Are Risk Indices Derived From CGM Interchangeable With SMBG-Based Indices?

Abstract

Background:

The risk of hypo- and hyperglycemia has been assessed for years by computing the well-known low blood glucose index (LBGI) and high blood glucose index (HBGI) on sparse self-monitoring blood glucose (SMBG) readings. These metrics have been shown to be predictive of future glycemic events and clinically relevant cutoff values to classify the state of a patient have been defined, but their application to continuous glucose monitoring (CGM) profiles has not been validated yet. The aim of this article is to explore the relationship between CGM-based and SMBG-based LBGI/HBGI, and provide a guideline to follow when these indices are computed on CGM time series.

Methods:

Twenty-eight subjects with type 1 diabetes mellitus (T1DM) were monitored in daily-life conditions for up to 4 weeks with both SMBG and CGM systems. Linear and nonlinear models were considered to describe the relationship between risk indices evaluated on SMBG and CGM data.

Results:

LBGI values obtained from CGM did not match closely SMBG-based values, with clear underestimation especially in the low risk range, and a linear transformation performed best to match CGM-based LBGI to SMBG-based LBGI. For HBGI, a linear model with unitary slope and no intercept was reliable, suggesting that no correction is needed to compute this index from CGM time series.

Conclusions:

Alternate versions of LBGI and HBGI adapted to the characteristics of CGM signals have been proposed that enable extending results obtained for SMBG data and using clinically relevant cutoff values previously defined to promptly classify the glycemic condition of a patient.

Low blood glucose index (LBGI) and high blood glucose index (HBGI) are popular metrics used to quantify the risk of hypo- and hyperglycemia from sparse self-monitoring blood glucose (SMBG) samples.^1,2 They were designed based on a symmetrization of the blood glucose (BG) range¹ to summarize the number and extent of extreme BG fluctuations into single numbers, with LBGI accounting for hypoglycemic episodes and HBGI for hyperglycemic ones. Therefore, a higher LBGI may indicate a large number of mild hypoglycemic events, a small number of severe hypoglycemic events, or a combination of both, and the same can be said for HBGI with regard to hyperglycemia.

LBGI and HBGI have long been shown to be predictive of meaningful glycemic events and related to significant glycemic markers.^1-3 Moreover, the use of these indicators can be exploited in practice to promptly classify the overall glycemic control of a patient, given the existence of risk zones for hypo- and hyperglycemia defined based on LBGI and HBGI values.^2,3

Specifically, for LBGI, a strong relationship with the occurrence of severe hypoglycemia (SH) was proven.^1,2 LBGI was shown to be significantly higher for subjects with a history of SH, and, together with the occurrence of SH in the past year, resulted to be a significant predictor of the frequency of SH episodes in the subsequent 6 months, accounting for 40% of its variance.² Using the dependence between LBGI and the odds ratio for a subsequent SH episode, 2 cutoff values were identified for LBGI, and 3 risk zones given by LBGI < 2.5, LBGI between 2.5 and 5, and LBGI > 5, were defined to classify the risk of SH in subjects monitored through SMBG devices.²

For HBGI, a positive correlation was found with glycosylated hemoglobin (HbA1c),¹ the most commonly exploited marker of glycemic control related to the average BG in the 5 weeks preceding the examination. A regression model using HBGI, age, duration of diabetes, and patients’ daily insulin dose accounted for 57% of the variance of HbA1c, with HBGI being the most significant predictor.³ The relationship between HBGI and HbA1c in this regression was approximately linear and well described by a piecewise line with 2 cut points at HBGI = 4.5 and HBGI = 9, that marked changes in the slope of the relationship. Based on these cutoff values, 3 risk zones, that is, HBGI < 4.5, HBGI between 4.5 and 9, and HBGI > 9, were identified to classify the subjects’ risk of hyperglycemia from SMBG data points.³

