Addressing shortfalls of laboratory HbA1c using a model that incorporates red cell lifespan

Laboratory HbA1c does not always predict diabetes complications and our aim was to establish a glycaemic measure that better reflects intracellular glucose exposure in organs susceptible to complications. Six months of continuous glucose monitoring data and concurrent laboratory HbA1c were evaluated from 51 type 1 diabetes (T1D) and 80 type 2 diabetes (T2D) patients. Red blood cell (RBC) lifespan was estimated using a kinetic model of glucose and HbA1c, allowing the calculation of person-specific adjusted HbA1c (aHbA1c). Median (IQR) RBC lifespan was 100 (86–102) and 100 (83–101) days in T1D and T2D, respectively. The median (IQR) absolute difference between aHbA1c and laboratory HbA1c was 3.9 (3.0–14.3) mmol/mol [0.4 (0.3–1.3%)] in T1D and 5.3 (4.1–22.5) mmol/mol [0.5 (0.4–2.0%)] in T2D. aHbA1c and laboratory HbA1c showed clinically relevant differences. This suggests that the widely used measurement of HbA1c can underestimate or overestimate diabetes complication risks, which may have future clinical implications.


Introduction
High glucose exposure in specific organs (particularly eye, kidney, and nerve) is a critical factor for the development of diabetes complications (Marcovecchio, 2017;Giacco and Brownlee, 2010). Laboratory HbA 1c is routinely used to assess glycaemic control, but studies report a disconnect between this glycaemic marker and diabetes complications in some individuals (Cohen et al., 2003;Bonora and Tuomilehto, 2011). The exact mechanisms for this are not always clear but, at least in some cases, likely related to inaccurate estimation of intracellular glucose exposure in the affected organs.
While raised intracellular glucose is responsible for diabetes complications (Giacco and Brownlee, 2010;Brownlee, 2005), extracellular hyperglycaemia selectively damages cells with limited ability to adjust cross-membrane glucose transport effectively (Brownlee, 2005). HbA 1c has been used as a biomarker for diabetes-related intracellular hyperglycaemia for two main reasons. First, the glycation reaction occurs within red blood cells (RBCs) and therefore HbA 1c is modulated by intracellular glucose level. Second, RBCs do not have the capacity to adjust glucose transporter GLUT1 levels and thus are unable to modify glucose uptake, behaving similarly to cells that are selectively damaged by extracellular hyperglycaemia (Brownlee, 2005). Therefore, under conditions of fixed RBC lifespan and glucose uptake, HbA 1c mirrors intracellular glucose exposure in organs affected by diabetes complications. However, given the inter-individual variability in both glucose uptake and RBC lifespan Khera et al., 2008), laboratory HbA 1c may not always reflect intracellular RBC glucose exposure. While variation in RBC glucose uptake is likely relevant to the risk of diabetes complications in susceptible organs, variation in red cell lifespan can affect haemoglobin glycation and HbA1c values, in turn compromising the accuracy of this glycaemic marker in predicting risk of complications. This explains the inability to clinically rely on laboratory HbA 1c in those with haematological disorders characterised by abnormal RBC turnover (American Diabetes Association, 2019) and represents a possible explanation for the apparent 'disconnect' between laboratory HbA 1c and development of complications in some individuals with diabetes ( Figure 1).
A kinetic model, which considers individual variations in both RBC turnover and glucose uptake, has been developed to explain the disconcordance of the glucose-HbA 1c relationship on individual level (Xu et al., 2021a). The current work aims to extend this model by providing a way to normalise against RBC lifespan variation when individual RBC lifespan becomes available. We propose a new clinical marker, which we term adjusted HbA 1c (aHbA 1c ), by adjusting laboratory HbA 1c for a standard RBC lifespan of 106 days (English and Lenters-Westra, 2018) (equivalent to RBC turnover rate of 0.94 % per day). The new glyacemic marker, aHbA 1c , is likely to be the most accurate marker of organ exposure to hyperglycaemia and risk of future diabetes-related complications.

Results
Of the 287 individuals in the original studies, 218 had predefined continuous glucose monitoring (CGM) coverage between at least two HbA 1c measurements. Of these, 131 individuals had adequate continuous glucose data to estimate RBC lifespan and glucose uptake rate. The subject characteristics of this sub-cohort are presented in Table 1.

