Data from an actual clinical trial for the closed-loop artificial pancreas is summarized in the following cumulative histograms, where the percentage of blood glucose measurements below a particular value is plotted against the blood glucose value. The three curves denote: 

(i) actual blood glucose BG measurements collected from finger stick measurements (solid), 

(ii) one continuous glucose measurement sensor CGM2 (dashed), and 

(iii) a (redundant) second glucose measurement sensor CGM2 (dotted).

From a medical safety perspective, one would like to keep the blood glucose measurements in the range of 70€“180 mg/dL. 

(a) For each of the three measurements (two CGMs and actual BG), compute the fraction of the data that lies in the range 70€“180 mg/dL. Comment on the absolute and relative safety of an algorithm that uses these measurements.
(b) Repeat the calculations for the more stringent performance range of 80€“140 mg/dL. 

(c) Using the concepts introduce in Chapter 9, comment on the error characteristics of the two sensors, using the nomenclature introduced in Section 9.4.3.

100 90 80 70 60 50 40 Mean: BG .. Mean: CGM1 Mean: CGM2 20 10 250 350 50 100 150 200 300 400 Blood Glucose [mg / dL] Figure E23.8 Cumulative distribution [%]