The variability of blood glucose in type 1 diabetes
Stefan Du Rietz (e-mail: sdr (at) this domain)
How to show the BG variability
In order to get a quantitative image of collected blood glucose (BG) readings, one must produce a relevant graph. A convenient option is a plot of the cumulative probability distribution: the fraction (y) of the sample being smaller than a certain value of the measured variable (x). Fig. 1 shows such a graph of normally distributed data with mean = 0 and standard deviation SD = 1. The fraction is shown as percentage (percentile).
The centre white line in the grey area indicates the arithmetic mean. The other two white lines indicate mean ± SD, where the points A and B are situated, and the vertical outer edges of the grey area indicate mean ± 2 SD. Consequently, the width of the grey area includes about 95% of the data.
To the left, the curve is close to zero, i.e. there are very few data below -3. At x = -2 a few percent of the data have shown up and the curve has begun to rise. At point A (when x = -1, i.e. mean - SD) the curve has risen to 16%, indicating that 16% of the data are below -1. At x = 0, i.e. the mean, the curve has risen to 50%, indicating that 50% of the data are below 0 or that the remainder (100-50 = 50 %) are above 0. In other words, the mean is equal to the median. At point B (when x = 1, i.e. mean + SD) the curve has risen to 84%, indicating that 84% of the data are below 1 or that the remainder (100-84 = 16 %) are above 1. Consequently, 68% (84-16 %) of the data are between -1 and 1. In this way it is always easy to get the percentage of data within a certain range.
An example of actual BG readings
Fig. 2 shows a similar graph of all the regular (8/day) BG readings of the author (SDR) during his last 22 months of multiple daily injections (MDI) therapy. All the readings are from the same meter (One Touch Profile ).
Obviously, the probability distribution of BG readings is not normal and symmetric, but very skew. The arithmetic mean is not equal to the median (the 50:th percentile) and there are too many readings above mean + 2 SD (about 5 %) but no readings below mean - 2 SD. Therefore, conventional parametric statistical analyses cannot be made, which was stated by Kovatchev et al. in 1997 . This has, however, been greatly overlooked in diabetes research: the paper by Kovatchev et al. has so far (2002) only been cited three times by other articles, and then by its own authors! Consequently, in almost all studies, the comparisons of statistical parameters, e.g. mean and SD, of BG readings are erroneous!
However, after logarithmic transformation BG readings become normally distributed. This is due to the multiplicative nature of endocrine and metabolic processes and is in accordance with most biological parameters . The log-transformed BG readings of SDR are shown in fig. 3. Note the symmetric distribution and the nonlinear BG scale (compressed towards higher BG-values).
When statistical parameters have been computed on the logarithmic data, a back transformation returns the result expressed in original BG units (fig. 3). Because addition in the logarithmic domain is equivalent to multiplication in the linear domain, the following statements are valid:
The graphs can promote new concepts
In recent years, several papers have proposed strict avoidance of hypoglycaemia in order not to introduce "hypoglycaemia unawareness"  (see also my discussion of neuroglycopenia). The belief seems to be that it is possible to keep all BG readings above 4 mmol/l and still maintain HbA1c<7.0% (upper normal limit 5.5%).
Fig. 3 above shows the distribution of all the actual regular BG readings of the author (SDR) during MDI with a geometric mean of 5.12 mmol/l and therefore a HbA1c within the normal range (on average a few tenths below the upper normal limit). Due to the large BG variation (FV4 = 4.64), this low mean brings about a substantial fraction (25.7%) of BG readings below 4 mmol/l.
Because SDR has already tried to minimize the variation, he could only avoid any single reading below 4 mmol/l by increasing the average, which implies moving the curve to the right so that it does not begin to rise until the BG-value is 4 mmol/l. This is equivalent to multiplying all the readings by a factor of 2.88 which is the ratio of 4 mmol/l to the lowest actual BG reading, 1.39 mmol/l. Fig. 4 shows the result of this operation.
Note the large increase in GM (from 5.1 to 14.8 mmol/l) and the majority of BG readings being seriously hyperglycaemic (84% above 10 mmol/l). It goes without saying that the consequences in terms of complications must be devastating. Yet, the variability of the BG readings of SDR is probably lower than that of most individuals with longstanding type 1 diabetes. The common but inappropriate estimate of BG variability, the standard deviation of all blood-glucose values (SDBG), is 2.1 mmol/l in SDR vs. a mean SDBG of 3.9 ± 1.0 mmol/l in a cohort of one hundred patients . 
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© 2002-2013 Stefan Du Rietz. Last modified: 2012-04-08 18:55 (MEST).