HbA1c (A1C) is widely used to assess glycemic control in clinical and research settings, but the precise relationship between A1C and preceding self-monitored plasma glucose measurements is recognized to be complex. It has been reported that measuring plasma glucose levels in the 120 days before an A1C measurement has a nonuniform effect on the result depending on the time that has elapsed between the glucose level and subsequent A1C measurement (1). Tahara and Shima (2) attempted to model this weighted-average relationship between plasma glucose and A1C by measuring decreases in glucose and corresponding decreases in A1C in patients admitted to the hospital. Their model gives maximum weighting to glucose measurements immediately before the A1C measurement, with the weighting linearly decreasing for glucose measurements further back in time, reaching zero weighting for plasma glucose >120 days before the A1C.
Treviño (3) reported that this weighted-average relationship leads to an anomalous relationship between the exponential decay rates of glucose (Gt) and A1C. We have reviewed this result and believe that no such anomaly exists. Treviño subtracted A1C calculated from the Tahara model (Ht) from “the mean of patient-admission A1C values” (Hstart), obtaining the counterintuitive result that a faster decay in blood glucose results in a slower decay in (Hstart − Ht). However, this “inverted” decay is likely to be due to subtracting Ht from a constant value. His expression for Ht is an absolute A1C value, not a change in A1C. An initial value, Gs, has been specified for Gt, and hence an initial value is implicit in his calculations. Subtracting Ht from a constant would not be expected to give a valid A1C estimate.
To verify this conclusion, we simulated a patient with a constant glucose level followed by an exponential decay upon admission to the hospital. During the preadmission time period, the simulated A1C reached a steady state under the constant glucose conditions, which avoided any ambiguity over the initial value (Hstart) of A1C. In this simulation, the decay rates of Ht then varied in the same way as those for the glucose data, as would be intuitively expected. The use of two initial values by Treviño, one for H and one for G, appears to have led to the anomalous result previously reported, rather than any inherent defect in the weighted-average relationship proposed by Tahara and Shima.