Mechanistic modeling of hemoglobin glycation and red blood cell kinetics enables personalized diabetes monitoring

Abstract

The amount of glycated hemoglobin (HbA1c) in diabetic patients' blood provides the best estimate of the average blood glucose concentration over the preceding 2 to 3 months. It is therefore essential for disease management and is the best predictor of disease complications. Nevertheless, substantial unexplained glucose-independent variation in HbA1c makes its reflection of average glucose inaccurate and limits the precision of medical care for diabetics. The true average glucose concentration of a nondiabetic and a poorly controlled diabetic may differ by less than 15 mg/dl, but patients with identical HbA1c values may have true average glucose concentrations that differ by more than 60 mg/dl. We combined a mechanistic mathematical model of hemoglobin glycation and red blood cell kinetics with large sets of within-patient glucose measurements to derive patient-specific estimates of nonglycemic determinants of HbA1c, including mean red blood cell age. We found that between-patient variation in derived mean red blood cell age explains all glucose-independent variation in HbA1c. We then used our model to personalize prospective estimates of average glucose and reduced errors by more than 50% in four independent groups of greater than 200 patients. The current standard of care provided average glucose estimates with errors >15 mg/dl for one in three patients. Our patient-specific method reduced this error rate to 1 in 10. Our personalized approach should improve medical care for diabetes using existing clinical measurements.

Figure 1. Linear relationship between AG and HbA1c in diabetic and non-diabetic subjects

Data from the ADAG study (1): 507 subjects with type 1 (blue dots, n=268) and type 2 (green dots, n=159) diabetes, as well as non-diabetic subjects (red dots, n=80). The lower dashed line is the 6.5% threshold for initial diagnosis of diabetes, and the upper dashed line is the 7% treatment target.

Figure 2. The variance of HbA1c increases with AG and suggests that inter-patient differences in slope are more important than differences in intercept for determining non-glycemic variation in HbA1c

A deviation from the regression line in Figure 1 can be explained by a patient-specific line that has a different intercept, or a different slope, or both. Panel A shows that variation in the intercept (reticulocyte glycation fraction) alone will lead to fixed deviations from the regression line that are independent of the AG. Panel B shows in contrast that variation in the slope will lead to increased variance as AG increases. We can use the model to simulate the effect of each type of inter-patient difference and compare the simulation results with actual data. Panel C shows the effect of simulated inter-patient differences in the intercept (i.e, the reticulocyte glycation fraction). r_d² is the rank correlation coefficient for the raw ADAG data (hence the “d” in r_d²) shown as red dots in both (C) and (D) and its correlation is the same in each panel because it is independent of a model of the source of variation. r_s² (“s” for simulation) in panel (C) is the correlation for the blue dots in (C) which show the simulated effect of inter-patient differences in intercept on variance in AG. Their correlation (0.13) is quite different from r_d² (0.8). The simulations show that inter-patient differences in intercept would generate data (blue dots) whose trend (black line) is quite different from that actually seen in the real data (red dots). Panel D shows the effect of inter-patient differences in slope on AG variance. The raw data (red dots) is repeated from Panel C for comparison and has the same correlation coefficient (r_d²). r_s² (“s” for simulation) in panel (D) is the correlation for the blue dots in (D) which show the simulated effect of inter-patient differences in slope on variance in AG. This simulation shows that inter-patient differences in slope would generate data (blue dots) whose trend (black line) is consistent with that actually seen in the real data (red dots), and r_s² is similar to r_d².

Figure 3. Inter-patient variation in M_RBC is sufficient to explain all glucose-independent variation in HbA1c

We used a simulation to test the hypothesis that measured variation in M_RBC can generate all observed glucose-independent variation in HbA1c as a function of AG. The AG values from the ADAG(1) study were used as input to Equation (4) along with constant k_g, constant HbA1c(0), and an M_RBC randomly-sampled from a normal distribution with mean and standard deviation as measured in reference #(4). The medians are indistinguishable (p is the significance of a Kruskal-Wallis test of equal medians). (See “Model simulation” in Methods for more detail.)

Figure 4. Modeling M_RBC reduces errors in estimated AG

(Top panel) One patient’s modeled M_RBC was 45 days in the fall of 2014. The blue line (#1) shows the M_RBC-adjusted AG-HbA1c relationship personalized for this patient, in contrast to the red line showing the current standard AG-HbA1c formula. One year after the M_RBC estimation, the patient visited the clinic and had an HbA1c of 8.1% (gray horizontal line, #2). The current standard method predicted an AG of 186 mg/dL (red “X”). The model predicted 209 mg/dL (blue “X”). This patient had CGM data available providing a direct and independent measurement of AG equal to 210 mg/dL (green checkmark). This patient’s personalized AG-HbA1c model reduced the error in AG estimation from 24 mg/dL to 1 mg/dL. (Bottom panel) A second patient had a model-estimated M_RBC of 60 days in the spring of 2015, yielding a personalized AG-HbA1c relationship corresponding to the blue line (#1, bottom panel) in contrast to the red line showing the current standard formula. About 6 months later in the fall of 2015, the patient returned to the clinic and had an HbA1c of 10.5% (gray horizontal line, #2). The current standard method predicted an AG of 255 mg/dL (red “X”). The model predicted 205 mg/dL (blue “X”). This patient had CGM data available providing a direct and independent measurement of AG equal to 207 mg/dL (green checkmark). This patient’s personalized AG-HbA1c model reduced the error in AG estimation from 48 mg/dL to 2 mg/dL. These two examples highlight the fact that with current methods, a patient with lower AG (bottom) may actually have a significantly higher HbA1c than a patient with a higher AG (top), potentially compromising disease diagnosis and management.

Figure 5. Model-based inference of AG from HbA1c reduces estimation errors by about 50%

Top row shows histograms of errors in AG estimation for 4 different sets of patients using the current standard regression-based formula. Second row shows histograms of errors using model-based estimation of AG. Histograms include predictions where estimation methods differ by at least 10 mg/dL. Errors for model-based predictions are significantly more tightly clustered around zero. The bottom panel compares boxplots of median absolute error and shows that the model reduces error by at least 50% in each of the 4 independent sets of patients. The model-based estimates are superior to the standard method in all four cases with p < 0.001. (See “Patient sets” in Methods and Supplementary Results for more detail.)