Discussion
Variation in RBC lifespan and glucose uptake between individuals can lead to different laboratory HbA 1c despite similar hyperglycaemic exposure in the organs affected by diabetes complications. In order to individualise care and assess the personal risk of hyperglycaemic complications, laboratory HbA 1c levels should be adjusted to account for variability in RBC turnover through our proposed aHbA 1c . Without this adjustment, there is a risk of overestimating glucose levels that may cause hypoglycaemia through the unnecessary escalation of diabetes therapies, or alternatively, underestimation that may lead to undertreatment and subsequent high risk of complications. In addition, there are implications for the diagnosis of prediabetes and diabetes, as there may be misclassifications if the diagnosis is based solely on laboratory HbA 1c levels due to variable RBC lifespan across individuals.
RBC removal by senescence and erythrocyte apoptosis are complex processes, which can be affected by the presence of hyperglycaemia and known to vary both within and across individuals Figure 2. Distribution of red blood cell (RBC) lifespan for type 1 (n = 51) and type 2 (n = 80) diabetes and adjustment to laboratory HbA 1c by RBC lifespan. The number (percentage) of individuals having HbA 1c adjustments < 1 % (<11 mmol/mol), 1-2% (11-22 mmol/mol), 2-3% (22-33 mmol/mol), and >3% (>33 mmol/mol) were 90 (68%), 21 (16%), 12 (9%), and 8 (6%), respectively. (Lang et al., 2012). In the meantime, potential differences in RBC glucose uptake  can also affect the relationship between blood glucose and HbA 1c . Several mathematical models (Malka et al., 2016;Fabris et al., 2020) have been developed to estimate laboratory HbA 1c from glucose levels or time in range, emphasising the importance of this area. Accurate estimation of 'clinically relevant HbA1c' will allow each person with diabetes to have an individualised glycaemic target that ensures adequate treatment, thus reducing the risk of complications while minimising hypoglycaemic risk.
A unique feature of our model (Xu et al., 2021a) is the inclusion of individual-specific RBC lifespan and glycation rate in the calculations. A weakness of this model, however, is the absence of a direct measure of RBC lifespan, which remains an estimate based on a mathematical calculation. However, the ability of the model to reflect laboratory HbA 1c , as we have previously shown, indicates a good level of accuracy at estimating RBC lifespan ( Xu et al., 2021c). In addition, the method is far simpler than complex methods for estimating RBC lifespan through labelling experiments that are not suited for routine clinical practice . Future work may determine whether other measures, such as reticulocyte count or red cell distribution width (Brodksy, 2021;Kameyama et al., 2018;Kameyama et al., 2020), can further be added to the model to further improve the accuracy of estimating RBC lifespan and this remains an area for future research.
Since aHbA 1c reflects intracellular glucose exposure in RBCs, it is difficult to directly compare with extracellular glucose-derived glycaemic markers such as average glucose or time in range. As an intracellular marker, aHbA 1c should correlate with intracellular glucose levels, therefore providing a potentially accurate measure of glucose exposure of organs susceptible to diabetes complications. We summarise the advantages and drawbacks of different methods that measure average glucose control in Appendix 1-table 2.
Importantly, our study demonstrates that laboratory HbA 1c does not necessarily reflect intracellular glucose exposure of organs prone to diabetes complications. However, future work is required to show that adjusted A 1c is a better predictor of diabetes complications than laboratory HbA 1c . Moreover, it is unclear whether the use of aHbA 1c reduces the risk of hypoglycaemic complications as compared to reliance on laboratory HbA 1c , and these remain areas for future research.
In conclusion, quantitative aHbA 1c , derived from laboratory HbA 1c and CGM readings, has the potential to more accurately assess glycaemic exposure of different organs, providing a safer and more effective glycaemic guide for the management of individuals with diabetes. Future testing in larger populations and different ethnic groups is required to further increase confidence in the model. This to be followed by large prospective clinical studies to test the relationship between aHbA 1c and future microvascular/macrovascular diabetes complications as well as reducing the risk of hypoglycaemic exposure through avoidance of unnecessary therapy escalation.

