the simple Gaussian model against
empirical data. Moreover, literature evidences suggest that this simple model may
represent a suboptimal, too simplistic, description of the SMBG measurement error.
In particular, a critical point of this model concerns the use of a single canonical PDF
over the entire BG range. In fact, scatter plots reported in Refs. [1e3,6] show that
neither absolute nor relative error of SMBG data presents constant mean and SD
over the entire BG range.
To deal with this issue, in a work by Breton and Kovatchev [37] a Gaussian PDF
model with zero mean and SD dependent on the BG value was adopted. In particular,
the relationship between SD and BG was tuned to simulate the performance of a
meter satisfying the ISO 15197:2003 requirements, although Breton and Kovatchev
did not explicitly report the SD-BG relationship in their publication [37]. In a work
by Pretty et al. [38], a nonparametric approach was adopted, in which a bivariate
kernel density model of the joint distribution of SMBG measurements and reference
values was derived for the Abbott Optium Xceed (Abbott Diabetes Care, Alameda,