Given the capability of LBGI and HBGI of assessing the glycemic condition of a patient, their evaluation in the quantification of glucose variability (GV) was largely exploited in the literature,^4-16 replacing less sensitive markers such as mean and standard deviation (SD).^4,5 LBGI and HBGI were used to characterize the different GV of subjects with type 1 diabetes mellitus (T1DM) as compared to type 2 diabetes patients6, within the artificial pancreas to assess the performance of the control algorithm in terms of GV-related risk⁷, and, as computed on 1-hour segments of continuous glucose monitoring (CGM) profiles, to provide graphic representations of the evolution of the risk of hypo- and hyperglycemia as a function of the time of the day⁸. Based on a structured theory of risk analysis of BG data presented in Kovatchev et al.³, performance of glycemic control was widely assessed using LBGI/HBGI^9,10, and 2 diabetes-specific computational algorithms were designed to predict probability of future hypoglycemic events and HbA1c levels^11-14, which established LBGI and HBGI as necessary mediators in the algorithmic evaluation of risk of SH and metabolic control. If combined within the average daily risk range (ADRR) metric,¹⁵ LBGI and HBGI were also shown to relate to insulin sensitivity and epinephrine counterregulation after hypoglycemia,¹⁶ with an increased GV as quantified by ADRR occurring with higher insulin sensitivity and lower epinephrine response.

The relevance of LBGI an HBGI as metrics related to significant glycemic events and indicators, however, was documented in the literature only when these metrics are computed from SMBG profiles, and the same can be said for the exploitation of risk zones for the immediate classification of patient’s risk of hypo- and hyperglycemia. If derived from CGM time series, LBGI and HBGI, and their use for the assessment of the goodness of glycemic control have not been validated yet. Given that and the growing use of CGM systems in the clinical practice, this manuscript aims to describe the relationship between CGM-based and SMBG-based LBGI/HBGI and provide guidelines to apply when the indices are computed from CGM time series. Here, we propose a simple adaptation of LBGI and HBGI to allow references to previously defined clinical thresholds.

Methods

Subjects

Data used in this work were collected at the University of Virginia (Charlottesville, VA, USA) and are baseline data from a study aimed at investigating how GV is affected by factors such as preceding hypoglycemia, insulin treatment inadequacy, and metabolic markers such as insulin sensitivity. Thirty T1DM subjects were recruited. All subjects were using insulin pumps, and monitored for up to 4 weeks with both SMBG and CGM systems. After 2 weeks, they received a liquid mixed-meal in an inpatient setting, and had their BG monitored to study insulin sensitivity; then, they received addition insulin injections to cause a condition of low BG, to understand how the body responds to hypoglycemia. All subjects were closely monitored during the time insulin was given by frequent checks of BG and constant medical and nursing supervision. Beyond the inpatient day, subjects were in daily-life conditions. During the study, participants were asked to use their own insulin pump and glucose meter, and the same glucose meter had to be used for the entire study. CGM profiles were collected using the Dexcom G4 CGM system. The study was approved by the local ethical committee and registered at ClinicalTrials.Gov with the identifier number NCT01835964.

Twenty-eight subjects were selected for the analysis presented in this article; 2 subjects were dropped because of issues occurred with either the CGM sensor or the insulin pump. Demographic characteristics of the subjects are presented in Table 1 as mean ± SD values.

Table 1.

Demographic Characteristics of the Subjects.

	Mean ± SD
Number	28
Gender (male/female)	15/13
Age (years)	43 ± 11
Baseline HbA1c (%)	8 ± 1
Duration of diabetes (years)	23 ± 11
Duration of pump therapy (years)	11 ± 7

