Digital Health Care by In Silico Glycation of HbA1 Blood Cells

Abstract

Background:

Diabetes health care relies on the HbA1c (A1c) assay and associated average glucose (AG) to evaluate and control chronic glycemia. However, the A1c assay is plagued with significant noise, lag time, and specificity issues. Current studies support the significant health care advantage of clinical action based on real-time blood glucose (BG) metrics. We seek to improve diabetes management by directly relating such metrics to AG levels as mediated by recently discovered recurrent endocrine cycles.

Methods:

Several studies collected multiple months of BG data on 111 subjects totaling 261 893 CGM measurements and 29 278 meter readings. These data are a rich source of multiday metrics in terms of the CGM and SMBG daily profiles. The recurrent endocrine patterns expose key metric relationships for monitoring AG related to A1c using CGM and SMBG data. Consequently, day-to-day tracking of AG is expressed as a simple two-parameter function of fasting BG for all studies.

Results:

Consequently, when applied to 2518 qualified days of 64 subjects, the function predicts daily AG values with 2% relative standard error. All studies produced compatible results. By restricting one parameter to a constant, the error increased to 3%.

Conclusions:

The recurrent endocrine patterns revealed a persistent structure hidden within the multiday fluctuations that becomes a simple meter-compatible equation that accurately measures real-time trending of AG using fasting BG values. This enables a digital health monitoring service and self-monitoring device that reveals immediate disease progression as well as the impact of interventions and medications better than possible with the A1c assay.

Methods to control chronic glycemia rely on periodic A1c evaluations every several months.¹ For clinical support, Nathan et al developed a simple equation with tables predicting average glucose (AG) given A1c, where AG was estimated using a sampling combination of CGM and SMBG profiles.^2,3 Currently, several studies support the health care advantage of real-time actions, as enabled by BG tracking^4-6 combined with interactive communication with innovative wireless/Internet systems.⁷ This motivates a need for a relation between real-time BG readings and AG status thereby guiding immediate clinical evaluation and expedited glycemic control. Unfortunately, the chaotic nature of blood glucose fluctuations challenges any such direct connection between AG and typical self-monitor readings. Also, due to its traditional association with A1c, AG is considered to be a metric restricted to long-term diabetic condition. Fortunately, specialized phase portraits led to the discovery of recurrent endocrine patterns embedded within the sea of these chaotic multiday fluctuations.^8,9 Based on these cycles, the first practical solution to this challenge was introduced at the ADA 73rd and 75th tech conferences.^9,10 Other more recent attempts rely on assumed kinetics and significant monitoring burden.¹¹

The object of this study is to explore the real-time tracking of AG by SMBG events as supported by these multiday endocrine cycles.

Research Design and Methods

Historical studies captured 1-4 months of CGM data and self-monitoring blood glucose (SMBG) events of deidentified patients (no patient-specific information).^12-14 Such data enable the comprehensive direct calculation of AG versus the sampled version used by Nathan et al.² Daily metrics of special interest are mean BG (DA) and fasting before-breakfast BG (AMG).

The CGM clinical studies monitored 41 subjects at sampling rates of 5 or 10 minutes. All subjects take diabetes medications and thirty are type 1 requiring insulin. Missing data restrictions passed 932 evaluable CGM days out of a possible 1734 subject days. Hence, AMG and bedtime BG levels must be reported for evaluable days.

Data from a different older study consists of BG meter readings from outpatient care on 70 ambulatory type 1 and type 2 subjects taken at time events designated as miscellaneous, presnack, and pre-/postbreakfast, lunch, and supper. Twenty-three of these subjects provided data adequate for cycle analysis, totaling 1586 monitored days of primarily four to five BG readings per day.

We now introduce a graphical (modeless) approach to capture diabetes status and trends for both patient and doctor.

Within the resolution of the data, phase analytics of day-to-day fluctuations indicate that two independent metrics captured the collective result of endocrine dynamics. Consequently, two-dimensional phase plots reveal comprehensive patterns of recurrent endocrine cycles as fully described in recent articles.^8,9

Figure 1 overlays time-shifted phase portraits of two daily metrics of a patient. Note these portraits require the next-day (shifted) version of each metric as an independent coordinate.⁸

Figure 1.

