## The variability of blood glucose in type 1 diabetes
## How to show the BG variabilityIn 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 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 ## An example of actual BG readingsFig. 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 very few readings below mean - 2 SD. Therefore, conventional parametric statistical analyses cannot be made, which was stated by Kovatchev et al. in 1997 [1]. 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, 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 [2]. 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 arithmetic mean of log-transformed BG readings is equivalent to the
*geometric mean*(GM) of original readings. In the graphs, the centre white border in the grey area indicates GM. Compare this to the*median*value which is the 50th percentile: there are as many smaller as larger readings. If the statistical model were perfect, GM would be identical with the median. - The standard deviation of log-transformed readings is equivalent to a dimensionless
*factor*for original readings, denominated*factor of variation*(FV) in documents by the author. - FV
^{4}(the factor of variation multiplied by itself 4 times) is the*ratio*of the BG-value corresponding to mean + 2 SD in the log-transformed readings to the BG-value corresponding to mean - 2 SD in the log-transformed readings. This ratio, which is indicated in the graphs by the total width of the grey area, is an estimate of the variation range in 95% of the readings.
## The graphs can promote new conceptsIn recent years, several papers have proposed strict avoidance of hypoglycaemia in order not to introduce "hypoglycaemia unawareness" [3] (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 HbA 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 HbA 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 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 [4]. [5]
- The Y-axis indicates percentile.
- The X-axis indicates BG readings (whole blood in mmol/l) on a
*logarithmic*scale. - The total width of the grey area is an estimate of the variation range including 95% of the readings.
- The centre white line in the grey area indicates GM and the other two white lines indicate GM / FV and GM × FV, respectively.
## References- Kovatchev BP, Cox DJ, Gonder-Frederick LA, Clarke W: "Symmetrization of the blood glucose measurement scale and its applications."
*Diabetes Care*20(11): 1655-8, 1997. PubMed abstract - Zhang CL, Popp FA: "Log-normal distribution of physiological parameters and the coherence of biological systems."
*Med Hypotheses*43(1): 11-6, 1994. PubMed abstract - Bolli GB: "How to ameliorate the problem of hypoglycemia in intensive as well as nonintensive treatment of type 1 diabetes."
*Diabetes Care*22(3) Suppl 2: B43-52, 1999. Abstract Full text - Moberg E, Kollind M, Lins PE, Adamson U: "Estimation of blood-glucose variability in patients with insulin-dependent diabetes mellitus."
*Scand J Clin Lab Invest*53(5): 507-14, 1993. Abstract - Derr R, Garrett E, Stacy GA, Saudek CD: "Is HbA1c Affected by Glycemic Instability?"
*Diabetes Care*26(10): 2728-33, 2003. Abstract Full text
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