Page 89 - Glucose Monitoring Devices

88 CHAPTER 5 Modeling the SMBG measurement error

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2
independent N(0,1) random variables and defining u 1 ¼ d$u 0 þ 1 d $r. Then,
in the second step, a random number z sampled from a skew-normal PDF with
parameters x ¼ 0, u ¼ 1 and as0 is obtained as follows:

u 1 if u 0 0
z ¼ (5.9)
u 1 otherwise
As the third step, the realization sampled from the skew-normal PDF with
parameters x, u, and a is finally obtained setting y ¼ x þ u∙z.
For each of the M simulated samples, first, the empirical distribution function
(EDF) is calculated, which represents an estimate of the cumulative distribution
function. In particular, given a generic random sample, Y j , j ¼ 1, . n, its EDF is
defined as follows:
n
1 X
b
FðyÞ¼ I ½ ∞ yŠ ðY j Þ (5.10)
n
j¼1
where I is 1 if Y j y and 0 otherwise. Then, the MAD between the EDF of
½ ∞ yŠ
each simulated sample and the EDF of the test set is calculated, and its average value
across the M simulated samples is obtained.
Finally, each of the M simulated samples is compared to the test set error data by
performing, with significance level b, the two-sample KS and CvM tests, that is,
nonparametric tests for the null hypothesis H 0 ¼ “the two samples are drawn
from the same distribution” ¼ based on a measure of distance between the EDFs
of the two samples. The percentage of simulated samples for which KS and CvM
tests reject H 0 is calculated, which should be small if the identified model of
SMBG error PDF is accurate.
To avoid the results of the validation being dependent on the particular realiza-
tion of random samples, we recommend repeating these validation steps N times
(e.g., N ¼ 100). Specifically, the average MAD and the percentage of samples for
which KS and CvM tests reject H 0 can be obtained for the N groups of M random
samples and finally their mean, minimum, and maximum values can be calculated.

Derivation of a model of SMBG error distribution for two
commercial devices
Case study 1: modeling the One Touch Ultra 2 measurement error
Dataset
The One Touch Ultra 2 (OTU2) dataset was obtained from a larger dataset collected
as part of a multicenter study conducted in 2011 (with the original specific aim being
to assess the accuracy of a CGM sensor) [44]. For our purpose, in particular, it is
relevant to report that 72 subjects (60 with T1D, 12 with type 2 diabetes [T2D])
participated in three clinical sessions in which SMBG measurements were collected