Predicting Upcoming Glucose Levels in Patients with Type 1 Diabetes Using a Generalized Autoregressive Conditional Heteroscedasticity Modelling Approach
DOI:
https://doi.org/10.6000/1929-6029.2015.04.02.4Keywords:
Diabetes, blood glucose prediction, generalized ARCH models, glycaemic management.Abstract
Continuous blood glucose monitoring systems (CGMS) capture interstitial glucose levels at frequent intervals over time, and are used by people with diabetes and their health care professionals to assess glycaemic variability. This information helps to adjust treatment to achieve optimum glycaemic control, as well as potentially providing early warning of imminent and dangerous hypoglycaemia. Although a number of studies has reported the possibilities of predicting hypoglycaemia in insulin dependent type 1 diabetes (T1DM) patients, the prediction paradigm is still unreliable, as glucose fluctuations in people with diabetes are highly volatile and depend on many factors. Studies have proposed the use of linear auto-regressive (AR) and state space time series models to analyse the glucose profiles for predicting upcoming glucose levels. However, these modelling approaches have not adequately addressed the inherent dependencies and volatility aspects in the glucose profiles. We have investigated the utility of generalized autoregressive conditional heteroscedasticity (GARCH) models to explore glucose time-series trends and volatility, and possibility of reliable short-term forecasting of glucose levels. GARCH models were explored using CGMS profiles of young children (4 to <10 years) with T1DM. The prediction performances of GARCH approach were compared with other contemporary modelling approaches such as lower and higher order AR, and the state space models. The GARCH approach appears to be successful in both realizing the volatility in glucose profiles and offering potentially more reliable forecasting of upcoming glucose levels.
References
Khunti K, Davies M, Majeed A, Thorsted BL, Wolden ML, Paul SK. Hypoglycemia and Risk of Cardiovascular Disease and All-Cause Mortality in Insulin-Treated People With Type 1 and Type 2 Diabetes: A Cohort Study. Diabetes Care 2015; 38(2): 316-22. http://dx.doi.org/10.2337/dc14-0920 DOI: https://doi.org/10.2337/dc14-0920
Standards of Medical Care in Diabetes—2015: Summary of Revisions. Diabetes Care 2015; 38(Supplement 1): S4. http://dx.doi.org/10.2337/dc15-S003 DOI: https://doi.org/10.2337/dc15-S003
Guerra S, Sparacino G, Facchinetti A, Schiavon M, Man CD, Cobelli C. A dynamic risk measure from continuous glucose monitoring data. Diabetes Technol Ther 2011 13(8): 843-52. http://dx.doi.org/10.1089/dia.2011.0006
Pérez-Gandía C, Facchinetti A, Sparacino G, Cobelli C, Gómez EJ, Rigla M, et al. A dynamic risk measure from continuous glucose monitoring data. Diabetes Technology & Therapeutics 2011; 13(8): 843-52. http://dx.doi.org/10.1089/dia.2011.0006 DOI: https://doi.org/10.1089/dia.2011.0006
Sparacino G, Zanderigo F, Maran A, Cobelli C. Continuous glucose monitoring and hypo/hyperglycaemia prediction. Diabetes Research and Clinical Practice 2006; 74, Supplement 2(0): S160-S3. DOI: https://doi.org/10.1016/S0168-8227(06)70023-7
Hoeks LBEA, Greven WL, de Valk HW. Real-time continuous glucose monitoring system for treatment of diabetes: a systematic review. Diabetic Medicine 2011; 28(4): 386-94. http://dx.doi.org/10.1111/j.1464-5491.2010.03177.x DOI: https://doi.org/10.1111/j.1464-5491.2010.03177.x
Whitelaw BC, Choudhary P, Hopkins D. Evaluating rate of change as an index of glycemic variability, using continuous glucose monitoring data. Diabetes Technol Ther 2011; 13(6): 631-6. http://dx.doi.org/10.1089/dia.2010.0215 DOI: https://doi.org/10.1089/dia.2010.0215
