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Original Studies |
University of Virginia Health System and National Science Foundation Center for Biological Timing, University of Virginia (M.S.), Charlottesville, Virginia 22908
Address all correspondence and requests for reprints to: Dr. Boris P. Kovatchev, University of Virginia Health System, Box 800137, Charlottesville, Virginia 22908.
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Abstract |
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 Top Abstract IntroductionExperimental SubjectsMaterials and MethodsResultsDiscussionReferences |
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Introduction |
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TopAbstractIntroductionExperimental SubjectsMaterials and MethodsResultsDiscussionReferences |
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A major challenge of breaking this "vicious circle" is the detection of hypoglycemia before development of neuroglycopenia. Numerous studies have investigated the occurrence of hypoglycemia-related symptoms and generally found that such warning signs occur, but may be recognized by patients in less than 50% of all hypoglycemic episodes with low BG levels of 3.9 mmol/L and below (9, 10, 11, 12). This means that up to half of all hypoglycemic episodes may be asymptomatic or unrecognized, and even if recognized, in many cases recognition occurs at a BG too low to permit self-treatment. On the other hand, contemporary BG monitors provide the means for frequent BG determinations and eventual prediction of imminent hypoglycemia that is independent of symptoms. The problem with self-monitoring of BG (SMBG) is that currently there is no reliable method for recognition of imminent hypoglycemia based on SMBG readings (13). Indeed, there is no reliable prediction of patients’ immediate risk for SH from any data. Various approaches to assess the risk of SH have been tested using history of SH, low hemoglobin A1c (HbA1c), hypoglycemia unawareness, etc. (4, 5, 14). The DCCT concluded that only about 8% of future SH could be predicted from known variables (4), and a recent structural equation model accounted for 18% of the variance in SH using history of SH, hypoglycemia awareness, and autonomic symptom score (14).
As we previously reported (15), one reason for such poor prediction is purely mathematical. The problem is that the BG scale is substantially asymmetric, and the hypoglycemic range (<3.9 mmol/L) is numerically much smaller than the hyperglycemic range (>10 mmol/L). As a result, standard statistics, such as the mean and SD, tend to underestimate patients’ risk for hypoglycemia. To correct that, we introduced and validated the low BG index (LBGI), a measure of the risk of SH in patients with T1DM, that takes into account the specific distribution of BG data (15, 16, 17). Using this new approach we were able to account for 40% of the variance in SH episodes in the subsequent 6 months on the basis of history of SH and SMBG data (17) and later to enhance this prediction to 46% (18) by introducing a temporal component into our model. In addition, we documented three ranges for LBGI (below 2.5, 2.5–5, and above 5) that identified three categories of subjects at low, moderate, and high risk of subsequent SH (17). The subjects in the high risk category reported 5.2 SH episodes in the following 6 months, compared with 0.4 and 2.3 for the low and moderate risk categories (17). A recent report presents the mathematical foundation of this technique in detail (19).
The purpose of this study is to extend these findings by investigating the relative short-term changes in LBGI and other BG parameters associated with episodes of SH. We hypothesized that SH episodes are preceded and followed by measurable BG disturbances. Further, we hypothesized such disturbances can be quantified from SMBG data, which, in turn, would allow identification of subjects at risk for SH and for on-line prediction of imminent SH in individual patients.
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Experimental Subjects |
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TopAbstractIntroductionExperimental SubjectsMaterials and MethodsResultsDiscussionReferences |
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presents the demographic
characteristics of the participants;
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Materials and Methods |
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TopAbstractIntroductionExperimental SubjectsMaterials and MethodsResultsDiscussionReferences |
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, no significant change in HbA1c was
observed before vs. after the study (pre-post;
t = 1.25; P = 0.2); the pre-post
HbA1c values were highly correlated (r =
0.83; P < 0.001). The timing of SMBG and SH
The memory meter stores SMBG readings together with the date and exact time (hour, minute, and second) of each reading. Thus, for each subject we had a 6- to 8-month temporal sequence of SMBG records, and from subjects’ monthly diaries, we had the date and time of SH episodes that had occurred.2 Specialized software was developed for preprocessing of the data. This included 1) assembling the memory meter data for each subject into a continuous 6- to 8-month sequence of BG readings and scanning/cleaning of the data from test trials and artifacts, such as battery failures; and 2) matching of each subject’s records of SH with this sequence by date and time. The latter was performed as follows. For each SMBG reading the time (hours/minutes) until the nearest SH episode and the time elapsed from the last SH episode were computed. Thus, it was possible to 1) time 24-h periods backward and forward from each SH episode, and 2) time 24-h periods backward from each SMBG reading. As explained in Results, these two methods were used to 1) identify BG disturbances preceding and following SH, and 2) design an algorithm tracking risk of imminent SH on the basis of SMBG. For any 24-h period we computed average, minimum, maximum, and SD of BG and the LBGI. Due to the nature of SH (stupor, unconsciousness), no SMBG was performed exactly at the time of SH, but in a few cases SMBG was performed shortly before SH. The average per SH episode minimum elapsed time between SH and the nearest preceding SMBG reading was 5.2 ± 4.1 h; 29 SH episodes (7%) were preceded by a SMBG reading within 15 min.
