Page 91 - Glucose Monitoring Devices

90 CHAPTER 5 Modeling the SMBG measurement error

Fig. 5.2). In particular, we adopt an empirical rule according to which a YSI sample
is considered not compatible with the BG pattern if it deviates upward/downward
more than a certain quantity q from the previous and the following YSI samples,
and the following YSI sample is in line with the previous YSI sample, that is, it
does not deviate upward/downward more than ε from the previous YSI sample.
More specifically, the jth YSI sample (empty red circles in Fig. 5.2), YSI j ,is
removed if YSI j < YSI j 1 q(YSI j 1 ), YSI j < YSI jþ1 q(YSI jþ1 ) and
YSI jþ1 >YSI j 1 ε, or YSI j > YSI j 1 þ q(YSI j 1 ), YSI j > YSI jþ1 þ q(YSI jþ1 )
and YSI jþ1 <YSI j 1 þε. In particular, we set ε to be 5 mg/dL and q(x)tobe
15 mg/dL when x 100 mg/dL and 15%∙x when x > 100 mg/dL.
In the second step, from each 12-h YSI sequence, an estimate of the BG profile is
reconstructed on a quasicontinuous time grid, for example, with a 1-min step, by the
nonparametric smoothing stochastic approach described in Ref. [45], which allows
to compensate for the unavoidable presence of measurement error in YSI samples
(zero-mean, uncorrelated and with constant CV equal to 2%, according to
Ref. [46]). Notably, as shown in Ref. [45], the use of an ML smoothing criterion
in this method limits the risk of introducing distortion/bias in the BG profile recon-
structed from the YSI samples (as visible in the representative example of Fig. 5.2).
Samples of the BG profile reconstructed on the 1-min step virtual grid (contin-
uous line in Fig. 5.2) can be used as references for the calculation of the SMBG mea-
surement error. For such a scope, each SMBG sample (empty blue triangles in
Fig. 5.2) was matched to the nearest (in time) sample of the reconstructed BG
profile. Hence, the temporal distance between the SMBG sample and the reference
sample was not greater than 30 s.
Of note, when one or more YSI samples are missing, and thus two consecutive
YSI measurements are 30 min or more apart, the reconstruction of the BG profile
over the gaps could be not reliable. Therefore SMBG measurements falling inside
these gaps, that is, 4.37% of all the available SMBG measurements, were excluded
from the analysis (full blue triangles in Fig. 5.2).
After preprocessing the data as described, the SMBG samples selected for the
analysis resulted well distributed in the glycemic range, with a number of samples
in hypoglycemia and hyperglycemia sufficiently high to allow for an accurate
description of the SMBG measurement error also in these extreme conditions. In
particular, the SMBG samples selected for the analysis were distributed in the gly-
cemic range as follows: 356 samples were in hypoglycemia below or equal to 50 mg/
dL, 930 in hypoglycemia above 50 mg/dL and below or equal to 70 mg/dL, 2958 in
euglycemia between 70 mg/dL and 180 mg/dL, 1479 in hyperglycemia equal to or
above 180 mg/dL and below 250 mg/dL, and 881 in hyperglycemia equal to or
above 250 mg/dL.
Model development
The obtained SMBG-BG matched pairs were used to calculate SMBG absolute and
relative errors as in Eq. (5.2). Then, the whole set of SMBG error data, with cardi-
nality n tot ¼ 6604, was divided into a training set with cardinality n training ¼ 2/3$n tot