Addressing shortfalls of laboratory HbA_{1c} using a model that incorporates red cell lifespan
Abstract
Laboratory HbA_{1c} 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 HbA_{1c} 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 HbA_{1c}, allowing the calculation of personspecific adjusted HbA_{1c} (aHbA_{1c}). Median (IQR) RBC lifespan was 100 (86–102) and 100 (83–101) days in T1D and T2D, respectively. The median (IQR) absolute difference between aHbA_{1c} and laboratory HbA_{1c} 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. aHbA_{1c} and laboratory HbA_{1c} showed clinically relevant differences. This suggests that the widely used measurement of HbA_{1c} 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 crossmembrane glucose transport effectively (Brownlee, 2005). HbA_{1c} has been used as a biomarker for diabetesrelated 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 interindividual variability in both glucose uptake and RBC lifespan (Cohen et al., 2008; 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 glucoseHbA_{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 LentersWestra, 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 diabetesrelated 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 subcohort are presented in Table 1.
Mean (median, IQR) RBC lifespan was 94 (100, 86–102) days in those with T1D and 92 (100, 83–101) in those with T2D (Figure 2). In this cohort, the mean, median, IQR of the absolute difference between aHbA_{1c} and laboratory HbA_{1c} were 11.0, 3.9, 3.0–14.3 mmol/mol (1.0, 0.4, 0.3–1.3%) for T1D, and marginally higher at 15.1, 5.3, 4.1–22.5 mmol/mol (1.4, 0.5, 0.4–2.0%) for T2D subjects. As illustrated in the figure, those with the shorter RBC lifespan of 80 days showed around 22 mmol/mol (2%) lower laboratory HbA_{1c} than aHbA_{1c}. This may lead to underestimating intracellular glucose exposure in susceptible organs, in turn increasing the risk of complications. In contrast, those with RBC lifespan of 130 days demonstrated higher laboratory HbA_{1c} than aHbA_{1c}, which can give the impression of inadequate glycaemic control, leading to therapy escalation and predisposition to hypoglycaemia.
To further put these results into clinical context, two subjects with an identical laboratory HbA_{1c} of 63 mmol/mol (7.9%) but different RBC lifespans of 89 and 107 days, would have RBClifespanadjusted aHbA_{1c} values of 78 mmol/mol (9.3%) and 62 mmol/mol (7.8%), respectively, indicating different future risk of diabetes complications. Another two individuals with different laboratory HbA_{1c} of 60 mmol/mol (7.6%) and 75 mmol/mol (9.0%), and corresponding RBC lifespans of 89 and 107 days, would have identical aHbA_{1c} value of 74 mmol/mol (8.9%). This would place them at similar risk of diabetes complications, despite the significantly different laboratory HbA_{1c} values. Generally, in individuals with RBC lifespan of approximately 93–123 days, aHbA_{1c} and laboratory HbA_{1c} showed relatively small differences (<11 mmol/mol or 1% when laboratory HbA_{1c} < 64 mmol/mol or 8%). In this cohort, 90 (69%) subjects were within RBC lifespan range of 93–123 days, while 39 (30%) subjects had RBC lifespan below 93 days and 2 (1.5%) subjects above 123 days.
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 (Lang et al., 2012). In the meantime, potential differences in RBC glucose uptake (Khera et al., 2008) 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 individualspecific 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 (Cohen et al., 2008). 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 glucosederived 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 sensorbased 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 betweenday glucose changes, the parameters were successfully estimated for those individuals with sufficient daytoday 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 CGMderived 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 CGMderived 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.
In an approximation, $aHbA1c\frac{{k}_{age}}{{k}_{age}^{ref}}HbA1c$, where HbA_{1c} is laboratory HbA_{1c}, k_{age} is individual RBC turnover rate (%/day), ${k}_{age}^{ref}$ is standard RBC turnover rate (0.94%/day). HbA_{1c} and aHbA_{1c} are in NGSP unit and decimal values should be used. For example, 8% HbA_{1c} should be applied as 0.08. Equation 1 for IFCC unit is available in Appendix 1.
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 interconverted using the simple formula: $2*M{A}_{RBC}={L}_{RBC}=\frac{1}{{k}_{age}}$ . 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.
Appendix 1
Derivation of Equation (1): kinetic model review
The previously published kinetic model (Xu et al., 2021a) for glucose and HbA_{1c} relationship led to Equation (1), shown in the main text. We further describe here the derivation of the model for the convenience of the reader. We also cover how the model can be used to estimate personal kinetic parameters for RBC glucose uptake and RBC turnover rate.
Our model assumes: (1) firstorder dependencies for concentrations of both haemoglobin in RBCs and intracellular glucose; (2) newly generated RBCs have a negligible amount of glycated haemoglobin; (3) RBCs have a fixed life, so that they are generated constantly and eliminated from circulation when they reach an age that is individualspecific.