The LBGI is a previously introduced predictor of SH, based on a
logarithmic transformation of the BG scale (15) and a
previously published risk analysis theory (19). In
general, the LBGI value can be computed on a single BG reading or
derived from any set of BG readings. For this study we computed the
LBGI of each subject for various 24-h periods and for the entire
duration of the study. The computation of the LBGI follows these steps.
First, symmetrization of the BG scale is performed using the
transformation f(BG, 
,ß, 
) =
[(ln(BG)) - ß]. The parameters were
= 1.026, ß = 1.861, and = 1.794 derived from
clinical assumptions [if BG is measured in milligrams per dL, the
parameters of f(BG) are as follows; = 1.084, ß = 5.381,
and = 1.509]. Next, computation of the BG risk function
r(BG) = 10.f(BG) is performed. The function r(BG) ranges from
0–100. Its minimum value of zero is achieved at BG = 6.25 mmol/L,
a safe euglycemic BG reading, whereas its maximum is reached at the
extreme ends of the BG scale. Thus, r(BG) can be interpreted as a
measure of the risk associated with a certain BG level. Let
x1, x2, .. xn be a series of n
BG readings, and let rl(BG) = r(BG) if f(BG)<0 and 0 otherwise.
The low BG risk index is then defined as LBGI =
(1/n)
i=1nrl(xi).
In summary, the LBGI is a nonnegative quantity that increases when the number and/or the absolute extent (not relative to the mean extent, as it would be in a SD computation) of low BG readings increases. The advantage of computing the LBGI, as opposed to simply taking the mean and SD of BG, is that the LBGI is not influenced by hyperglycemia (all readings above 6.25 mmol/L have zero loads). In addition, the LBGI was designed as a risk measure targeting a specific condition (hypoglycemia) and has been proven to predict SH better than any other standard statistic (17, 18).
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Results |
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TopAbstractIntroductionExperimental SubjectsMaterials and MethodsResultsDiscussionReferences |
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Recurrent severe hypoglycemia
During the study 20 subjects experienced recurrent (within 48 h) SH. Fifty-three sequences of 2 and 9 sequences of 3 recurrent SH episodes were observed. Thirty-two SH episodes were followed by a single SH episode within 24 h, and 21 SH episodes were followed by another SH between 24 and 48 h later. Nine SH episodes were followed by SH within 24 h and another SH on the day after. In general, 18% of all SH episodes were followed within 48 h by a recurrent SH.
BG disturbances before and after severe hypoglycemia
This analysis uses SMBG characteristics computed within 24-h
intervals timed from a SH episode. Figure 1 presents the typical picture of BG
disturbances observed before and after an episode of severe
hypoglycemia. In the period 48 to 24 h before SH, the average BG
level decreased, and the BG variance (assessed as SD of BG)
increased. In the 24-h period immediately preceding SH, the average BG
level dropped further, and the variance in BG continued to increase. In
the 24-h period after SH, the average BG level normalized; however, the
BG variance remained greatly increased. Both the average BG and its
variance returned to baseline levels within 48 h after SH. In the
following, we use the LBGI to quantify these disturbances, specifically
emphasizing hypoglycemia.