Time-shifted phase portraits of DA and AMG.

Each point is labeled by the day number of the study (“day”). Note the “Next day” axis plots the shifted next-day version of each metric.⁸ To visualize each cycle in the figure, start at its respective day 16 and trace its line style to day 24. These two orbits form similar polygonal paths and appear to have quasi-weekly recurrent cycles of about 7 days. Distorted by significant error and missing days, these parallel patterns demonstrate the concept of synchronized chaotic cycles between two metrics.⁸ The DA and AMG orbits have overlapping geometric regions, and their centroids are separated by a translation vector, called “Offset.” The orbit size reflects the multiday volatility of each metric. Note the AMG size is about twice the DA size.

The cycles capture important BG features easily tracked by simple day-incremental moving averages, which in effect represents “in silico glycation” to mimic biochemical glycation. This in silico process combines summary metrics over a sliding span of days. The oldest level is removed while the newest level is included as the span moves forward day by day. This averaging span can cover a minimum of one cycle of a few days up to multiple cycles spanning 120 days, that is, the expected life time of A1c cells that represent the very slow kinetics of biochemical glycation. This incremental process is adjusted for missing days and optionally weighted to represent the aging distribution of glycated blood cells.^15,16 Figure 2 shows typical moving average profiles within the DA data. Be aware, atypical trending after significant interventions may be too fast for A1c tracking. One can identify these fast events by comparing customized in silico fast tracking with the slow A1c tracking profiles, as shown in Figure 3. This motivates the concept of “smart” in silico glycation that adapts to match the real-time trending of AG as in Figure 3.

Figure 2.

Two slow trending metrics (weighted moving averages of DA and AMG) of a subject monitored by CGM data.

Figure 3.

Fast-trending centroid (weighted fast-moving averages of DA) for a subject monitored by CGM data.

This incremental moving average of monitored days that are appropriately distributed around the polygon’s perimeter estimates the centroid of the pattern with minimal bias as well as reducing statistical error. In effect the cycles capture their centroid as verified by the optimality requirements of statistical design of experiments (DOE).^17,18 The moving average converges rapidly from initial transients to its tracking level typically within ~one or two cycles depending on noise factors. Hence, 3 to 12 monitored days are sufficient to identify the structure of the pattern and its centroid as illustrated in Figure 2. Note the metric and its day-shifted version have the same statistical properties; so, the moving average of the metric estimates the plot position on both axes of the cycle centroid. Since A1c-related or A1c-derived AG (ADAG) trends tend to be either stationary or slowly changing over time, the DA centroid essentially equals AG after two cycles. For clinical reasons, one can invert Nathan et al’s equation² using this calculated AG to predict A1c and avoid specificity noise that plagues the clinical A1c assays.^2,6,16

In summary, the visual evaluations provide serial DA values orbiting around a slowly trending centroid representing chronic BG (cBG). A moving average over multiple months correlates closely with the typical AG associated with the A1c assay.^5,16 Given the 96% correlation of their respective moving averages, one may use SMBG profiles to approximate DA if CGM data are not available. Note 3 to 4 SMBG readings provide an adequate but noisy estimate of DA.³

One can now use a simple linear model to represent the graphical associations.

For each patient the phase-portrait cycles support the following moving-average equation relating the centroids of DA and AMG over a progressive sequence of days:

$${\mathrm{DA}}_{\mathrm{ma}}{=\mathrm{Offset}+\mathrm{b}*\mathrm{AMG}}_{\mathrm{ma}}\pm \mathrm{SD},$$

where “X”_ma is the symbol for the moving average of metric “X,” “b” is a scale factor aligning their trends, and “Offset” measures the separation between their centroid profiles. Note that “b” scales the size of AMG orbits to approximate DA orbits while “Offset” overlays the centroid profiles of the two moving averages. For each patient the equation and both parameters may be optimized by simple linear regression on any series of moving-average days, where SD absorbs the error of approximations and ignored variables. The persistence of the cycle structure extends the prediction fidelity of the optimized equation to multiple months and across missing days. Figures 1, 2, and 3 support these concepts.

In Figures 2 and 3 the triangles mark the data points of daily means, DA. Note the essentially parallel moving-average levels for DA and AMG of the first two cycles extending beyond 100 days. These parallel profiles demonstrate the two parameters of the moving-average equation: “b” and Offset. Recall “b” in effect optimizes the parallelism of the two moving averages, while “Offset” matches their profiles.

