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1.INTRODUCTIONAs wearable glucose monitors continue to mature and gain popularity, continuous glucose monitoring (CGM) devices have been widely integrated into patients’ daily lives [1,2]. It has become an indispensable part of diabetes management. CGM data can reflect the 24-hour glucose excursions in patients with type 2 diabetes mellitus (T2DM). However, analyzing these extensive, complex CGM data and extracting their deep clinical value is crucial for improving diabetes outcomes and patients’ quality of life, which need to be solved urgently [3]. Existing studies mainly focus on using clinical knowledge to extract CGM metrics, such as time in range (TIR), standard deviation of sensor glucose (SDSG), and mean sensor glucose (MSG), and hence analyzing the relevant properties of glucose levels. Even though these methods have succeed to some extent, they ignored the fact that glucose dynamics are non-stationary, dynamically fluctuating, non-linear, irregular, and exhibit substantial complexity [4–6]. Therefore, a novel method to deeply parse CGM data was needed. Entropy analysis has shown its value as a statistical tool for assessing the complexity and unpredictability of physiological time series data, such as ECG and EEG. Ning et al. [7] adopted the approximate entropy (ApEn), initially introduced by Pincus et al. [8], and developed an enhanced ApEn algorithm, focusing on wave modes to distinguish between patients with heart disease and healthy individuals. There have been many scholars to analyze the CGM time series data by entropy value. For example, Li et al. [9] analyzed the complexity of glucose time series index using a refined composite multiscale entropy method to characterize the CGM dataset. Entropy analysis could measure the irregularity and complexity of data. Therefore, we proposed the approach using entropy analysis to analyze the complexity of CGM data. 2.MATERIALS AND METHODS2.1. Study populationThe dataset used in the current study was derived from comprehensive survey data of CGM from multiple centers in China between 2007 and 2009 [10,11], which included records from 858 type 2 diabetes patients. The survey included CGM records of 858 patients with type 2 diabetes. Participants were outpatient volunteers from 11 different Chinese hospitals. The criteria for participant selection have been described in earlier publications [10,11]. The present study adhered to the Declaration of Helsinki and was approved by the corresponding ethics committee. 2.2.CGM parametersAll subjects in this study received a retrospective analysis of a CGM system. The device used is the CGMS GOLD (Medtronic Inc., Northridge, CA, USA). The same group of trained nurses was responsible for inserting the CGM system at each hospital. The first calibration via fingertip blood was performed at the hospital 1 hour after initialization of the CGM system, after which the subjects wore the CGM device for 7 consecutive days. Subjects were instructed to perform at least four fingertip blood glucose measurements per day using a SureStep blood glucose meter (LifeScan, Milpitas, CA, USA) for CGM calibration. Participants were recommended to follow a prescribed diet with specific meal times, and to maintain normal daily activities without heavy physical activity to improve the authenticity and reliability of data analysis. 2.3.Calculation of entropyFirst, the ApEn of the CGM time series data was calculated. The ApEn is a tool used to quantify complexity in timeseries data by measuring the frequency of new or irregular patterns within the dataset. The calculation of ApEn follows this formula: where 𝑚 denotes the embedding dimension, which is the number of data points used in similarity calculations; 𝑟 is the threshold of similarity; and 𝑁 is the total number of data points in the time series. Then, we calculated the composite multiscale entropy (CMSE) [12] for the CGM time series data. The core principle of the CMSE algorithm is to employ sample entropy (SampEn) for assessing CGM time-series data irregularities across multiple time scales, thereby unveiling the data’s inherent dynamic complexity. CMSE is calculated using the following formula: where 𝑠 is the number of time scales; 𝑚 is the embedding dimension, here the embedding dimension is taken to be 2; 𝑟 is the threshold of similarity, which is 20% of the standard deviation of the data series; 𝑁 is the total number of data points in the original time series; and 𝑁τ is the total number of data points in the coarsely grained time series at time scale τ. At each time scale, the original CGM time-series data is divided into several non-overlapping segments, and the data points in each segment are averaged to obtain the coarse-grained time series at the corresponding scale. Subsequently, SampEn is computed on each coarse-grained time series using the CMSE method to quantify the