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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
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