In Figure 3 the in silico kinetics for A1c-AG (~DAma) detects a trend but is too slow to track it properly. By restricting the moving average span to 14 days, one gets faster in silico glycation (DAmaf solid line) that tracks better but is noisier. This is an application of customized in silico tracking where we have increased the emulated glycation rate.

Excluding a total of 310 days of outliers (initializing transients), fitting the equation over the complete profiles of every patient verifies the association of the two metrics. However, to test the incremental properties of the equation, one can fit the equation to an initial subset of days (one or two cycles) excluding transients to predict all of the profile days.

These analyses compiled over all patients provides the ensemble relative standard error, defined as (root mean square prediction error)/(mean BG). We use the relative error since the prediction error tends to be proportional to BG level as shown by Nathan et al.² Also reported are the range of the Offset distribution and standard error of the “b” estimate. Note that Figure 1 comparing cycle sizes implies “b” is near 0.5.

All statistical data analysis, phase portraits, and profile figures are produced by JMP® 8.0.2 of SAS Institute Inc.¹⁷

Results

Given the precision of the tracking term b*AMG_ma, one can monitor the trend of cBG on a daily basis with good precision even without the Offset term. However, Offset is useful as it contains the impact of food/exercise and medications.

For all 64 subjects, the fasting BG function fits A1c-related AG (estimated ADAG) with relative standard error less than 2%, as compared to Nathan et al’s ~10% error.² Setting b to 0.47, increased this error to 3%.

By optimizing the two function parameters for each patient restricted to an initial small subset of data (less than 14 days), one incrementally predicts all cBG (~AG) values with 3% error. For the CGM studies the relative error was less than 2% compared to 3.5% for the older SMBG study.

Hence, for each patient one has extensive profiles of AG trends and volatility. Standard linear regression analyses quantify this trending when applied to fit the profiles as created by these incremental moving averages.¹⁰ For example, we found significant changes of AG in 25 of the 41 CGM subjects, including lowering of AG in 9 of the 11 subjects who are testing an injected medication. Also, significant changes in volatility (cycle radius) occurred in 5 subjects.

Conclusions

The concept of phase analytics applied to the daily summary variables of BG data revealed distinct cycle patterns embedded within the chaotic noise of their fluctuations. With significantly less noise and better specificity versus clinical A1c, the cycles reveal a practical and efficient method to track not only changes in AG but also AG volatility using fasting BG levels. The method produced compatible results for the CGM versus SMBG studies.

Hence, one avoids the long-term delay, noise levels, and specificity problems associated with the traditional A1c assay. Statistical analysis of the tracking profiles provides accurate long-term evaluations of diabetes status and progression.

One can immediately apply the AG function to fasting data by using b = 0.47 with naive Offset approximated by 87 mg/dL as implied by Table 1. When available, one updates this tracking equation for AG or related A1c using the nearest A1c assay. Also, the Offset can be simply adjusted using a series of daily continuous or fingerprick BG profiles and their estimated AG. An alert to improve BG maintenance occurs if Offset goes outside of 87 ± 21 mg/dL. Hence, this simple method transforms glucose meters to become “A1c meters.”

Table 1.

Equation Statistics.

Predict AG using fasting BG	Fit profiles	Predict profiles*	Global b fit**
R-square adj	0.99	NA	0.98
Root mean square error	2.70	4.91	4.14
Mean of response	159.84	159.84	159.84
# Observations	2518	2518	2518
Relative standard error	< 2%	3%	3%
b ± standard error	0.48 ± 0.05	0.47± 0.04	0.47 ± 0.01
Offset ± standard deviation	81.81 ± 53.44	78.94 ± 58.06	86.62 ± 20.77

^*Calculate b and offset for small initial subset of each patient’s profile (less than 14 days) and then predict all days of the profile.

^**set b = 0.47 for all patients, while offset is optimized for each patient. Offset deviation is not an error metric but indicates span across all patients.

The results show that the cycle-mediated digital health tracking approach would not only improve diabetic health care and medical research but also benefit other diseases requiring similar vigilant monitoring such as asthma and heart diseases.