LBGI and HBGI

The definition of LBGI and HBGI derives from a logarithmic transformation of the BG scale that balances the amplitude of hypo- and hyperglycemic ranges (enlarging the former and shrinking the latter), and makes the transformed data symmetric around zero and fitting a normal distribution.¹ If BG measurements are expressed in mg/dl, the transformed data (BG^new) are given by

$${\mathrm{BG}}^{\mathrm{new}}=1.509\cdot ({[\log (\mathrm{BG})]}^{1.084}-5.381)$$ (1)

and are used to define a BG risk function¹

$$r(\mathrm{BG})=10\cdot {\mathrm{BG}}^{\mathrm{new}2}$$ (2)

that associates to each BG reading a measure of its risk, as expressed with a number in the 0 to 100 range. The risk function assigns maximum risk to BG levels of 20 and 600 mg/dl, and zero risk to a normoglycemic BG of 112.5 mg/dl. Defining the risk of hypo- (rl(BG)) and hyperglycemia (rh(BG)) as r(BG) for BG lower and greater than 112.5 mg/dl, respectively, and zero otherwise, if the SMBG profile is made up of N readings, LBGI² and HBGI³ are designed as

$$\mathrm{LBGI}=\frac{1}{\mathrm{N}}{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{N}}{\mathrm{rl}(\mathrm{BG}}_{\mathrm{i}})}\mathrm{HBGI}=\frac{1}{\mathrm{N}}{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{N}}{\mathrm{rh}(\mathrm{BG}}_{\mathrm{i}}\mathrm{)}}$$ (3)

and provide a rapid way to classify the overall glycemic condition of a diabetic subject.

Correction of CGM-Based Indices

The relationship between CGM-based and SMBG-based LBGI/HBGI was described using linear and nonlinear models. The acceptance/rejection of a model was made through the assessment of the obtained fit, statistical significance of parameter estimates, residuals, and QQ-plot of residuals. Performance in terms of classification of the subjects’ risk of hypo/hyperglycemia as compared to the SMBG-based one was also evaluated to prove the need of a correction or to discriminate between different models.

Defining the index computed from CGM as the independent variable or predictor (x) and that computed from SMBG as the dependent one (y), the linear model was the canonical straight line described as

$$y=mx+q.$$ (4)

When a liner description was not satisfactory to match CGM-based and SMBG-based LBGI/HBGI, the following 3-parameter nonlinear model was considered

$$y=ax+b-\frac{1}{c+x}.$$ (5a)

The number of model parameters was also reduced by imposing the reasonable constraint of having a curve meeting the origin of the Cartesian coordinate system. This led to the following 2-parameter formulation

$$y=ax+\frac{1}{b}-\frac{1}{b+x}.$$ (5b)

Models were identified on the available data using the least squares estimator.

Results

Data Characterization

To avoid any influence of the clinical protocol on the results, the inpatient day was removed from SMBG and CGM profiles. Days where sensor issues occurred and no CGM points were stored were removed also from the SMBG time series. Beyond this, all data points collected were kept in the study. The subject with the fewest data had an SMBG profile made up of 2.57 samples/day on average with 72 measurements acquired over the entire 4 weeks. The highest frequency tester was made up of 315 data points, with 11.25 samples/day on average. Mean value over the whole population of the average length per day was 5.28 samples and of the entire length was 147.96. CGM data were collected with a sampling time of 5 minutes. An example of data collected from a representative subject is shown in Figure 1. Figure 2 shows histograms of the distribution of SMBG and CGM data points across the time of the day, where it can be seen that CGM data are acquired almost constantly throughout the day, while SMBGs are mostly acquired around meal times. As shown in Figure 3, the distribution of SMBG readings across the BG range is comparable to the distribution observed in the general T1DM population (see Kovatchev et al¹), and we therefore assume that previously observed association of LBGI, HBGI to clinical outcomes can be extended to this population.

Figure 1.

Example of data used in the study. SMBG and CGM data are shown as red triangles and blue profile, respectively. Pink lines from left to right represent beginning of the first week; end of the first week/beginning of the second week; end of the second week; beginning of the third week; end of the third week/beginning of the fourth week; end of the fourth week. Black line is at noon of the inpatient day.

Figure 2.

Distribution of SMBG (top panel) and CGM (bottom panel) samples across the day (average values over all days and subjects).

Figure 3.

Distribution of SMBG value across the BG range (average over all subjects).