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is a three-panel plot of the BG
disturbances observed at the group level in three variables in the
periods -48 to -24 h, -24 to 0 h, 0 to 24 h, and 24 to
48 h. from a SH. The 24-h LBGI is presented along with the 24-h
average BG level and BG variance. Repeated measures ANOVA was used to
compare each 24-h period to a baseline computed on all 24-h periods
that were at least 48 h away from SH. Figure 2 includes
t values and P levels for all
contrasts3 between a 24-h
period and the baseline. We can conclude that 1) the average BG level
was significantly lower -24 to 0 h before SH (P =
0.001), with a trend toward decrease in the -48 to -24 h period
(P = 0.04); and 2) the variance in BG increased
steadily -48 to 0 h before SH and was even larger on the day
after SH (P < 0.001). The LBGI increased sharply in
the 24 h before SH (P < 0.001) and remained
elevated for 24 h after SH.
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Identifying subjects at risk for SH
The average LBGI computed for the entire study was 4.75 ±
2.7. As stated in the introduction, on the basis of the LBGI we
previously identified 3 categories of subjects with LBGI of 2.5 or
less, between 2.5–5, and greater than 5 who were at low, moderate, and
high risk for SH, respectively. According to this previous
classification, during this study the participants were, on the
average, at moderate to high risk of SH, which reflects the selective
inclusion of subjects with a history of multiple SH episodes.
Specifically, judging from the LBGI during this study, 11 subjects were
in the low risk, 42 were in the moderate risk, and 32 were in the high
risk category. Table 2 presents the
distribution of SH episodes across these 3 categories together with a
group comparison showing significant differences in SH frequency
(P < 0.005).
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illustrates this classification
with data for two subjects A and B, who reported 31 and 3 SH episodes
during the study, respectively. Despite his higher frequency of SH,
subject A had a higher average BG and a higher
HbA1c than subject B. The LBGI, however,
classified subject A in the high risk category and subject B in the
moderate risk category.
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For this analysis we designed an algorithm that at each SMBG reading retrieves the SMBG data in the preceding 24-h period of time and judges whether these data are likely to indicate upcoming SH. The judgment was made on the basis of a risk value derived from the current LBGI value and the average LBGI in the preceding 24 h. The algorithm simulated the action of a hypothetical SMBG device that at each reading computes current LBGI and average LBGI from the previous 24 h and decides whether these values exceed a certain threshold. If the threshold was exceeded, the algorithm identified the following 24 h as a period of high risk for SH. An optimal threshold was derived from an optimization along the following restrictions: 1) the algorithm had to predict a maximum percentage of SH episodes, and 2) the algorithm had to identify as risky no more than 15% of the total time of the study (1 day a week on the average) to prevent overestimation of the risk. The optimal threshold was held constant for all subjects. In short, 24 h of SMBG timed back from a SMBG reading were used to judge whether the next 24-h period is risky for SH.
Figure 3 illustrated the action of the
algorithm over 10 weeks of data (approximately one third of the study)
for the 2 subjects, A and B, whose data were used in Table 3. The SH
episodes are marked by triangles; subject A reported 9 SH
episodes, whereas subject B reported 1 SH episode during that time. The
risk values, derived from SMBG, are presented by a black
line. Every time a risk value exceeds the threshold, the algorithm
would declare the next 24-h period as high risk for SH. These high risk
periods are marked by gray bars. SH episodes that occur
within the gray area are predicted by the algorithm. High risk periods
that do not include a SH episode indicate that the subject avoided
potential SH. For subject A, there are 5 of 10 high risk periods that
do not include SH; for subject B there are 3 of 4 high risk periods
that do not include SH. This indicated that subject B was better
controlling his SH risk, which is also evident by his overall data
(Table 3).
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Finally, we analyzed BG levels occurring during high risk periods that did not contain SH, i.e. after false alarms. The average nadir of such BG levels was 2.3 ± 0.2 vs. 5.9 ± 1.7 mmol/L (t = 19.5; P < 0.0001) for all nonrisk periods, including all SH episodes that remained unaccounted for. This indicates that although SH did not occur, BG levels within high risk periods were notably low.
