I read with keen interest the statement of the Consensus Committee on the pending worldwide standardization of hemoglobin A1C measurement (1) and felt compelled to offer a more “believable” reason why the data supporting the premise that A1C assay reflects average glycemia over the preceding few months “are not exceptionally robust.” The Consensus Committee contends that “glucose concentrations were not measured frequently enough to compute a true ‘average.'”
The more believable reason is this: a variation of parameter analysis was carried out in ref. 2, and it was shown therein that A1C curves decay in a manner “opposite” to the way they should, as the magnitude of the “disappearance constant” changes. It was reported there that this inverted decay suggests the particular “nonphysical” behavior that A1C percentage is decreasing faster, while plasma glucose level is decreasing slower, thus discrediting the weighted-average relationship now believed to be the cornerstone for the assessment of diabetes care.
That work led to a second effort (3) where the genesis of the flaw revealed in ref. 2 was identified. Specifically, Shi et al. (4) derived a differential equation between the fraction of glycated protein h and glucose level G and then solved it to obtain h = 1 − exp[−k ∫ G(t)dt]. They then invoke the condition that the fraction of glycated protein is “small” and subsequently linearize the solution to read h ≈ k ∫ G(t)dt. The linearized version, however, is not a “solution” to their derived differential equation. In effect, linearizing the solution unacceptably distorts the physics. Specifically, it eliminates the nonlinearity that manifests through the coupling Gh and reduces a behavior where cause and effect are not proportional to one another (nonlinear) to one where cause and effect are proportional to one another (linear). For example, doubling G in h ≈ k ∫ G(t)dt immediately doubles h; doubling G in h = 1 − exp[−k ∫ G(t)dt] does not. The first-order nonlinear estimate of the solution, viz. h ≈ k ∫ G(t)dt − 0.5k2[∫ G(t)dt]2, will (for obvious reasons) yield more palatable results.
In short, a better understanding of the relationship between A1C and average blood glucose cannot be attained using exclusively “frequent capillary measurements and continuous glucose monitoring” (1). Any approach that avoids addressing the evident nonlinearity is doomed from inception. Further, computing a “true ‘average'” cannot be achieved using garden-variety arithmetic averaging (5). Glucose values drawn as a time series from one individual are inherently correlated; standard averaging techniques require that the analyzed data be uncorrelated.