The rate of change in glycated and nonglycated haemoglobin in RBCs can be modelled by differential equations:
[HbG] and [Hb] are the concentrations of glycated and nonglycated haemoglobin, respectively, while [GI] is intracellular glucose concentration. The k_{g} is the rate constant of haemoglobin glycation reaction in unit of (concentration*time)^{–1}, with a reported value of about 0.0019 dL/mg/day (Higgins and Bunn, 1981). C is the total haemoglobin concentration C = [Hb] + [HbG]. A_{1c} is the fraction of glycated haemoglobin [HbG]/C, r is RBC removal rate in unit of concentration/time, α is a coefficient used to scale HbA_{1c} to the fraction of glycated haemoglobin to be removed (has no units of measurement).
The glucose transporters on RBC membranes (GLUT1) follows MichaelisMenten kinetic with a universal K_{M} approximately 26 mM (Ladyzynski et al., 2011). Intracellular glucose can be modelled with $d\left[GI\right]/dt={V}_{max}\mathrm{*}\left[G\right]/({K}_{M}+[G\left]\mathrm{}\right){k}_{c}\mathrm{*}\left[GI\right]$, where [G] is the extracellular glucose concentration and k_{c} is the rate of glucose consumption within RBCs. The maximum rate V_{max} should be proportional to the GLUT1 level on the membrane and we assume both k_{c} and V_{max} can vary between individuals. Since this process is fast, we use the equilibrium condition:
where $g=\left({K}_{M}*\right[G\left]\right)/({K}_{M}+[G\left]\right)$ and ${k}_{gly}={k}_{g}*{V}_{max}/{(k}_{c}*{K}_{M})$.
By definition, HbA_{1c} is the fraction of glycated haemoglobin found in RBCs:
In steady state, $d\left[Hb\right]/dt=d\left[HbG\right]/dt=0$, Equation (a1) becomes
Combining with Equation (a3):
By combining all parameters associated with crossmembrane glucose transport and glycation from the righthand side of Equation (a4), we define the composite glycation rate constant
${k}_{gly}={k}_{g}*{V}_{max}/{(k}_{c}*{K}_{M})$, where k_{g} and K_{M} are universal constants for the nonenzymatic haemoglobin glycation reaction and glucose affinity to GLUT1, respectively. Therefore, k_{gly} can vary between individuals depending on k_{c} and V_{max}.
We attribute the rest of the parameters to RBC turnover k_{age} = 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 rewritten to $K=(C[Hb\left]\right)/\left(g*\right[Hb\left]\right)$. 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 daytoday glucose profile.
From Equation (a3): $\left[GI\right]=\frac{{V}_{max}}{{K}_{M}*{k}_{c}}g=\frac{{k}_{gly}}{{k}_{g}}g$, and substituting into Equation (a6) gives:
Imaging two individuals who have identical intracellular glucose level ${\left[GI\right]}_{{k}_{age}}={\left[GI\right]}_{{k}_{age}^{ref}}$ , one with ${k}_{age}$ and the other with reference ${k}_{age}^{ref}$ . The relationship of their equilibrium HbA_{1c} values is:
Again, k_{g} is the universal composite rate constant for glucose haemoglobin composite reaction. Simplifying this equation we have:
In a steady state, $E{A}_{{k}_{age}}$ is the HbA_{1c} under RBC turnover rate of ${k}_{age}$ . The $E{A}_{{k}_{age}^{ref}}$ is the HbA_{1c} under the same intracellular glucose level, when RBC turnover rate is a reference value of ${k}_{age}^{ref}$ . Therefore, if we were to compare intracellular glucose exposure, steadystate HbA_{1c} should be adjusted to a reference RBC turnover rate, which lead to the aHbA_{1c} in Equation (a1) by replacing $E{A}_{{k}_{age}^{ref}}$ with aHbA_{1c} and $E{A}_{{k}_{age}}$ with HbA_{1c}:
To simplify the above, an approximation to Equation (a1) is $aHbA1C\frac{{k}_{age}}{{k}_{age}^{ref}}HbA1c$. Note that $\frac{{k}_{age}}{{k}_{age}^{ref}}=\frac{{M}_{RBC}^{ref}}{{M}_{RBC}}=\frac{{L}_{RBC}^{ref}}{{L}_{RBC}}$ , where M_{RBC} is the mean RBC age and L_{RBC} is the RBC lifespan.
The HbA_{1c} and aHbA_{1c} take NGSP unit in decimal form by default. For example, the decimal form of HbA_{1c} of 8% is 0.08. The unit for ${k}_{age}^{ref}$ and ${k}_{age}$ should be %/day.
When IFCC unit (mmol/mol) is used for HbA_{1c} and aHbA_{1c}, Equation (a1) becomes:
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:
Equation (a9) describes HbA_{1c} change from time 0 to time z. A_{1c0} and A_{1cz} are the starting and ending HbA_{1c} values. The time period is split into z time intervals with lengths of t_{i} (i = 1,2,3, …, z), where ${D}_{i}={e}^{\left({k}_{gly}*{g}_{i}+{k}_{age}\right){t}_{i}}$ and $E{A}_{i}=\frac{{g}_{i}}{{K}^{1}+{g}_{i}}$ , and ${g}_{i}$ can be calculated from the average glucose (AG) in the time interval ${g}_{i}=\left({K}_{M}*{\mathrm{A}\mathrm{G}}_{\mathrm{i}}\right)/({K}_{M}+{\mathrm{A}\mathrm{G}}_{\mathrm{i}}\mathrm{})$.
