Of the 30 patients recruited, three actively withdrew from the study before 3 months. Two of these individuals provided the data they had recorded up to the time of withdrawal. Three additional patients' data were lost to the study for various reasons, meaning that 24 patients followed through to the 3-month follow-up. All patients were given the opportunity to continue using the equipment for a further 3-month period; 19 patients accepted this and were followed up for a total of 6 months. Not all patients used the equipment actively during the period they had it.
As a measure of overall usage, we used the total number of blood glucose measurements, insulin injections recorded, and food items recorded in the period. The results for each patient are summarized in . Because physical activity and symptoms were recorded to a significantly lower degree (compare ), we did not use these data in the analysis. To test for covariates we used a linear regression model on sex, age, and prestudy HbA1c. Results show that usage was positively correlated with age (regression coefficient, 55.8 recordings/year; P=0.009). Usage was not significantly correlated with prestudy HbA1c (P=0.34) or sex (P=0.10).
FIG. 2. Usage statistics for all recruited patients who contributed any data. Each column is, from the bottom to the top, the number of recordings in the logs for blood glucose (n.BG), insulin, activity, and food, respectively. The patients classified as adopters (more ...)
There was no change in mean HbA1c for the cohort or any correlation between HbA1c and any parameters of usage. There was no significant change in weight over the course of the study or any correlation between change in weight and usage parameters.
For further analysis, we divided the patients into two disjoint groups: “adopters” and “nonadopters.” The adopters were 18 patients who recorded data reliably (i.e., without considerable interruptions) for at least 80 days. The patient characteristics of the two groups are shown in . For the adopters, usage of blood glucose, insulin, and food measurements was relatively frequent and stable. It is notable, as can be seen in , that there was much variation in the usage among patients within the adopter group.
Patients Characteristics for the Groups of Adopters and Nonadopters
The uneven sampling rate of the SMBG measurements allows for period detection at frequencies above the Nyquist frequency by using periodograms for unevenly sampled data such as the Lomb–Scargle periodogram.16,17
The Lomb–Scargle periodogram is a linear best fit to a sine curve with the given period and arbitrary phase. Using the fact that the power is exponentially distributed one can find the significance of the period. If a significant period is identified, this can be visualized to the user for example in the form of a smoothed kernel regression curve over the given period.18
We searched for periodicities in the complete data from all adopters by computing the Lomb–Scargle periodogram for the period ranges 24±1
h (weekly), and 720±150
h (30 days/month), and we identified the most significant peak in each range. If the most significant peak occurs at a frequency f
and has power P
), the P
value is approximated as p
. To confirm the validity of this assumption we performed Monte Carlo tests for a few selected values and found good agreement.
In , the significance of periodicities on a daily, weekly and monthly basis for each patient in the adopter group is shown. Because we used the same data to test for three different periodicities, we corrected the significance levels by Bonferroni's correction, such that a 0.05 overall significance level corresponds to a 0.05/3=0.017 individual significance level. Thus, any patient who has a significant periodicity has consistent sine-like variation with that period. For instance, a patient's blood glucose level may be typically higher in the evenings, which will emerge as a significant periodicity after data from a certain number of days are recorded. The pattern can subsequently be visualized to the patient so that the patient can be informed and make appropriate changes or discuss the pattern with his or her physician.
Estimated P Values for Each Periodicity and Each Patient
For visualization of the periodic pattern, we use kernel regression smoothing with a fixed bandwidth. It is still necessary to display an indication of the error because this will typically vary. In particular, there are likely to be few measurements (and high error) during the night. The nightly measurements may also carry higher bias because patients are more likely to wake up and measure their blood glucose when it is outside the normal range.
Using and fine-tuning pattern recognition methods is laborious, but despite our best efforts we could not find any technique that performed substantially better than random at predicting future blood glucose values based on statistical learning techniques.19
We also constructed a three-way classification problem for the classes low, high, and normal range, which is a simpler problem compared with predictive regression. The limits of the ranges of each class were determined individually in the training set by the 20% and 80% quantiles in order to avoid empty training sets. Thus, the classes did not necessarily reflect medical hypo- or hyperglycemia, but rather unusually low or high blood glucose values. The classifier was trained on the data recorded up to the current time and predicted the probability of low or high glucose at the next blood glucose measurement. If a pattern that indicated low blood glucose was identified, for example, the important predictors could be presented to the user, enabling the user to learn from typical undesirable situations that had not been identified previously.
The results indicate that pattern recognition methods for prediction or predictive classification are not useful for these data. We tested several different classifiers, including random forests, support vector machines, and quadratic discriminant analysis. We found that generally support vector machines with radial basis function performed the best of these, including providing the best balancing of the classes. However, the classification was not good enough to provide meaningful insight from the feature selection (i.e., we could not discriminate which features were important for classification). We performed two independent binary classifications for the problems low versus not low and high versus not high, and whenever there were conflicting results for any data point, the prediction was set to the normal range. Thus we could compute the precision and recall for the results, and the corresponding points in the receiver operating characteristics plot shown in for both problems. Although most results were above the non-discrimination diagonal line, they were only slightly better than random guessing. The best prediction results were for hyperglycemia, performing somewhat better than the best hypoglycemia results.
FIG. 3. Receiver operating characteristics plot for classification of low or high blood glucose using support vector machines with a radial kernel function. Gray dots indicate high glucose (80% quantile), black dots low glucose (20% quantile), and each dot corresponds (more ...)
Significant change points
The large amount of noise in the SMBG measurements makes it difficult to identify trends apart from obvious ones when a simple scatterplot is presented such as in the current version of FTA (). SMBG values are not necessarily an unbiased sampling of actual blood glucose because measurements typically are preprandial or measured when the user suspects low or high blood glucose values. Nevertheless, trends in the measured values can be valuable as indicators of physiological change.
An appropriate tool to identify changes in live systems is the c-SiZer algorithm, which detects changes very early and at any scale of observation (S.O. Skrøvseth, J.G. Bellika, and F. Godtliebsen, “Causality in scale space as an approach to change detection,” manuscript submitted for publication). The latter property is important because trends may appear at distinct scales simultaneously. For example, a user may experience a short-term significant increase in blood glucose as part of a long-term significant decrease. c-SiZer allows for detection and visualization of these trends as they appear.
c-SiZer is based on the SiZer (Significant Zero-crossings of derivatives) methodology, which defines a scale space spanned by a bandwidth and time and performs a hypothesis test of the derivative of the signal at every point in scale space.20
c-SiZer is a causal version that is adapted for live processes such as sensor data.21
Thus changes can be detected live during data acquisition and presented to the user.
All adopters had significant trends at some point, most commonly on smaller scales, typically of one or a few hours. Large-scale trends on several days or more also appeared in most patients.
Example of three patients' time series and significant trends are shown in . All these patients exhibit trends on both small and large scales. Although some trends are significant at several scales, in most cases a trend appears on only one of the selected scales. On a few occasions there are also conflicting trends (i.e., a significant increasing trend on one scale may overlap with a significant decreasing trend on another scale). There is no contradiction in this because long-term trends inevitably contain small-scale variations that may themselves be significant.
FIG. 4. Significant scale-space trends for three selected patients. Gray dots are blood glucose measurements, the y-axis is cropped for visibility, and black vertical lines indicate measurements above the selected range. Black smooth lines are kernel regression (more ...)