Glycation is the process by which a monosaccharide, most commonly glucose, attaches nonenzymatically to a protein. Hemoglobin A_{1c}(Hb A_{1c})^{3} forms when hemoglobin is glycated at the N-terminal valine of the β-chain. Measurement of Hb A_{1c} is integral to the diagnosis and management of diabetes because it reflects the average glucose (AG) over the preceding 120 days. Further, the mean Hb A_{1c} over time determines the risk of microvascular complications of diabetes. However, a major limitation of its use is that some nonglycemic factors can influence Hb A_{1c} concentration. A few substances (e.g., certain drugs, carbamylated hemoglobin, or labile Hb A_{1c}) have been reported to interfere with Hb A_{1c} measurement, but these interferences have been eliminated from most modern methods. Physiological and pathophysiological conditions reported to change Hb A_{1c} values independently of glucose include advanced age, race, iron deficiency (with or without anemia), hemoglobin variants, and chronic kidney disease (1).

In addition, many clinicians have patients with none of these factors; yet, Hb A_{1c} values are inconsistent with glucose concentrations. Evaluation of these patients includes hemoglobin electrophoresis to identify clinically silent hemoglobin variants and measurement of erythrocyte-independent markers of chronic glycemia, such as fructosamine or glycated albumin. In several patients no explanation is identified for the inconsistency between the Hb A_{1c} value and other measures of glycemia. Congruent with this, the A1c-Derived Average Glucose study showed that, although the relationship between Hb A_{1c} and AG was linear, wide variation was observed between individuals (2). An Hb A_{1c} concentration of 6.5% (the threshold for diagnosis) was associated with AG from 125 to 175 mg/dL, while Hb A_{1c} values ranged between 5.5% and 8.0% when AG was 150 mg/dL.

Interpretation of Hb A_{1c} values is based on the assumption that erythrocytes are freely permeable to glucose and that neither glucose entry, the rate of glycation, nor erythrocyte life span differs significantly among individuals. Some investigators claim interindividual variation in glucose entry and the rate of glycation, but no convincing evidence supports these assertions (3).

Erythrocyte life span is different because interindividual variation is well documented. Studies suggest approximately 15% variation in erythrocyte survival between individuals, but erythrocyte survival is stable over time in an individual. Nevertheless, a relatively small change in this parameter can substantially alter Hb A_{1c} values. For example, an Hb A_{1c} concentration of 6.0% with a normal erythrocyte life span of 120 days would be reduced to 5.5% if erythrocytes lived 110 days and increased to 6.5% if erythrocytes survived 130 days (1). Correcting Hb A_{1c} values for erythrocyte age would eliminate the effect of this variation. Unfortunately, it is extremely difficult to measure erythrocyte life span. Methods used include carbon monoxide production or labeling erythrocytes with biotin or radioactive isotopes (e.g., ^{99}Tc, ^{59}Fe, ^{15}N-glycine, or ^{51}Cr) (4). These methods are all labor-intensive, very expensive, may require ex vivo labeling followed by intravenous infusion, and are clearly not feasible for routine patient care. Another limitation is that different techniques produce different results, with average values ranging from 88 to 122 days and within-method SDs from 15% to 30% (4).

A recent study by Higgins and colleagues (5) adopted a different strategy to address this problem. To describe the mechanistic physiologic processes, they propose an elegant mathematical model that is expressed as a differential equation relating the Hb A_{1c} in an erythrocyte to time-varying glucose concentrations. Integrating the solution of the differential equation over the distribution of erythrocyte ages in a subject, they obtain nonlinear functions relating the glucose concentrations to Hb A_{1c}. They then derive simpler linear equations (Eq. 1–3 herein) to provide patient-specific estimates of Hb A_{1c} derived from an AG and the mean age of the red blood cell (M_{RBC}), and estimates of M_{RBC} derived from AG and Hb A_{1c}. Hb A_{1c} results from the irreversible chemical reaction of hemoglobin with glucose. The rate of change in Hb A_{1c} increases as the glucose concentration increases, and it decreases as the concentration of nonglycohemoglobin (Hb − Hb A_{1c}) decreases. The rate further depends on a certain glycation rate parameter (k_{g}) that is the proportionality factor relating the change in Hb A_{1c} to the glucose concentration and the nonglycohemoglobin. While it is currently impossible to measure k_{g} directly in vivo, estimates range between 6.07 × 10^{−6} and 10.30 × 10^{−6} dL/mg/day. In the model computations, k_{g} is assumed to be nearly constant in the population. An ordinary differential equation describing the model inside a single RBC yields an exact solution, from which a simple linear equation expressing Hb A_{1c} as a function of AG and the mean age of all RBCs in circulation at a point in time (5) is obtained:
(Eq. 1) where α = Hb A_{1c}(0) is the intercept and β = [1 − Hb A_{1c}(0)] × k_{g} × M_{RBC} is the slope.

Hb A_{1c} is measured. AG is calculated from continuous interstitial glucose monitoring (CGM), which measures glucose concentrations every 5 min over several days (2, 5). The intercept Hb A_{1c}(0) is the % Hb A_{1c} in the RBC when it is a reticulocyte and has just entered the circulation. The slope is a product of 1 − Hb A_{1c}(0), k_{g}, and the M_{RBC} in circulation at that time. Based on previously published data, the intersubject variability of Hb A_{1c}(0) is very small (approximately 0.3%).

Other studies have shown that the relationship between Hb A_{1c} and AG is strongly linear, but some departures from the regression line are observed (2). Malka et al. (5) suggest that these departures cannot be explained by the small intersubject variability in the Hb A_{1c}(0), the intercept in their model, leading them to conclude that these departures are a result of intersubject variation in the slope. In other words, the slope of the relationship between Hb A_{1c} and AG is subject specific, or varies from subject to subject as a function of the M_{RBC}. Because the intercept is assumed fixed, it can be obtained using available (published) data, so it is assumed known.