complexity of the CGM time series data at that scale. In our analysis of ApEn, we primarily focus on the cases where the embedding dimension is 2. And we focus on the case in the study of CMSE where the time-scale factor is 1. We notice that with a timescale factor of 1, CMSE actually reverts to SampEn. Originally proposed by Richman et al. [13], it is an important tool in assessing the complexity of the data and is particularly suited to analyzing the case of short-time-series data. The elimination of repetitive patterns in the data is then a much clearer and stronger way to measure the irregularity and complexity of the data in time series. Further research will continue investigating the application of these two specific cases and their possible value for blood glucose monitoring data analysis. 2.4.Correlation analysisA Spearman correlation matrix evaluated the association between ApEn, SampEn, and physiological indexes like HbA1c. The correlation matrix is expressed as: wherere 𝑆𝑖𝑗 presents the Spearman correlation coefficient between the i-th class entropy (ApEn or SampEn) and the j-th class physiological indicator 𝑃𝑗. 2.5.Statistical analysesThe ApEn and SampEn were calculated for the CGM data using the EntropyHub toolbox in MATLAB [14]. In addition, all other data analysis procedures were performed in the MATLAB 2022b and Python 3.11.9 environment. The correlation between the complexity of the CGM time series data and the levels of physiological indices, such as HbA1c and GA were evaluated using Spearman’s correlation coefficient, the p-values for significance testing were derived using a t-test. Statistical significance was determined at P<0.05 (two-tailed test). 3.RESULTS3.1.Clinical characteristics of the participants with T2DMIn this study, we applied entropy analysis to explore the inherent complexity of glucose series. After screening and cleaning data, a total of 858 patients (328 women and 530 men, median age 61.0 years) were included from which detailed clinical characteristics were extracted (Table 1). Table 1.Clinical characteristics of the participants with T2DM
Given the skewed distribution of the data, they are expressed as median (interquartile spacing range 25%-75%) or number of individuals n. BMI, body mass index; SBP, systolic blood pressure; DBP, diastolic blood pressure; HbA1c, glycated hemoglobin A1c; GA, glycated albumin; FPG, fasting plasma glucose. TIR, time in range; TOR, time out of range; LBGI, low blood glucose index; HBGI, high blood glucose index; AUCIR, range of increase in blood glucose within area curve. 3.2.Correlation analysis between entropy and clinical characteristicsIn this study, we further elaborated the correlation of entropy values with clinical characteristics of diabetic patients; entropy value was used as a quantitative index of dynamic changes in blood glucose to understand its correlation with clinical parameters of patients. The present study disclosed results related to specific correlation analysis in Table 2. Table 2.Correlation analysis between entropy values and clinical characteristics
The correlation coefficients between ApEn and HbA1c, GA and fasting glucose (FPG) were -0.40, -0.39 and -0.07, respectively, while the correlation coefficients of SampEn were -0.29, -0.26 and -0.06, respectively, (with the correlation coefficient of -0.06 for FPG not passing the significance test, all other P values < 0.001), These results confirmed the effectiveness of entropy analysis in the assessment of glycemic control quality, suggesting that ApEn and SampEn can be used as sensitive indicators of glycemic control quality, which can effectively reflect the changes of glycemic stability in diabetic patients, and have the potential to be used in clinical practice to assess glycemic control. 3.3.Estimate steady-state beta cell function (HOMA-B) and insulin sensitivity (HOMA-S)In this study, we used the Homeostasis Model Assessment (HOMA) calculator (http://www.dtu.ox.ac.uk) [15], a common evaluation tool for β-cell function (HOMA-B) and insulin sensitivity (HOMA-S), for comprehensive understanding of the metabolic status of diabetic patients. Comparisons were made between β-cell function (HOMA-B) and insulin sensitivity (HOMA-S) assessed by the HOMA calculator with non-stationary models like hyperinsulinemic, hyperglycemic clamps and glucose tolerance tests. The results showed high agreement, evidencing that the HOMA model assessment of β-cell function and insulin sensitivity is reliable. Additionally, we paid attention to the correlation between the three metrics HOMA2 %B, HOMA2 %S and HOMA2 insulin resistance (HOMA2 IR), and the entropy values obtained through CGM data (Table 3). This approach aimed to uncover and clarify how HOMA modeling metrics correlate with glycemic variability. Our goal was to deepen the understanding and improve the management of metabolic status in patients with diabetes. Table 3.Correlation analysis of entropy value and HOMA2