The value A_{1cz} is equivalent to calculated HbA_{1c} (cHbA_{1c}) at the end of time interval t_{z}. 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 k_{gly} and k_{age}, 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 inbetween. The optimised individual k_{gly} and k_{age} pair should best align the HbA_{1c} and cHbA_{1c}, minimising the preferred error function, such as mean difference or sumsquared difference.
Once an individual’s k_{gly} and k_{age} 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 k_{gly} and k_{age} pairs, and the heldout 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.
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.
Data availability
Data file for figures have been provided.
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Decision letter

Rachel PerryReviewing Editor; Yale, United States

Nancy CarrascoSenior Editor; Vanderbilt University School of Medicine, United States

Agnieszka SzadkowskaReviewer

Masashi KameyamaReviewer
In the interests of transparency, eLife publishes the most substantive revision requests and the accompanying author responses.
Acceptance summary:
This paper will be of interest to clinicians who provide care for persons with diabetes, educators who prepare these clinicians, as well as persons with diabetes who wish to be proactive participants in their own care. The calculation for an adjusted Hemoglobin A1c proposed by the authors can correct for individual red blood cell lifespan variations that can lead to misrepresentation of glycemic control. With the addition of a datadriven comparison to other means of assessing glycemic control, the adjusted HbA1c has the potential to improve care and subsequently decrease morbidity and mortality for persons with diabetes.
Decision letter after peer review:
Thank you for submitting your article "HbA_{1c} and Red Blood Cell Lifespan: Addressing shortfalls of the laboratory measure" for consideration by eLife. Your article has been reviewed by 3 peer reviewers, and the evaluation has been overseen by a Reviewing Editor and Nancy Carrasco as the Senior Editor. The following individuals involved in review of your submission have agreed to reveal their identity: Agnieszka Szadkowska (Reviewer #2); Masashi Kameyama (Reviewer #3).
The reviewers have discussed their reviews with one another, and the Reviewing Editor has drafted this to help you prepare a revised submission.
Essential revisions:
1) A more complete description of the derivation of the model – more detail is required as to how the computations were done.
2) A comparison to other methods of assessing glycemic control (CGM, A1c). While assessment of how the authors' model predicts complications will not be required, a comparison (or at the very least, detailed discussion) of how it can compare to standard means of assessing glycemic control is necessary.Reviewer #1:
The strengths of this paper include that it builds on previous research and its sample size. However, the calculation for the individual RBC turnover rate, k age, is not included. The calculation for the adjusted HbA1c is too unwieldy for the clinician to use in practice where there is increased pressure to see many patients on a timely basis. If a "calculator" could be formulated allowing the clinician to plug in the relevant values and get the adjusted HbA1c, this could be widely used to improve patient care at the point of care which is the ultimate goal of this research.
The author's claims of a proposed adjusted HbA1c which is more accurate in predicting adverse outcomes due to diabetes is supported by the data.
There is a model to estimate RBC lifespan using reticulocyte count: Brodsky, R. A. Diagnosis of hemolytic anemia in the adult. In J. S. Timauer (Ed.) UpToDate, Retrieved February 17, 2020 from https://www.uptodate.com/contents/diagnosisofhemolyticanemiaintheadult?search=hemolytic%20anemia&source=search_result&selectedTitle=1~150&usage_type=default&display_rank=1.Reviewer #2:
Laboratory HbA1c values are routinely used to assess glycemic control, but differences in red blood cell lifespan can affect hemoglobin glycation and HbA1c values. The authors developed a formula for adjusted HbA1c to account for red blood cell lifespan, which would better represent hemoglobin glycation and thus could better estimate the risk of disease complications.
The authors based their formula for aHbA1c calculation on laboratory measurements of HbA1c and CGM data performed with FreeStyle Libre. When using CGM systems, we often see falsified results for the duration of hypoglycemia, especially at night, due to sensor compression. The authors did not address these technical problems that may affect the aHbA1c result.
Using CGM we now have simple parameters to assess metabolic control of diabetes on the basis of CGM: TIR, GMI, CV. What I miss is a comparative analysis between these parameters and aHbA1c to convince readers that aHbA1c will be a better parameter for long term assessment for risk of complications.
The authors achieved their goal, and the results support their conclusions.
The use of aHbA1c in daily practice can be difficult because usually the clinician wants a ready result, but for research purposes, especially in patients with shorter red blood cell lifespans, it could be useful.
It will be interesting to see if its usefulness in estimating the risk of complications will be greater than TIR or GMI with CV.