Cichosz SL, Frystyk J, Hejlesen OK, Tarnow L, Fleischer J. A novel algorithm for prediction and detection of hypoglycemia based on continuous glucose monitoring and heart rate variability in patients with type 1 diabetes. J Diabetes Sci Technol 2014; 8(4): 731-7. http://dx.doi.org/10.1177/1932296814528838 DOI: https://doi.org/10.1177/1932296814528838
Sudharsan B, Peeples M, Shomali M. Hypoglycemia prediction using machine learning models for patients with type 2 diabetes. J Diabetes Sci Technol 2015; 9(1): 86-90. http://dx.doi.org/10.1177/1932296814554260 DOI: https://doi.org/10.1177/1932296814554260
Cox DJ, Gonder-Frederick L, Ritterband L, Clarke W, Kovatchev BP. Prediction of Severe Hypoglycemia. Diabetes Care 2007; 30(6): 1370-3. http://dx.doi.org/10.2337/dc06-1386 DOI: https://doi.org/10.2337/dc06-1386
Turksoy K, Bayrak ES, Quinn L, Littlejohn E, Rollins D, Cinar A. Hypoglycemia Early Alarm Systems Based On Multivariable Models. Industrial & engineering chemistry research 2013; 52(35). http://dx.doi.org/10.1021/ie3034015 DOI: https://doi.org/10.1021/ie3034015
Mancini L, Trojani F. Robust Value at Risk Prediction. Journal of Financial Econometrics 2011; 9(2): 281-313. http://dx.doi.org/10.1093/jjfinec/nbq035 DOI: https://doi.org/10.1093/jjfinec/nbq035
Battelino T, Phillip M, Bratina N, Nimri R, Oskarsson P, Bolinder J. Effect of Continuous Glucose Monitoring on Hypoglycemia in Type 1 Diabetes. Diabetes Care 2011; 34(4): 795-800. http://dx.doi.org/10.2337/dc10-1989 DOI: https://doi.org/10.2337/dc10-1989
Sparacino G, Facchinetti A, Maran A, Cobelli C. Continuous glucose monitoring time series and hypo/hyperglycemia prevention: requirements, methods, open problems 2008. 181-92 p. DOI: https://doi.org/10.2174/157339908785294361
Paul SK, Agbeve J, Maggs D, Best JH. Comparison of trajectories of self monitored glucose levels by hypoglycaemia status over 52 weeks of treatment with insulin glargine or exenatide once weekly. Journal of Diabetes 2015: n/a-n/a. DOI: https://doi.org/10.1111/1753-0407.12269
Desai SJ, Tamada RK, Potts R. Predicting glucose values from previous measurements. Diabetes Technol Ther 2002; 4: 215.
Magni P, Bellazzi R. A Stochastic Model to Assess the Variability of Blood Glucose Time Series in Diabetic Patients Self-Monitoring. IEEE Transactions on Biomedical Engineering 2006; 53(6): 977-85. http://dx.doi.org/10.1109/TBME.2006.873388 DOI: https://doi.org/10.1109/TBME.2006.873388
Briegel T, Tresp V. A Nonlinear State Space Model for the Blood Glucose Metabolism of a Diabetic. Automatisierungstechnik 2002; 50: 228-36. http://dx.doi.org/10.1524/auto.2002.50.5.228 DOI: https://doi.org/10.1524/auto.2002.50.5.228
Gani A, Gribok AV, Lu Y, Ward WK, Vigersky RA, Reifman J. Universal glucose models for predicting subcutaneous glucose concentration in humans. Trans Info Tech Biomed 2010; 14(1): 157-65. http://dx.doi.org/10.1109/TITB.2009.2034141 DOI: https://doi.org/10.1109/TITB.2009.2034141
Gani A, Gribok AV, Rajaraman S, Ward WK, Reifman J. Predicting subcutaneous glucose concentration in humans: Data-driven glucose modeling. IEEE Transactions on Biomedical Engineering 2009; 56(2): 246-54. http://dx.doi.org/10.1109/TBME.2008.2005937 DOI: https://doi.org/10.1109/TBME.2008.2005937
Facchinetti A, Sparacino G, Trifoglio E, Cobelli C. A new index to optimally design and compare continuous glucose monitoring glucose prediction algorithms. Diabetes technology & therapeutics 2011; 13(2): 111-9. http://dx.doi.org/10.1089/dia.2010.0151 DOI: https://doi.org/10.1089/dia.2010.0151
Dassau E, Cameron F, Lee H, Bequette BW, Zisser H, Jovanovič L, et al. Real-Time Hypoglycemia Prediction Suite Using Continuous Glucose Monitoring. Diabetes Care 2010; 33(6): 1249-54. http://dx.doi.org/10.2337/dc09-1487 DOI: https://doi.org/10.2337/dc09-1487
