Bayesian denoising algorithm dealing with colored, non-stationary noise in continuous glucose monitoring timeseries

Abstract

Introduction: The retrospective analysis of continuous glucose monitoring (CGM) timeseries can be hampered by colored and non-stationary measurement noise. Here, we introduce a Bayesian denoising (BD) algorithm to address both autocorrelation of measurement noise and temporal variability of its variance. Methods: BD utilizes adaptive, a-priori models of signal and noise, whose unknown variances are derived on partially-overlapped CGM windows, via smoothing approach based on linear mean square estimation. The CGM signal and noise variability profiles are then reconstructed using a kernel smoother. BD is first assessed on two simulated datasets, D_S1 and D_S2. On D_S1, the effectiveness of accounting for colored noise is evaluated by comparison against a literature algorithm; on D_S2, the effectiveness of accounting for the noise variance temporal variability is evaluated by comparison against a Butterworth filter. BD is then evaluated on 15 CGM timeseries measured by the Dexcom G6 (D_R). Results: On D_S1, BD allows reducing the root-mean-square-error (RMSE) from 8.10 [6.79-9.24] mg/dL to 6.28 [5.47-7.27] mg/dL (median [IQR]); on D_S2, RMSE decreases from 6.85 [5.50-8.72] mg/dL to 5.35 [4.48-6.49] mg/dL. On D_R, BD performs a reasonable tracking of noise variance variability and a satisfactory denoising. Discussion: The new algorithm effectively addresses the nature of CGM measurement error, outperforming existing denoising algorithms.

Keywords: Bayesian denoising; Butterworth filter; continuous glucose monitoring; correlation; stationarity.