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242 CHAPTER 12 Modeling the CGM measurement error
reference BG [13]. Thus in accuracy studies, the first step of the analysis should be
the investigation of calibration errors via simulated recalibration, using all avail-
able reference data points. Furthermore, because CGMs operate in the interstitial
compartment, which is presumably related to the blood via diffusion across the
capillary wall, the second step should entail modeling the sensor deviations
from BG describing this diffusion process. Models of blood-to-interstitial glucose
transport have been proposed and are reasonably well accepted by the scientific
community as an approximation of the possible physiological time lag between
BG and IG concentration [15e17]. The second principle stipulates that the tempo-
ral structure of CGM data is important and should be taken into account by the
analysis of CGM errors. In particular, established accuracy measures, such as
mean absolute/relative difference, present an incomplete picture of sensor accu-
racy because these measures judge the proximity between sensor and reference
BG at isolated points in time, without taking into account the temporal structure
of the data. In other words, a random reshuffling of the sensor-reference data pairs
in time will not change these accuracy estimates. Thus, to account for the dynamics
of sensor errors, higher-order temporal properties need to be investigated. A wide
array of modeling techniques is offered by time-series methods, such as autore-
gression, autocorrelation, and spectral analysis. In this chapter, we review the
use of an autoregressive moving average (ARMA) model to account for the time
dependence of consecutive sensor errors.
Finally, the detailed understanding and modeling of sensor errors allow the next
step: their computer simulation. This, in turn, allows the development of a simulated
“sensor,” which is useful for in silico testing of diabetes treatment strategies, such as
open- or closed-loop control, under the realistic conditions of imperfect CGM.
Methods
To decompose the sensor errors, we used techniques from linear regression, kernel
density estimation, derivative estimation, and time-series analysis, each allowing
us to access specific characteristics of the sensor/BG discrepancy. We also
provided examples of each analysis using data provided by Abbott Diabetes
Care (Alameda, CA).
Datasets
The data used as an example in this chapter come from two different datasets
provided by Abbott Diabetes Care:
1. The first dataset is a home-use dataset containing sensor readings from the
FreeStyle Navigator taken every 10 min in 136 subjects, for an average of
40 days (e.g., eight sensors, 5-day insertions). The dataset contains 1062
sensors, totaling approximately 4000 days of recording, with 40,745 irregularly