Some comments on the methods and results:
Methods:
1. The study is based on CGM performed with FreeStyle Libre. From experience, we know that patients often have false hypoglycemia at night due to compression of the sensor. Has this been taken into account in the analysis?
2. Currently we use TIR and GMI to assess metabolic control in CGM users. Since aHbA1c, a new parameter will require additional calculations from me as a clinician, does it have advantages over these parameters in assessing the risk of chronic complications. It may be worth doing additional analysis comparing aHbA1c with these parameters.
3. As this is proof of concept, the details of creating the equation should be described, probably in some supplement. In addition, the idea behind the mathematical formula might help explain the equation to the readers. Secondly, the equation presented here is not clear in terms of units, and additionally operates slightly differently than the one in executed in provided excel file. The units for HbA1c here must be better emphasized. For example, if we assume HbA1c 9%, HbA1c in the numerator is treated as is (9%, % as a unit is preserved), but HbA1cs in the denominator have their units dropped (changed from 9% to 0.09). In parallel, the formula in excel does the same but multiplies the nominator by 100 (9% > 900 %) and leaves HbA1cs in the denominator as is (and 1 becomes 100%). This creates some confusion and should be better explained, or an example calculation could be shown.
Results:
1. I think, that any characteristics of this group in needed. They come from alreadyreported cohorts but this is only a subgroup, so some basic clinical characteristics (if available) would be welcome.
2. Ad Figure 2 May be it should be consider adding a scatter plot showing individual patients or HbA1c measurements. Or, for simplicity, mark how many patients (N, %) had their HbA1c adjusted by up to 1, 12, 23 and >3%. This will provide a good estimate as to the range of applicability of your equation.
Reviewer #3:
The authors tried to adjust HbA1c to remove influence of erythrocyte lifespan. I admit the need for the adjustment, however, the study seems to lack the confirmation of their method.
1. The authors did not confirm the usefulness of their aHbA1c. The best way may be to confirm future diabetes complications as they mentioned, but it takes many years. I recommend to compare aHbA1c and average glucose derived by CGM.
2. The method requires complicated calculation from CGM data. I am not sure if the method is better than the simple average glucose derived CGM. Maybe, the kinetic method does not require steady state.
3. The value of k_{gly} was not stabilized; from 4.04E6 to 9.95E6. k_{gly} is a constant of nonenzymic process. It was estimated to be 610E6, but the most recent one was 7.0E6 (Kameyama et al. 2021). The average value of 5.86E6 is smaller than the previously estimated value. I think that this instability is attributable to the nature of the calculation asking both k_{gly} and k_{age}.
4. The value of HbA1c should be converted to IFCC value.
"While the National Glycohemoglobin Standardization Program (NGSP) is used to express HbA1c in many clinical research and medical care settings, NGSP is measured by an old standardized method and at the time of conception, HPLC was not able to distinguish true HbA1c from other products. HPLC technology later advanced, however the derived HbA1c value is adjusted to NGSP in the interest of consistency. IFCC provides a strict definition of iA1c as hemoglobin with a glycated valine in the Nterminal βchain. Thus, iA1c value is preferred value for estimation of hemoglobin glycation." (Kameyama et al., 2021)
5. The authors chose random destruction model of erythrocytes, however "unlike some other species including mice, all normal human RBCs have about the same lifespan and thus exhibit nonrandom removal ( Franco, 2009 )." Kameyama et al., (2018) provided erythrocyte model based on Γdistribution by Shrestha et al., (2016). Program Modification from random destruction model to the uniform distribution of RBC ages model (Γmodel requires 2 parameters, so model that every RBC dies at the same age would be better to program) may be troublesome, but I think it is worth.
6. Equation 1 needs the derivation. i.e. d HbA1c/dt = 0; k_{age} HbA1c + k_{gly} AG(1HbA1c) = 0, k_{age}^{ref} HbA1c + k_{gly} AG(1HbA1c) = 0
Kameyama M, et al., Estimation of the hemoglobin glycation rate constant. Sci Rep. 2021 Jan 13;11(1):986. doi: 10.1038/s41598020800247.
Franco RS. The measurement and importance of red cell survival. Am J Hematol. 2009 Feb;84(2):10914. doi: 10.1002/ajh.21298.
Kameyama M, Takeuchi S, Ishii S. Steadystate relationship between average glucose, HbA1c and RBC lifespan. J Theor Biol. 2018 Jun 14;447:111117. doi: 10.1016/j.jtbi.2018.03.023.
Shrestha RP et al. Models for the red blood cell lifespan. J Pharmacokinet Pharmacodyn. 2016 Jun;43(3):25974. doi: 10.1007/s1092801694704.
I think that the merit of the author's method is to obtain the erythrocyte lifespan. It would be interesting to compare mean erythrocyte age by Kameyama's equation (M_{rbc} = HbA1c / ((1(2/3)HbA1c)k_{g} AG)) and k_{age}.
https://doi.org/10.7554/eLife.69456.sa1Author response
Essential revisions:
1) A more complete description of the derivation of the model – more detail is required as to how the computations were done.
