Page 189 - Glucose Monitoring Devices

The Bayesian approach applied to the calibration problem 191

Similarly, a Bayesian prior is built for the parameter vector p.
In the online working modality, as the number of BG measurements available
was not sufficient to estimate an individual value for s, we fixed its value to the prior
mean m obtained from the training set at each iteration of the cross-validation.
s
Regarding the other parameters, given the stability of the ratio between parameters
s 1 and s 2 , to facilitate model identifiability in online modality (when only a few BG
references are available) the ratio s 1 was fixed to the constant 4. The value of 4 is
s 2
estimated, at each iteration of the cross-validation, from the mean value of its distri-
bution on the corresponding training set of size N t . Thus, Eq. (9.18) represents the
the samples of the parameters vector
final parameter vector. Defining P ¼ p 1 ; :::; p N t
p, a Bayesian prior is built by assuming a distribution with prior mean m and prior
p
covariance matrix S p , where the ith element of m , m , and the ijth element of S p , s ij ,
p
i
are defined as follows:
1 X
N t
m ¼ p k;i
i
N t
k¼1
(9.31)
N t
1 X
s i;j ¼ p k;i m i p k;j m j
N t 1
k¼1
Training set data are used also to estimate the error covariance matrix S w , used in
Eq. (9.21). The error variance is assumed constant over time and its value is
estimated from the distribution of the differences between SMBG measurements
and the correspondent calibrated values (in mg/dL) given by the manufacturer. In
particular, for all SMBG samples available in the training set the correspondent
CGM calibrated value is matched following the procedure described in Section
Description of a Bayesian calibration algorithm and the difference between the
two measurements is computed. The error variance is thus obtained, at each
cross-validation iteration, from the distribution of the SMBGeCGM error on the
training set.
Calibration scenarios
The calibration algorithm is applied to the test set by simulating an online working
modality. In particular, for each sensor in the test group, the raw current signal y I ðtÞ
is calibrated by exploiting a set of BG references provided by SMBG measurements.
Different calibration schedules are tested, to assess the accuracy of the calibrated
profiles using a different number of SMBG samples per day, that is, varying the
frequency at which parameters of the calibration model are updated. In particular,
apart from the first calibration, which is always performed about 2 h after sensor
insertion (exploiting a pair of SMBG samples acquired a few minutes of distance
from each other), the following schedules are tested:
• one calibration about every day;
• one calibration about every 2 days;
• one calibration about every 4 days.