Correction of HBGI

The linear model detailed by Equation 4 was used to describe the relationship between SMBG-based and CGM-based HBGI. Fit, residuals, and QQ-plot of residuals are shown in Figure 4, upper, lower-left, and lower-right panels, respectively; results from identification are summarized in the upper rows of Table 2. The table shows the estimates of parameters, their precision expressed as standard errors (SE), t statistics for testing the null hypothesis that parameters are zero, and P values associated with t statistics. A P value lower than .05 is considered to be statistically significant and allows the rejection of the null hypothesis. As apparent from the top panel of Figure 4, fit is extremely satisfactory; the mean squared error (MSE) for this model is equal to 6.2 and a value of 75% was obtained for the coefficient of determination (R²), revealing that the model can account for 75% of the variance of the original SMBG-based HBGI values. Looking at residuals, they appear sufficiently uncorrelated and, except from some outliers probably related to biasing SMBG sampling designs, QQ-plot suggests to consider them as drawn from a normal distribution. The last column of Table 2, however, shows that the P value associated with q is much greater than .05, indicating that the parameter is not statistically significant within the model. Because of this finding, a linear model with slope and intercept forced to zero was then identified on experimental data. Fit, residuals, and QQ-plot of residuals are shown in Figure 5, upper, lower-left, and lower-right panels, respectively, and results are summarized in the lower rows of Table 2. Fit and residuals are as satisfactory as for the previous model, with MSE equal to 6, and the obtained estimate for m is extremely close to one, suggesting the possibility of using no transformation to compute HBGI from CGM time series.

Figure 4.

Model prediction (red line) and experimental data points (blue circles) for HBGI correction as described with a full linear model (upper panel), together with residuals (lower-left panel) and their QQ-plot (lower-right panel).

Table 2.

Results From the Identification of a Linear Model With and Without Intercept for HBGI.

HBGI
	Estimate	SE	t	P value
Linear model with slope and intercept
m	1.0436	0.1182	8.8319	2.6354∙10-9
q	−0.0619	1.0451	−0.0593	0.9532
Linear model with slope (intercept forced to zero)
m	1.0374	0.0523	19.8356	3.2566∙10-17
q	0	—	—	—

Figure 5.

Model prediction (red line) and experimental data points (blue circles) for HBGI correction as described with a linear model with slope and intercept forced to zero (upper panel), together with residuals (lower-left panel) and their QQ-plot (lower-right panel).

To assess the reliability of this result, the CGM-based classification of the patients’ risk of hyperglycemia was compared with the traditional SMBG-based one. Table 3 shows how subjects were assigned to the different classes of risk in the 2 cases (left columns), and what kind of errors were computed in the CGM-based classification (right columns). These results are satisfactory not only because 82% of patients were classified correctly, but also observing that misclassification was of only 1 class (no subject at low risk was classified at high risk, and vice versa) and extremely balanced in over- and underestimation. This suggests that there is no systematic error that needs to be corrected, and classification errors are random and clearly linked to the potentially biasing design used to collect SMBG readings and/or to possible miscalibration of the sensors.

Table 3.

Classification of the Risk of Hyperglycemia as Assessed by HBGI Computed on SMBG and CGM.

HBGI
Low risk	Medium risk	High risk	Underest errors	UNDEREST errors	Overest errors	OVEREST errors
SMBG-based classification
8	9	11	—	—	—	—
CGM-based classification
7	11	10	3	0	2	0

Left side of the table: subjects assigned to each risk group; right side of the table: under- and overestimation errors due to the assessment of HBGI on CGM (underest/overest errors stand for misclassification of 1 class; UNDEREST/OVEREST errors stand for misclassification of 2 classes).

To conclude, the one-parameter linear model is considered reliable to describe the relationship between SMBG-based and CGM-based HBGI, and HBGI as derived from CGM time series is interchangeable with SMBG-based HBGI.