As requested, we now provide further details on model derivation and validation. The additional details have been added to the main text and supplementary materials. More specifically, the following items have been added:
1. Derivation of the model and equation (1) (supplementary materials).
Please see under “Derivation of equation (1): kinetic model review”.
2. Kinetic parameter estimation (main text as below):
“Briefly, the model aligns laboratory HbA1c and the contemporaneous CGMderived estimate of HbA1c 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 HbA1c and CGMderived estimate are minimized. While 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 [9]. Detailed model description and derivation are provided in the supplementary materials.”
3. Using data from various cohorts, including different ages (paediatric, adult, old), populations (UK, DE, JP) and devices (Abbott, Medtronic), we further validate the model and compare with GMI (Table S1 added to supplementary material).
2) A comparison to other methods of assessing glycemic control (CGM, A1c). While assessment of how the authors' model predicts complications will not be required, a comparison (or at the very least, detailed discussion) of how it can compare to standard means of assessing glycemic control is necessary.
We have added to the Discussion and Supplementary material the differences, advantages and disadvantages of using different average glycemic measures for the management of individuals with diabetes with a summary table (Table S2).
Reviewer #1:
The strengths of this paper include that it builds on previous research and its sample size. However, the calculation for the individual RBC turnover rate, k age , is not included. The calculation for the adjusted HbA1c is too unwieldy for the clinician to use in practice where there is increased pressure to see many patients on a timely basis. If a "calculator" could be formulated allowing the clinician to plug in the relevant values and get the adjusted HbA1c, this could be widely used to improve patient care at the point of care which is the ultimate goal of this research.
We would like to thank the reviewer for this pragmatic suggestion. Our model provides a method to calculate RBC lifespan from glucose and HbA_{1c} data. The optimization algorithm requires powerful software, inclusion of large data sets and complex calculations to accurately derive aHbA_{1c}, hindering current use in routine clinical practice. However, it is envisaged that the software will be included in future CGM devices, which will be able to automatically calculate aHbA_{1c} once provided the necessary HbA_{1c} and CGM data.
To satisfy the reviewer, we do provide a simplified approach to calculate approximate aHbA_{1c} that can be provisionally used in clinical practice, provided there is access to high quality CGM data and two laboratory HbA_{1c} measurements. In following steps, the RBC turnover rate may be estimated from glucose and HbA_{1c} data in the supplementary materials, based on the previous publication [9].
1. For each data sections that contains a CGM trace and beginning and ending HbA_{1c} values, a series of daily average glucose are computed.
2. Feed the daily average glucose series to equation (s9) and perform a search for optimal parameter pair of k_{gly} and k_{age} that A1c_{Z} values best agree with lab values in all data sections available. Once k_{age} is available, equation (1) can be used to provide adjusted HbA_{1c}. The RBC lifespan can be estimated roughly from reticulocyte count as pointed out by the reviewer:
RBC lifespan (days) ≈ 100 ÷ [Reticulocytes (percent) ÷ RLS (days)]
The reticulocyte life span (RLS) is 1.0, 1.5, 2.0, or 2.5 days at hematocrits of 45, 35, 25, and 15 percent, respectively. It can also be estimated by other measurements such as erythrocyte creatine, RDW.
The author's claims of a proposed adjusted HbA1c which is more accurate in predicting adverse outcomes due to diabetes is supported by the data.
Thank you for the comment, in the manuscript we state that this model has the potential to provide a more accurate measure of future diabetes complications but future large scale longitudinal studies are required to assess the clinical role of adjusted HbA_{1c}.
There is a model to estimate RBC lifespan using reticulocyte count: Brodsky, R. A. Diagnosis of hemolytic anemia in the adult. In J. S. Timauer (Ed.) UpToDate, Retrieved February 17, 2020 from https://www.uptodate.com/contents/diagnosisofhemolyticanemiaintheadult?search=hemolytic%20anemia&source=search_result&selectedTitle=1~150&usage_type=default&display_rank=1
We would like to thank the reviewer for this helpful suggestion. We are aware of the method estimating RBC lifespan using reticulocyte count but it has a number of drawbacks making it difficult to implement. First, it is a crude calculation of RBC lifespan and therefore the data generated are unlikely to be sensitive to small physiological changes in this parameter, encountered between different individuals. Second, it relies on steady state, indicating the need to take average of several measurements, adding difficulties to data collection and interpretation. Third, it requires repeated reticulocyte data, which are not usually performed in routine clinical practice.
We would have liked to analyse the role of incorporating reticulocytes into the model but we do not have the necessary data to undertake the work. We are evaluating multiple ways of estimating RBC lifespan and glucose uptake rate (added reference [20] in discussion) and will certainly consider adding reticulocyte count as an additional measure to investigate whether this improves the accuracy of the model.
Reviewer #2:
Laboratory HbA1c values are routinely used to assess glycemic control, but differences in red blood cell lifespan can affect hemoglobin glycation and HbA1c values. The authors developed a formula for adjusted HbA1c to account for red blood cell lifespan, which would better represent hemoglobin glycation and thus could better estimate the risk of disease complications.