Beta cell function HOMA2 %B showed a significant positive correlation with both ApEn and SampEn (correlation coefficients of 0.29 and 0.17, respectively, P<0.001), whereas HOMA2 %S showed a significant negative correlation with ApEn and SampEn (correlation coefficients of - 0.14 and -0.12, both P<0.001). This preliminary result revealed a positive association between beta cell function and glucose dynamics, and a potential negative association between insulin sensitivity and glucose dynamics. The findings of this study provided new perspectives for understanding changes in insulin secretion and sensitivity in patients with T2DM. 4.DISCUSSIONThis study focused on CGM-derived time series data analyzed by an entropy analysis approach. Initial results suggested that the complexity of the CGM-derived glucose time series had significant correlation with physiological and CGM metrics The Correlations for β-cell function (HOMA-B) and insulin sensitivity (HOMA-S)-related metrics were also high. These results propose that the entropy analysis method may provide a novel methodology in further clinical investigations. A new experiment was designed further to illustrate the effectiveness of the entropy analysis method. The HbA1c levels were categorized into two classes based on the threshold of 6.5%, which was set as the threshold in clinical. Logistic regression modeling was then applied. The whole dataset contained 858 patients was divided into a training set 644 and a test set 214, with a ratio of 75% and 25%, respectively. This division of data was very helpful for proper training and validation of the model and at the same time provided a reasonable assessment of the generalization ability of the model. The predictive features of ApEn and SampEn showed the experimental results in models performed at 0.9023 with an accuracy, 0.9476 with F1 score, and an AUC of 0.81. The ROC curve performance of the model is evaluated and presented in Figure 1. The curve depicted the relation of the true positive rate (TPR) and false positive rate (FPR) of the model at various thresholds. As the FPR increases, the TPR also increases, indicating that the model has a strong discriminatory ability at each decision threshold. Furthermore, the stepped curve pattern indicates changes in model sensitivity at specific threshold points. The area under the receiver operating characteristic curve (AUC) was 0.81, significantly exceeding the criterion for random guessing (AUC=0.5), demonstrating the model’s high diagnostic accuracy. This result indicated the effectiveness of the entropy analysis in enhancing the model’s ability to predict glycemic control. The experiment also divided the GA level based on the 17% threshold and applied the logistic regression model (figure 1). The results showed that using entropy values as predictive features resulted in an AUC score of 0.73, Overall, the results of this experiment further validated the value of using ApEn and SampEn metrics in the prediction of glycemic control status. Although this study provided useful insights into the state of glycemic control, there were some limitations. First, the length of CGM data used in the study was only 7 days, which may not have been sufficient to assess individual glucose fluctuations comprehensively. Second, although participants received dietary and activity recommendations, actual adherence was not rigorously monitored, which may have affected the study results. Therefore, our findings need to be scrutinized under a more rigorous analytical framework. In summary, this study not only revealed the significance of entropy values in identifying and assessing the quality of glycemic control, but also emphasized the significant link between entropy values and clinical features. We have established a time-series analysis method using entropy analysis that enhances understanding of CGM complexity. In clinical practice, with the deep integration of CGM technology and AI, complex analysis of glucose time series is expected to provide more information about glucose characteristics and further enhance the efficiency of diabetes management. ACKNOWLEDGEMENTThis work was supported by National Natural Science Foundation of China (61973067) and the Northeastern University (China) Student Innovation Training Program Grant (230268). REFERENCEST. Battelino, T. Danne, R.M. Bergenstal, S.A. Amiel, R. Beck, T. Biester, E. Bosi, B.A. Buckingham, W.T. Cefalu, K.L. Close, C. Cobelli, E. Dassau, J.H. DeVries, K.C. Donaghue, K. Dovc, F.J. Doyle, S. Garg, G. Grunberger, S. Heller, L. Heinemann, I.B. Hirsch, R. Hovorka, W. Jia, O. Kordonouri, B. Kovatchev, A. Kowalski, L. Laffel, B. Levine, A. Mayorov, C. Mathieu, H.R. Murphy, R. Nimri, K. Norgaard, C.G. Parkin, E. Renard, D. Rodbard, B. Saboo, D. Schatz, K. Stoner, T. Urakami, S.A. Weinzimer, M. Phillip,
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