Correction of LBGI

The first model identified on SMBG-based LBGI values was the linear one of Equation 4, with parameter estimates summarized in the upper rows of Table 4. Along with parameter values, as for HBGI, Table 4 shows their precision expressed in terms of SE, t statistics to test the null hypothesis that parameters are equal to zero, and P values to be considered in accepting or rejecting that hypothesis. For the linear model, both parameters were statistically significant, MSE of 0.68 was obtained, and R² resulted equal to 76%. However, despite acceptable residuals (lower-left and lower-right panel of Figure 6), it appears clear that a straight line cannot provide a reliable description of the relationship between SMBG-based and CGM-based LBGI at the lowest LBGI values (upper panel of Figure 6). The nonlinear model described by Equation 5b was thus identified; results from the identification are reported in the lower rows of Table 4, model prediction is plotted against experimental data in the upper panel of Figure 7, and residuals and QQ-plot are shown in the lower-left and lower-right panel of Figure 7, respectively. Again both parameters were statistically significant and estimated with good precision. The MSE obtained for this model was equal to 0.62, and residuals are satisfactory. Nonetheless, in choosing the best model to be used to transform CGM-based LBGI, it is worth observing that the nonlinear model shows better performance than the linear one only at very low LBGI values, where there is no significant glycemic risk and a lower degree of precision in describing the data could be still adequate.

Table 4.

Results From the Identification of a Linear and Nonlinear Model for LBGI.

LBGI
	Estimate	SE	t	P value
Linear model with slope and intercept
m	1.0199	0.1125	9.0661	1.5674∙10-9
q	0.6521	0.2519	2.5893	0.0156
Nonlinear model without saturation
a	0.8346	0.1284	6.5026	6.8204∙10-7
b	0.6476	0.1412	4.5876	1.1107∙10-5

Figure 6.

Model prediction (red line) and experimental data points (blue circles) for LBGI correction as described with a full linear model (upper panel), together with residuals (lower-left panel) and their QQ-plot (lower-right panel).

Figure 7.

Model prediction (red line) and experimental data points (blue circles) for LBGI correction as described with a nonlinear model (upper panel), together with residuals (lower-left panel) and their QQ-plot (lower-right panel).

To assess the actual need for a correction and to investigate if the nonlinear model could make any significant difference, the comparison of the classification of subjects’ risk of hypoglycemia was performed as done for HBGI. Table 5 shows the assignment of subjects to the corresponding risk group based on LBGI computed from SMBG, CGM, linearly corrected CGM, and nonlinearly corrected CGM. We can observe from the table that applying the linear transformation to correct the CGM-based LBGI dramatically changed the assessment of the risk of hypoglycemia, with classification performances largely improved after the correction. Errors in identifying the risk zone decreased from 7 to 5 (with 82% of subjects correctly classified), became random and balanced in over- and underestimation, and the 2-class error performed without correcting LBGI was avoided. The same results were obtained applying the nonlinear transformation to CGM-based LBGI values.

Table 5.

Classification of the Risk of Hypoglycemia as Assessed by LBGI Computed on SMBG and CGM.

LBGI
Low risk	Medium risk	High risk	Underest errors	UNDEREST errors	Overest errors	OVEREST errors
SMBG-based classification
18	6	4	—	—	—	—
CGM-based classification
23	4	1	6	1	0	0
Linearly corrected CGM-based classification
16	9	3	2	0	3	0
Nonlinearly corrected CGM-based classification
16	9	3	2	0	3	0

Left side of the table: subjects assigned to each risk group; right side of the table: under and overestimation errors due to the assessment of LBGI on CGM (underest/overest errors stand for misclassification of 1 class; UNDEREST/OVEREST errors stand for misclassification of 2 classes); bottom part of the table: classification performances with LBGI from CGM conveniently corrected.

From this analysis, we can conclude that the computation of LBGI from CGM time series is biased, with a clear underestimation of the actual risk of hypoglycemia, and a correction is needed. Though the nonlinear transformation is more accurate at low LBGI values, no advantage was visible in terms of classification. As already mentioned, this is due to the fact that the nonlinear model works better in a very low risk zone, where a high degree of precision is not needed. Given that, the linear model can be considered satisfactory in describing the relationship between SMBG-based and CGM-based LBGI, turning out to be the transformation function that better adapts LBGI to the characteristics of CGM signals.