Materials and methods
CGM and laboratory HbA 1c data from 139 type 1 (T1D) and 148 type 2 diabetes (T2D) patients, enrolled in two previous European clinical studies (Bolinder et al., 2016;Haak et al., 2017), were evaluated to calculate aHbA 1c as detailed below. These studies were designed to evaluate the benefits of CGM in those with T1D and those with T2D using multiple daily injections of insulin. Both studies were conducted after appropriate ethical approval and participants gave written informed consent. A total of 6 months' CGM data were collected using the sensor-based flash glucose monitoring system (FreeStyle Libre; Abbott Diabetes Care, Witney, UK), while HbA 1c was measured by a central laboratory (ICON Laboratories, Dublin, Ireland) at 0, 3, and 6 months of the study. For T1D participants, the mean age was 44 years (range 18-70 years), 17 (33%) of whom were females. For T2D, the mean age was 59 years (range 33-77 years), 28 (35%) of whom were females.
Each subject had at least one data section consisting of two HbA 1c measurements connected by CGM data. Since the kinetic parameters are more sensitive to the data sections with larger between-day glucose changes, the parameters were successfully estimated for those individuals with sufficient dayto-day glucose variability, as evidenced by the model fit of RBC life converging between 50 and 180 days. These individual RBC lifespans or turnover rates were calculated according to previous model (Xu et al., 2021a) that considers both RBC turnover rate and glucose uptake. Briefly, the model aligns laboratory HbA 1c and the contemporaneous CGM-derived estimate of HbA 1c under optimal values for RBC turnover and glucose uptake of each individual. Since there is no simple clinical assay for RBC turnover and glucose uptake, these RBC parameters are estimated using a numerical method such that differences between laboratory HbA 1c and CGM-derived estimate are minimized. While the parameter identification method can be performed by repeated permutations across all reasonably possible values for RBC lifespan and uptake, our approach uses a far more efficient and reliable numerical method, as previously described (Xu et al., 2021a). Detailed model description and derivation are provided in Appendix 1. Deriving from the same model, we constructed aHbA 1c (Equation 1) that adjusts laboratory HbA 1c for individual RBC turnover variation for potential clinical use. Under the assumption of individually constant RBC life, the relationship between RBC turnover rate (k age ), RBC lifespan (L RBC ) and mean RBC age (MA RBC ) can be inter-converted using the simple formula: 2 * MARBC = LRBC = 1 kage . Therefore, 0.94%/day standard RBC turnover rate is equivalent to 106 days of RBC life and 53 days of mean RBC age. Of note, the adjustment is not linear, decreasing RBC lifespan corresponds to more pronounced aHbA 1c adjustment than a seemingly comparable increase in RBC lifespan. All calculations in this study were done with Python/SciPy (Virtanen et al., 2020) software package.
Full derivation of the model is further provided in Appendix 1.

Acknowledgements
This work was funded by Abbott Diabetes Care.

Competing interests
and kgly = kg * Vmax/ ( kc * KM ) . By definition, HbA 1c is the fraction of glycated haemoglobin found in RBCs: Combining with Equation (a3): By combining all parameters associated with cross-membrane glucose transport and glycation from the right-hand side of Equation (a4), we define the composite glycation rate constant , where kg and K M are universal constants for the non-enzymatic haemoglobin glycation reaction and glucose affinity to GLUT1, respectively. Therefore, kgly can vary between individuals depending on kc and Vmax.
We attribute the rest of the parameters to RBC turnover kage = α*r/C, which leads to the definition of the apparent glycation parameter K: Under a hypothetical steady state of constant glucose level, HbA 1c should reach an equilibrium level, which is the 'equilibrium HbA 1c ' or EA. Since C= [HbG]+[Hb], Equation (a5) can be re-written . Applying the definition HbA 1c = HbG/C = (C−[Hb])/C, we have: This relationship approximates the average glucose and HbA 1c for an individual with a stable day-to-day glucose profile.
From Equation (a3): = Vmax KM * kc g = kgly kg g , and substituting into Equation (a6) gives: Estimations of k gly and k age from glucose and HbA 1c data and prospective validation: kinetic model review Our previous publication (Xu et al., 2021a) gave the following relationship by solving the differential Equation (a1): Equation (a8) is suitable for a short time interval. For a longer time period, a recursive form is required: . The value A 1cz is equivalent to calculated HbA 1c (cHbA 1c ) at the end of time interval tz. While shorter time intervals -such as 4-6 hr -are expected to produce better results, we have shown that a time interval of 24 hr has produced acceptable performance (Xu et al., 2021a). Equation (a9) is central to our kinetic model. To estimate personal parameters kgly and kage, one or more data sections are needed, where a data section contains two HbA 1c measurements, one at the start of the time period and one at the end, with frequent (i.e. every 15 min) glucose levels in-between. The optimised individual kgly and kage pair should best align the HbA 1c and cHbA 1c , minimising the preferred error function, such as mean difference or sum-squared difference.
Once an individual's kgly and kage pair are available, Equation (a9) is used to project future HbA 1c if provided frequent glucose measurements. Therefore, prospective model validation is possible when multiple data sections are available, such that one or more can be held out of the parameter estimation to be used for prospective evaluation. Appendix 1-table 1 summarises results (Xu et al., 2021a;Xu et al., 2021c;Xu et al., 2021b) when all but the last data section is used to determine the individual kgly and kage pairs, and the held-out final data section is used for evaluation. The agreement between the last HbA 1c and cHbA 1c is compared to the agreement between the last HbA 1c and the glucose management indicator (GMI) (Xu et al., 2021a;Xu et al., 2021c;Xu et al., 2021b). These studies demonstrated the superior accuracy of the kinetic model compared to the existing GMI method.
Appendix 1-table 1. Summary of kinetic model validation studies. The mean absolute deviation differences between calculated HbA 1c (cHbA 1c ) and glucose management indicator (GMI) are statically significant with p < 0.0001.

Glycaemic marker comparisons
Given the importance of intracellular glucose level in diabetes management. We provide following table to compare the intracellular aspects of some frequently used glycaemic markers.