Modeling the error of continuous glucose monitoring sensor data: critical aspects discussed through simulation studies

Abstract

Background: Knowing the statistical properties of continuous glucose monitoring (CGM) sensor errors can be important in several practical applications, e.g., in both open- and closed-loop control algorithms. Unfortunately, modeling the accuracy of CGM sensors is very difficult for both experimental and methodological reasons. It has been suggested that the time series of CGM sensor errors can be described as realization of the output of an autoregressive (AR) model of first order driven by a white noise process. The AR model was identified exploiting several reference blood glucose (BG) samples (collected frequently in parallel to the CGM signal), a procedure to recalibrate CGM data, and a linear time-invariant model of blood-to-interstitium glucose (BG-to-IG) kinetics. By resorting to simulation, this work shows that some assumptions made in the Breton and Kovatchev modeling approach may significantly affect the estimated sensor error and its statistical properties.

Method: Three simulation studies were performed. The first simulation was devoted to assessing the influence of CGM data recalibration, whereas the second and third simulations examined the role of the BG-to-IG kinetic model. Analysis was performed by comparing the "original" (synthetically generated) time series of sensor errors vs its "reconstructed" version in both time and frequency domains.

Results: Even small errors either in CGM data recalibration or in the description of BG-to-IG dynamics can severely affect the possibility of correctly reconstructing the statistical properties of sensor error. In particular, even if CGM sensor error is a white noise process, a spurious correlation among its samples originates from suboptimal recalibration or from imperfect knowledge of the BG-to-IG kinetics.

Conclusions: Modeling the statistical properties of CGM sensor errors from data collected in vivo is difficult because it requires perfect calibration and perfect knowledge of BG-to-IG dynamics. Results suggest that correct characterization of CGM sensor error is still an open issue and requires further development upon the pioneering contribution of Breton and Kovatchev.

Figure 1.

Representative subject data set. BG references (red stars) vs CGM data (blue line) profiles.

Figure 2.

Simulated time-varying calibration error s(t). Ideal condition is the red line, and calibration error realizations with maximum excursion equal to 10 and 2% of the reference value are blue and black lines, respectively.

Figure 3.

Simulation of time-varying calibration error. First row—Left: true BG (red), IG (green), SCGM with s(t) <10% (blue), and SCGM with s(t) <2% (black) profiles. Right: true time series of sensor errors. Second row—Left: model fit of SIG (green) vs SCGM with s(t) <10% (blue). Right: reconstructed time series of sensor errors. Third row—Left: model fit of SIG (green) vs SCGM with s(t) <2% (black). Right: reconstructed time series of sensor errors.

Figure 4.

Simulation of uncertainty of τ. First row—Left: true BG (red), IG (green), and SCGM (blue) time series. Right: true time series of sensor error. Second row—Left: model fit of SIG (green) vs SCGM (blue). Right: reconstructed time series of sensor error.

Figure 5.

Simulation of time variance of τ. First row—Left: true BG (red), IG (green), and SCGM (blue) time series. Right: true time series of sensor error. Second row—Left: model fit of SIG (green) vs SCGM (blue). Right: reconstructed time series of sensor error.

Figure 6.

ACF (left), PACF (middle), and PSD (right) of true sensor error time series (first row) and of reconstructed sensor error time series: s(t) <10% (second row); s(t) <2% (third row); error in τ determination (fourth row); time-varying τ (fifth row). Freq, frequency.