Discussion

The risk of hypo- and hyperglycemia can be assessed in a straightforward way by computing the LBGI and HBGI on collections of SMBG readings. These indicators have been shown to be predictive of future glycemic events (eg, LBGI of the frequency of future SH episodes) and clinically relevant cutoff values have been defined to classify the current condition of a patient based on his SMBG-based LBGI/HBGI. Because of their easy and fast implementation and immediate interpretation, LBGI and HBGI are powerful tools to assess glycemic variability and risk, and applicability to CGM devices could be of significant impact both from a scientific and a clinical viewpoint. This study aims at defining alternate versions of LBGI and HBGI that fit better the characteristics of CGM, providing transformations to apply when these indices are computed from CGM time series and enabling references to previously published works and relevant cutoff values.

In adapting LBGI and HBGI formulation to CGM profiles, the most relevant issue is related to the different sampling frequency of SMBG and CGM systems. SMBG devices capture hypo- and hyperglycemic events independently of their duration. In a regular non-oversampled SMBG profile, a hypoglycemic episode lasting 10 or 30 minutes (eg, a recover from a SH event) is very likely to be captured by the same SMBG sample acquired at the nadir of the BG profile. This means that the SMBG device looks at the 2 hypo events in the same way, and cannot account for their different duration. The influence of the sampling rate is even more emphasized if a hypoglycemic event is compared to a hyperglycemic one. Hypo- and hyperglycemia are, in fact, physiological phenomena characterized by significantly different time constants, and the actual time spent in hyperglycemia is usually much greater than the time spent in hypo. This unbalanced distribution of the BG profile between hypo- and hyperglycemia, the incapability of SMBG devices to capture it, and the intrinsic capability of CGM sensors to follow the real dynamics of hypo- and hyperglycemic phenomena are main factors that pushed us in looking for a correction of LBGI, HBGI formulation to enable their application to CGM recordings. As reported in Section 3, different results were obtained for LBGI and HBGI. Specifically, a real correction was shown to be needed only for LBGI, while HBGI seemed to be rather interchangeable when computed from SMBG and CGM profiles. If analyzed in the light of the different timings of hypo- and hyperglycemia, this finding is not really surprising. In the frequent sampling design of CGM systems, the increased number of BG samples is mostly associated to an increased number of high-BG samples, while the short duration of hypoglycemic episodes doesn’t allow a proper amplification of the contribution due to hypoglycemia in the overall glycemic profile. In terms of LBGI, this scenario is translated into a bias introduced by the small amount of low-BG data with respect to the total number of samples, with an average computed on risk values that are very often equal to zero and a systematic underestimation of LBGI as computed from CGM.

Nonetheless, it is unlikely that the presented corrections of LBGI and HBGI account only for the different sampling rate of SMBG and CGM systems, but may also account for sampling matrix differences (blood vs interstitium) and intrinsic characteristics and artifacts of CGM technology. This means that studies developed on data acquired with a CGM device different from the Dexcom G4 could provide additional information as to the optimal correction of LBGI and HBGI. Thus, further work shall consider the correction coefficients from a wider range of CGM systems and the potential need for a sensor-specific correction. Beyond this, other analyses to systematically assess the influence of the sampling frequency on LBGI/HBGI values are worthy of consideration in future research. Simulation studies could be used to recreate CGM time series and randomly downsample them up to recreating a full 7-point SMBG profile, with the aim of identifying the maximum number of BG samples that allows references to previous works without correction coefficients. Also, the effect of a significant decrease of the number of SMBGs should be investigated, to provide an inferior limit to be respected to obtain physiologically meaningful values of LBGI and HBGI. As an additional variable to be considered in all cases, the effect of the placement of SMBG samples across the day is likely to have a significant influence on the values obtained for LBGI and HBGI, and defining an optimal scenario for SMBG measurements could be really interesting and useful to get uniformity, for example, in clinical trials.