Statistica Sinica 23 (2013), 1595-1627

CONTINUOUS BLOOD GLUCOSE MONITORING:

A BAYES-HIDDEN MARKOV APPROACH

Lee H. Dicker$^1$, Tingni Sun$^2$, Cun-Hui Zhang$^1$, D. Barry Keenan$^3$ and

Larry Shepp$^2$

$^1$Rutgers University, $^2$University of Pennsylvania,

and $^3$Medtronic MiniMed

Abstract: Real-time monitoring of blood glucose density is essential for managing diabetes. Continuous glucose monitoring (CGM) systems have been developed to help address this need. Many CGM systems are built around an electrochemical biosensor that may be inserted into the subcutaneous tissue of an individual and allows for nearly continuous monitoring of an electrical current generated by glucose molecules near the sensor site. This electrical current is correlated with blood glucose density and, in principle, provides a means for real-time monitoring of blood glucose density. One of the major challenges in CGM is developing algorithms for converting sensor measurements into accurate estimates of blood glucose density in real time. In this paper, we describe fundamental statistical problems that arise in developing CGM algorithms. We propose statistical algorithms based on Kalman filtering, nonparametric empirical Bayes methods, and ideas from sequential change-point detection, and apply them to a very rich CGM dataset. The performance of our methods compares favorably to that of an existing widely used CGM algorithm. A simulation study sheds light on other interesting and important aspects of the problem. More broadly, this paper highlights an important application that has received little attention in the statistics literature and our results suggest that the appropriate application of statistical methodology may lead to significant contributions in diabetes technology research.

Key words and phrases: Diabetes technology, Kalman filtering, nonparametric empirical Bayes, sequential methods