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Discussion |
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TopAbstractIntroductionExperimental SubjectsMaterials and MethodsResultsDiscussionReferences |
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Level 1: subjects at risk for severe hypoglycemia
Previous studies demonstrated that SH usually occurs in subjects
with a history of SH (4). All subjects in this study were
selected as having a history of multiple SH, but not all subjects
experienced prospective SH to the same degree. Confirming our previous
report (17), our current data demonstrate that subjects at
high risk for SH can be identified as having elevated LBGI. Indeed,
subjects with LBGI of 5 or greater during the study reported more than
4 times as many SH episodes compared with subjects in the low risk
category (LBGI <2.5). This high risk group consisted of 38% of the
subjects and accounted for 60% of all SH episodes. Post-hoc
analysis demonstrated that a classification of the subjects with
respect to their risk for SH was not possible on the basis of known
SMBG variables, other than the LBGI. For example, our attempts to
develop a three-group classification based on the subjects’ average BG
yielded no result; the subjects in the three groups had 4.1, 4.8, and
5.2 SH episodes respectively (P = .77). This analysis
generalizes the illustrative results presented in Table 3.
Level 2: idiosyncratic risk periods for SH
Our data demonstrate that SH episodes are accompanied by measurable BG disturbances, generally reflected by a steady lowering of BG, an increase in its variance that begins 48 h before SH, and a normalizing of average BG, but a further increase in its variance, immediately after SH. A markedly sharp increase in the LBGI was observed in the 24-h periods preceding SH, and the LBGI remained elevated in the 24 h after SH. Although normalization of the average BG and the increase in BG variance immediately post-SH could be explained by changes in treatment after severe hypoglycemia, the fact that the LBGI remained elevated for 24 h indicates that the risk for SH remains high, after a SH episode. This is confirmed by our observation that 18% of all SH episodes were followed by recurrent SH. Thus, patients with a history of SH should be advised about the likelihood of recurrent SH episodes.
On the basis of the changes in the LBGI before SH, we devised an
algorithm for identification of idiosyncratic periods of high risk for
SH. Attempts to use in the algorithm other variables, such as average
BG and SD of BG, did not yield better results. Overall, in
this group of subjects, who were specially selected as having a history
of SH, the algorithm predicted 50% of all SH episodes. However, this
prediction was not equally good for all subjects; 67% of the SH
episodes were predicted for the 32 subjects in the high risk category
(Table 2), whereas 25% of SH episodes were predicted for the remaining
53 subjects. This indicates that although this approach could
potentially eliminate half of all SH episodes in the studied cohort,
the patients who would benefit most are those at highest risk for
SH.
The limitations of this means of data collection do not allow for a traditional optimization of the decision-making algorithm in terms of a true and false positives. The main reason for that is that a false positive cannot be objectively identified; a false positive could be a risk period not including SH because of glucose counterregulation or because of successful prevention through treatment. Therefore, we were forced to optimize our algorithm by imposing a somewhat arbitrary, but reasonable, assumption on the frequency of risk alerts. We imposed a requirement for no more than 15% of all 24-h time windows (or no more than 1 day a week) to be declared risky. Post-hoc analysis indicated that if the optimization criterion was loosened to allow for 23% high risk periods, the prediction of SH increased to 70%. Finally, even if not leading to SH, a high risk period is associated with dangerously low BG readings (an average nadir of 2.3 mmol/L), substantially lower that the nadir of low risk periods (P < 0.0001).
In conclusion, the proposed quantitative approach identified measurable BG disturbances associated with SH. It also demonstrated that subjects at high risk for SH can be identified, and more than 50% of SH episodes can be anticipated on-line from SMBG data and therefore potentially avoided. Although sensitive to SH and low BG, this method is still not sufficiently refined to be directly incorporated into automated devices for the prediction of imminent SH due to the limitations of this data collection method. Further data collection and theoretical research are needed to enhance its specificity and its predictive capabilities.
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Footnotes |
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2 These diary records were naturally less precise;
approximately 15% of all SH episodes were recorded by date only. To
restore the missing hour/minute of such SH episode, in the follow-up
interview the subject was asked to identify in his/her meter the SMBG
reading immediately preceding such a SH episode.
3 The contrasts that were used were comparisons of
each variable to a reference (the baseline). In the statistical package
SPSS used for this analysis this is referred to as simple
contrast.
Received April 25, 2000.
Revised July 20, 2000.
Accepted August 8, 2000.
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References |
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TopAbstractIntroductionExperimental SubjectsMaterials and MethodsResultsDiscussionReferences |
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