The authors based their formula for aHbA1c calculation on laboratory measurements of HbA1c and CGM data performed with FreeStyle Libre. When using CGM systems, we often see falsified results for the duration of hypoglycemia, especially at night, due to sensor compression. The authors did not address these technical problems that may affect the aHbA1c result.
The results should be sensor independent as evidenced by a published validation using Medtronic sensor data [17]. The calculation depends on series of daily average glucose between HbA_{1c} measurements. The nighttime low readings (due to compression or other artefacts) are usually short and should have a minimal effect on daily average glucose, particularly when large sets of data are collected.
In order to evaluate further, we divided CGM data into tertiles of hypoglycemic exposure (defined as glucose <54 mg/dl) during the period of 11PM – 6AM. The model validation was done by first calculating individual k_{gly} and k_{age} with the first data section and project HbA1c on the second heldout section. We validated the model by comparing the final lab HbA1c and CGMderived HbA1c. The mean ± SD of the absolute deviation in CGMderived HbA1c and lab HbA1c (NGSP %) in the lowest hypoglycemic tertile (01% or 04 mins/night) was 0.32±0.22, middle tertile (14% or 417 mins/night) was 0.32±0.20, and highest tertile (412% or 1750 mins/night) was 0.30±0.23, showing no difference (p>0.1). Therefore, we conclude that nocturnal hypoglycemic events, whether true or artificial due to sensor compression, do not affect the accuracy of the kinetic model calculation.
Using CGM we now have simple parameters to assess metabolic control of diabetes on the basis of CGM: TIR, GMI, CV. What I miss is a comparative analysis between these parameters and aHbA1c to convince readers that aHbA1c will be a better parameter for long term assessment for risk of complications.
Thank you for raising this point; aHbA_{1c} is an intracellular marker of glycation and thus likely more relevant to diabetes complications that TIR or GMI, which are simply based on plasma glucose levels. We elaborated further in the discussion to clarify this point:
“As a 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”
and also added Table S2 comparing aHbA_{1c} with other average glycemic measures (please see above).
The authors achieved their goal, and the results support their conclusions.
The use of aHbA1c in daily practice can be difficult because usually the clinician wants a ready result, but for research purposes, especially in patients with shorter red blood cell lifespans, it could be useful.
We would like to thank the reviewer for these positive comments.
It will be interesting to see if its usefulness in estimating the risk of complications will be greater than TIR or GMI with CV.
In theory, aHbA_{1c} should predict complication risk better than HbA_{1c}, or other glycemic markers, by better reflecting intracellular glucose exposure in organs prone to diabetes complications. However, we fully agree with the reviewer that longitudinal studies are required to assess the potential superiority of aHbA_{1c} over other glycaemic markers and this will be part of our longterm strategy.
Some comments on the methods and results:
Methods:
1. The study is based on CGM performed with FreeStyle Libre. From experience, we know that patients often have false hypoglycemia at night due to compression of the sensor. Has this been taken into account in the analysis?
Please see our response above.
2. Currently we use TIR and GMI to assess metabolic control in CGM users. Since aHbA1c, a new parameter will require additional calculations from me as a clinician, does it have advantages over these parameters in assessing the risk of chronic complications. It may be worth doing additional analysis comparing aHbA1c with these parameters.
aHbA_{1c} should reflect intracellular glucose exposure in organs prone to diabetes complications and our data suggests it would be superior to HbA_{1c}, which assesses RBC intracellular glucose exposure but fails to take into account potential artefacts generated by altered RBC lifespan. Also, aHbA_{1c} is potentially a better marker of future complication risk than average plasma extracellular glucose estimations such as TIR and GMI, which fail to take into account intracellular glucose exposure. However, largescale longitudinal will be required to prove that aHbA_{1c} is a superior marker of diabetes complications and this is our longterm aim. We expanded the discussion to cover the above points and also added a Table addressing differences between aHbA_{1c} and GMI in relation to HbA_{1c} (please see response to comments above).
3. As this is proof of concept, the details of creating the equation should be described, probably in some supplement. In addition, the idea behind the mathematical formula might help explain the equation to the readers. Secondly, the equation presented here is not clear in terms of units, and additionally operates slightly differently than the one in executed in provided excel file. The units for HbA1c here must be better emphasized. For example, if we assume HbA1c 9%, HbA1c in the numerator is treated as is (9%, % as a unit is preserved), but HbA1cs in the denominator have their units dropped (changed from 9% to 0.09). In parallel, the formula in excel does the same but multiplies the nominator by 100 (9% > 900 %) and leaves HbA1cs in the denominator as is (and 1 becomes 100%). This creates some confusion and should be better explained, or an example calculation could be shown.
We have added further clarifications as requested by the reviewer:
“HbA_{1c} and aHbA_{1c} are in NGSP unit and decimal values should be used. For example, 8% HbA1c should be applied as 0.08. Equation 1 for IFCC unit is available in the supplementary materials.”
