Contributions to Functional Beta Models for Continuous Glucose Monitoring (CGM) Data

N. Acar Denizli, P. F. Delicado Useros

We present a functional data analysis framework to analyze continuous glucose monitoring (CGM) data. We propose a local likelihood-based approach to estimate individual-level glucose functions using a Beta functional model with two time-varying parameters. A critical aspect of local likelihood estimation is bandwidth selection, which significantly impacts both estimation quality and computational efficiency. We develop and implement an approximation of the leave-one-out cross validation method for bandwidth selection. In a second step, we consider the set of Beta distributions with estimated time-varying parameters as an abstract functional data set. We propose a dimensionality reduction method (that combines MDS and FPCA) to extract common patterns from the individual estimations. The proposed methods are applied to a real-world CGM dataset coming from the REPLACE-BG randomized clinical trial, and their performances are compared to the alternative existing methods.

Keywords: Beta functional model, local likelihood estimation, continuous glucose monitoring,

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