From the expression for the slope in the equation above, since 1 − Hb A_{1c}(0) and k_{g} can be assumed fixed, it is further assumed that intersubject heterogeneity in M_{RBC} is the only nonglycemic factor that can influence the relationship of Hb A_{1c} with AG. This suggests that personalized expressions for Hb A_{1c} as a function of AG can be obtained once an estimate of M_{RBC} is available for that particular individual.

Solving (Eq. 1) for M_{RBC} yields the following expression:
(Eq. 2) It follows that an estimate of M_{RBC} (eM_{RBC}) for a given subject can be obtained from a single pair of Hb A_{1c} and AG values measured at the same time point, which can then be used prospectively or retrospectively to obtain estimated Hb A_{1c} values from past or future measurements of AG.

Then, substituting the given eM_{RBC} into (Eq. 1) and solving for AG yields the expression:
(Eq. 3) that can be used to obtain an estimate of the AG (eAG) given an Hb A_{1c} value at a given point in time, past or future.

The authors suggest that the proposed method explains the nonglycemic variation in Hb A_{1c} concentration and yields more accurate estimates of Hb A_{1c} values given AG measurements or vice versa, as a function of the M_{RBC}. The adjustment for the M_{RBC} can also be used to yield a corrected Hb A_{1c}. Importantly, the ability to amend Hb A_{1c} for M_{RBC} in an individual is likely to improve both the diagnostic accuracy of Hb A_{1c} and its efficacy in predicting diabetic complications.

A key assumption of the model is that the M_{RBC} is constant over time within a subject. This has been demonstrated for up to 5 years, but not over longer periods. Another is that all of the glucose-independent Hb A_{1c} variation among individuals is assumed to be due to variation in M_{RBC}. If validated, this observation is likely to stimulate investigators to develop simpler and more direct ways to measure M_{RBC}. The final assumption is that k_{g} and Hb A_{1c}(0) are constant across subjects.

Although these assumptions may be valid biologically, in practice there will be variation in the estimate of the M_{RBC} from one Hb A_{1c} and AG pair of measures to a different pair obtained from the same subject, and thus the expression for the estimated AG from a given Hb A_{1c} concentration may also vary depending on which pair of measures is used. If the model were generalized to allow for random variation in the estimated M_{RBC}, and for other sources of random variation (error) in the other model components, then more precise estimates of the M_{RBC} and the slope of the Hb A_{1c} to AG relationship could be obtained by fitting an appropriate regression model.

While CGM is used in some patients with type 1 diabetes, at present it is not feasible to obtain the “continuous” monitoring glucose data needed to apply this model for the vast majority of diabetic individuals. In addition to the high cost, CGM is technically demanding and patients require extensive training to enable them to use the devices. To do this on the estimated >400 million patients with diabetes, many of whom live in undeveloped countries, is clearly not a viable option.

This work is likely to generate several follow-up studies. It is important to validate the model by comparing its performance to direct measurements of erythrocyte life span. The model also needs to be evaluated in diverse patient populations; the current study was confined to individuals with type 1 diabetes. Whether M_{RBC} is a function of observed covariates (such as age and sex) could be easily addressed by including appropriate interaction terms in a linear model relating AG and Hb A_{1c}. In addition, it will be valuable to test the model in conditions that alter erythrocyte life span (e.g., chronic kidney disease, severe thalassemia, hemolytic anemia) to ascertain whether it is universally applicable. The duration of CGM to ascertain M_{RBC} and the long-term stability of the M_{RBC} also need to be determined. After these validation steps are performed, the clinical relevance of this personalized approach (i.e., improvement in prediction of complications) compared to the standard method will have to be evaluated.

Ideally, a high-throughput—and inexpensive—assay to measure erythrocyte life span would allow Hb A_{1c} concentration to be corrected for M_{RBC}, providing a more reliable measure of long-term glycemia. Unfortunately, this goal is unlikely to be attained in the immediate future. In the interim, the study by Malka et al. (5) provides a way to mathematically achieve this goal, thereby considerably enhancing the clinical value of Hb A_{1c}.

## Footnotes

↵3 Nonstandard abbreviations:

- Hb A
_{1c}, - hemoglobin A
_{1c}; - AG,
- average glucose;
- M
_{RBC}, - mean age of the red blood cell;
- k
_{g}, - glycation rate parameter;
- CGM,
- continuous glucose monitoring;
- eM
_{RBC}, - estimate of M
_{RBC}; - eAG,
- estimate of the AG.

- Hb A
**Author Contributions:***All authors confirmed they have contributed to the intellectual content of this paper and have met the following 3 requirements: (a) significant contributions to the conception and design, acquisition of data, or analysis and interpretation of data; (b) drafting or revising the article for intellectual content; and (c) final approval of the published article.***Authors' Disclosures or Potential Conflicts of Interest:***Upon manuscript submission, all authors completed the author disclosure form. Disclosures and/or potential conflicts of interest:***Employment or Leadership:**D.B. Sacks,*Clinical Chemistry*, AACC.**Consultant or Advisory Role:**None declared.**Stock Ownership:**None declared.**Honoraria:**None declared.**Research Funding:**D.B. Sacks, Intramural Research Program of the NIH; I. Bebu and J.M. Lachin, NIDDK, NIH (U01-DK-094176).**Expert Testimony:**None declared.**Patents:**None declared.

- Received for publication January 28, 2017.
- Accepted for publication March 9, 2017.

- © 2017 American Association for Clinical Chemistry