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The Bayesian approach applied to the calibration problem 183

Recursive approaches exploiting past CGM data
Current CGM products are available for continuous use and are replaced after
several days. However, none of the methods discussed so far have embedded any
features able to capture this essential cyclic nature by exploiting, for example, the
data from prior weeks to better calibrate new CGM data. The first attempt in this
direction was made by Lee and colleagues in Ref. [44], where a run-to-run strategy
that personalizes sensor calibration parameters using data from previous weeks’ use
was proposed. Before each weekly new sensor insertion, the algorithm minimizes a
cost function that penalizes differences between fingerprick reference values and
CGM output of previous weeks. Repeated iterations of the run-to-run procedure
demonstrated improved performance on synthetic data (summed square error
reduced by 20% after 2 weeks, and up to 50% after 6 weeks). On the same line,
another calibration algorithm, employing a time-varying linear calibration function
as in Ref. [42], was augmented with a weekly updating feature for parameter
optimization [45]. The algorithm estimates the calibration parameters through the
recursive least squares to fit SMBG measurements taken approximately every
12 h. Then, personalized calibration parameters are optimized after the first week
of use using past data, employing a forgetting factor to give more weight to the
most recent data.

Today’s challenges for CGM calibration algorithms
The literature calibration algorithms discussed earlier in the present section showed,
in general, several performance improvements compared to the simple linear regres-
sion methods described in Section Problem statement and implemented in the first
commercialized CGM sensors. However, none of them explicitly aimed at
enhancing sensor accuracy while reducing, at the same time, the frequency of cali-
brations, that is, the number of SMBG fingerprick measurements needed as input to
the calibration algorithm, which is an obvious reason of discomfort for the patients.
To pursue this objective, the use of the Bayesian estimation in the calibration
process, as proposed in Refs. [42,43], appears the most promising technique. Indeed,
by setting the calibration problem in the Bayesian framework, the information
brought by additional BG references could be substituted by a priori knowledge
on calibration parameters derived from ad hoc training sets, allowing, in principle,
the reduction of calibration frequency without scarifying sensor accuracy. The
following section gives a more detailed description of the application of the
Bayesian estimation to the calibration problem.

The Bayesian approach applied to the calibration problem
The key aspect of Bayesian estimation is that, in addition to experimental data, it
also considers statistical expectation on the unknown model parameters, usually
called “prior” (see Ref. [46] for a comprehensive review on the topic). With