Results:
1. I think, that any characteristics of this group in needed. They come from alreadyreported cohorts but this is only a subgroup, so some basic clinical characteristics (if available) would be welcome.
Basic characteristics of the groups have been added as requested in Table 1.
2. Ad Figure 2 May be it should be consider adding a scatter plot showing individual patients or HbA1c measurements. Or, for simplicity, mark how many patients (N, %) had their HbA1c adjusted by up to 1, 12, 23 and >3%. This will provide a good estimate as to the range of applicability of your equation.
This has been done as requested:
“The number (percentage) of individuals having HbA1c adjustments < 1% (<11mmol/mol), 12% (1122 mmol/mol), 23% (2233 mmol/mol) and >3% (>33 mmol/mol) were 90 (68%), 21 (16%), 12 (9%), and 8 (6%), respectively.”
Reviewer #3:
The authors tried to adjust HbA1c to remove influence of erythrocyte lifespan. I admit the need for the adjustment, however, the study seems to lack the confirmation of their method.
1. The authors did not confirm the usefulness of their aHbA1c. The best way may be to confirm future diabetes complications as they mentioned, but it takes many years. I recommend to compare aHbA1c and average glucose derived by CGM.
Based on the Brownlee’s work [reference 5], it is the high intracellular glucose exposure that is the main cause of tissue damage and diabetes complications. However, average glucose levels do not necessarily reflect intracellular glucose exposure. Therefore, adjusted HbA_{1c}, which reflects intracellular glycemia, is difficult to compare with average glucose (extracellular) and HbA_{1c} (affected by RBC lifespan). We added this to the discussion and also added Table S2 to summarise strengths and drawbacks of different average glycaemic measures.
2. The method requires complicated calculation from CGM data. I am not sure if the method is better than the simple average glucose derived CGM. Maybe, the kinetic method does not require steady state.
The kinetic parameter determination (for k_{gly} and k_{age}) does not require a steady state. Please refer to the first answer in reviewer #1 for more details on determining kinetic parameters. The kinetic model relies on data from CGMderived glucose levels and laboratory HbA_{1c}. We demonstrated superior accuracy of the kinetic model compared with the average glucose derived HbA1c (GMI) in the supplementary material (Table S1). The parameter k_{age} (or RBC lifespan) need to be determined before adjusted HbA_{1c} can be calculated. Again, adjusted HbA_{1c} is an intracellular marker, while average glucose is not. This would be particularly relevant in individuals with apparent high laboratory HbA_{1c} and repeated hypoglycaemia or in those with low HbA_{1c} but high average glucose.
3. The value of k_{gly} was not stabilized; from 4.04E6 to 9.95E6. k_{gly} is a constant of nonenzymic process. It was estimated to be 610E6, but the most recent one was 7.0E6 (Kameyama et al., 2021). The average value of 5.86E6 is smaller than the previously estimated value. I think that this instability is attributable to the nature of the calculation asking both k_{gly} and k_{age}.
Although hemoglobin glycation is a nonenzymatic reaction with constant rate parameters, the reaction is limited by intracellular glucose levels rather than plasma glucose. According to Khera [7], RBC glucose uptake rate or intra/extracellular glucose concentration ratio varies person to person. For this reason, k_{gly}, the overall glycation rate constant, should be an individual kinetic parameter, which explains various k_{gly} values reported in the literature. We highlight this in supplementary materials, summarizing our first publication of the model.
4. The value of HbA1c should be converted to IFCC value.
"While the National Glycohemoglobin Standardization Program (NGSP) is used to express HbA1c in many clinical research and medical care settings, NGSP is measured by an old standardized method and at the time of conception, HPLC was not able to distinguish true HbA1c from other products. HPLC technology later advanced, however the derived HbA1c value is adjusted to NGSP in the interest of consistency. IFCC provides a strict definition of iA1c as hemoglobin with a glycated valine in the Nterminal βchain. Thus, iA1c value is preferred value for estimation of hemoglobin glycation." (Kameyama et al., 2021)
Thank you for raising this topic. We added equation (1) under NGSP unit system in the supplementary materials.
5. The authors chose random destruction model of erythrocytes, however "unlike some other species including mice, all normal human RBCs have about the same lifespan and thus exhibit nonrandom removal ( Franco, 2009 )." Kameyama et al., (2018) provided erythrocyte model based on Γdistribution by Shrestha et al., (2016). Program Modification from random destruction model to the uniform distribution of RBC ages model (Γmodel requires 2 parameters, so model that every RBC dies at the same age would be better to program) may be troublesome, but I think it is worth.
Thank you for the helpful comment and for bringing new references to our attention.
The derivation starts with uniform age distribution or fixedlife model for RBC lifespan as suggested. We added the details to the supplementary materials. The additional complexity brought by glucose uptake following GLUT1 MichaelisMenten kinetics and the approximations used has led to the steadystate equation (1). These approximations enable a robust application to realworld, nonsteady state conditions. We have shown this reflects real world data well, given the accuracy of our validation studies [references 9, 17, 18]. We demonstrate below steadystate solution from a strict uniform age distribution, further confirming robustness of the model.
The steadystate equation (1) under the uniform age distribution is:
The circulating RBCs are produced within the last L days, where L is the expected lifespan. No RBC was lost until age>L. For a small fraction of RBC of age=t, where t<L:
${\text{hBg}}_{t}=\text{}{k}_{g}\ast GI\ast C\ast \text{}\frac{\text{dt}}{L}\ast t,$where C is total hemoglobin (C = Hb + HbG)
Therefore, the total glycated hemoglobin is:
$HbG=\text{}{\int}_{O}^{L}{k}_{g}\ast GI\ast \text{}\frac{C}{L}\ast t\ast dt=\text{}\frac{1}{2}{k}_{g}\ast L\ast GI\ast C=\text{}\frac{{k}_{g}}{{2\ast K}_{\text{age}}}\ast GI\ast C$Where,$k}_{\text{age}}=\text{}\frac{1}{L$
Since $H\text{bA}1c=\text{}\frac{\text{HbG}}{C}$, steady state$HbA1c:\text{}\text{EA}=\frac{{k}_{g}}{{2\ast K}_{\text{age}}}\ast GI$
Equation (1) is about finding HbA1c under a reference k_{age} with the same intracellular glucose level. Therefore, the HbA1c with equivalent intracellular glucose under a reference ${K}_{\text{age}}\text{}\left({\text{GI}}_{{k}_{\text{age}}}=\text{}{\text{GI}}_{{K}_{\text{age}}^{\text{ref}}}\right)$ is:$\text{EA}}_{{K}_{\text{age}}^{\text{ref}}}=\text{}\frac{{k}_{\text{age}}}{{k}_{\text{age}}^{\text{ref}}}\ast \text{}{\text{EA}}_{{k}_{\text{age}}$ equation (1) becomes:
This function is very close to equation (1) numerically. Note that equation (1f) is an approximation form of equation (1). In general, the differences between equation (1) and (1f) are less than 0.25% (NGSP) within +/ 20% change of RBC lifespan and HbA1c range of 510% (NGSP).
6. Equation 1 needs the derivation. i.e. d HbA1c/dt = 0; k_{age} HbA1c + k_{gly} AG(1HbA1c) = 0, k_{age}^{ref} HbA1c + k_{gly} AG(1HbA1c) = 0
Kameyama M, et al. Estimation of the hemoglobin glycation rate constant. Sci Rep. 2021 Jan 13;11(1):986. doi: 10.1038/s41598020800247.
Franco RS. The measurement and importance of red cell survival. Am J Hematol. 2009 Feb;84(2):10914. doi: 10.1002/ajh.21298.
Kameyama M, Takeuchi S, Ishii S. Steadystate relationship between average glucose, HbA1c and RBC lifespan. J Theor Biol. 2018 Jun 14;447:111117. doi: 10.1016/j.jtbi.2018.03.023.
Shrestha RP et al. Models for the red blood cell lifespan. J Pharmacokinet Pharmacodyn. 2016 Jun;43(3):25974. doi: 10.1007/s1092801694704.
Thank you for the new references, the majority of which have been incorporated into the current version of the manuscript. Please refer to our reply to essential revision (1) and additional supplementary materials for the derivation of equation 1.
I think that the merit of the author's method is to obtain the erythrocyte lifespan. It would be interesting to compare mean erythrocyte age by Kameyama's equation (M_{rbc} = HbA1c / ((1(2/3)HbA1c)k_{g} AG)) and k_{age}.
Future work is required for developing practical and robust methods that accurately measure RBC lifespan. Comparing to Kameyama's equation which has a universal glucose uptake (k_{gly}), our model evaluates k_{gly} as individualspecific variable. Therefore, it is problematic to compare the two methods directly by k_{age} and M_{RBC}. However, the ratio k_{gly}/k_{age} may be comparable with M_{RBC} as per Kameyama’s work. While taking this caveat into account, we investigated the relationship between M_{RBC} and K and found a positive correlation (R=0.62, p<0.0001), providing additional evidence to support of our model.
https://doi.org/10.7554/eLife.69456.sa2Article and author information
Author details
Funding
Abbott Diabetes Care
 Yongjin Xu
 Timothy C Dunn
The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.
Acknowledgements
This work was funded by Abbott Diabetes Care.
Ethics
Data were used from two previously published clinical studies in Europe (reference 10 and 11). Both studies were conducted after appropriate ethical approval and participants gave written informed consent.
Senior Editor
 Nancy Carrasco, Vanderbilt University School of Medicine, United States
Reviewing Editor
 Rachel Perry, Yale, United States
Reviewers
 Agnieszka Szadkowska
 Masashi Kameyama
Version history
 Received: April 15, 2021
 Accepted: August 24, 2021
 Version of Record published: September 13, 2021 (version 1)
 Version of Record updated: October 5, 2021 (version 2)
Copyright
© 2021, Xu et al.
This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.
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