Cameron F, Niemeyer G, Gundy-Burlet K, Buckingham B. Statistical hypoglycemia prediction. Journal of diabetes science and technology 2008; 2(4): 612-21. http://dx.doi.org/10.1177/193229680800200412 DOI: https://doi.org/10.1177/193229680800200412
Eren-Oruklu M, Cinar A, Quinn L. Hypoglycemia prediction with subject-specific recursive time-series models. Journal of diabetes science and technology 2010; 4(1): 25-33. http://dx.doi.org/10.1177/193229681000400104 DOI: https://doi.org/10.1177/193229681000400104
Cobelli C, Renard E, Kovatchev B. Artificial pancreas: past, present, future. Diabetes 2011; 60(11): 2672-82. http://dx.doi.org/10.2337/db11-0654 DOI: https://doi.org/10.2337/db11-0654
Daskalaki E, Prountzou A, Diem P, Mougiakakou SG. Real-time adaptive models for the personalized prediction of glycemic profile in type 1 diabetes patients. Diabetes technology & therapeutics 2012; 14(2): 168-74. http://dx.doi.org/10.1089/dia.2011.0093 DOI: https://doi.org/10.1089/dia.2011.0093
Eren-Oruklu M, Cinar A, Quinn L, Smith DB. Estimation of Future Glucose Concentrationswith Subject-Specific Recursive Linear Models. Diabetes Technology & Therapeutics 2009; 11(4): 243-53. http://dx.doi.org/10.1089/dia.2008.0065 DOI: https://doi.org/10.1089/dia.2008.0065
Qian Wang PM, Saurabh Harsh, Kenneth Freeman, Jinyu Xie, Carol Gold, Mike Rovine, Jan Ulbrecht. Personalized State-space Modeling of Glucose Dynamics for Type 1 Dia-betes Using Continuously Monitored Glucose, Insulin Dose, and Meal IntakeAn Extended Kalman Filter Approach. J Diabet Sci Technol 2014; 8: 331-45. http://dx.doi.org/10.1177/1932296814524080 DOI: https://doi.org/10.1177/1932296814524080
Zanderigo F, Sparacino G, Kovatchev B, Cobelli C. Glucose Prediction Algorithms from Continuous Monitoring Data: Assessment of Accuracy via Continuous Glucose Error-Grid Analysis. Journal of Diabetes Science and Technology 2007; 1(5): 645-51. http://dx.doi.org/10.1177/193229680700100508 DOI: https://doi.org/10.1177/193229680700100508
The Juvenile Diabetes Research Foundation Continuous Glucose Monitoring Study Group. Continuous Glucose Monitoring and Intensive Treatment of Type 1 Diabetes. New England Journal of Medicine 2008; 359(14): 1464-76. http://dx.doi.org/10.1056/NEJMoa0805017 DOI: https://doi.org/10.1056/NEJMoa0805017
Engle RF, Ng VK. Measuring and Testing the Impact of News on Volatility. The Journal of Finance 1993; 48(5): 1749-78. http://dx.doi.org/10.1111/j.1540-6261.1993.tb05127.x DOI: https://doi.org/10.1111/j.1540-6261.1993.tb05127.x
Bollerslev T, Chou RY, Kroner KF. ARCH modeling in finance. A review of the theory and empirical evidence, Journal of Econometrics 1992; 52 5-59. http://dx.doi.org/10.1016/0304-4076(92)90064-X DOI: https://doi.org/10.1016/0304-4076(92)90064-X
Paul SK, Holman RR. A Generalized Autoregressive Conditional Heteroscedasticity Model (GARCH) to Analyze Continuous Blood Glucose Monitoring Data for Diabetic Patients. International Biometric Conference; 13 - 18 July 2008; Dublin, Ireland 2008.
Tsay RS. Analysis of Financial Time Series. 3, Revised ed: John Wiley & Sons, Inc. Publication; 2010. DOI: https://doi.org/10.1002/9780470644560
Mauras N, Beck R, Xing D, Ruedy K, Buckingham B, Tansey M, et al. A Randomized Clinical Trial to Assess the Efficacy and Safety of Real-Time Continuous Glucose Monitoring in the Management of Type 1 Diabetes in Young Children Aged 4 to <10 Years. Diabetes Care 2012; 35(2): 204-10. http://dx.doi.org/10.2337/dc11-1746 DOI: https://doi.org/10.2337/dc11-1746
Engle RF. Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica 1982; 50(4): 987-1007. http://dx.doi.org/10.2307/1912773 DOI: https://doi.org/10.2307/1912773
Lee JHH, King ML. A Locally Most Mean Powerful Based Score Test for ARCH and GARCH Regression Disturbances. Journal of Business & Economic Statistics 1993; 11(1): 17-27. DOI: https://doi.org/10.1080/07350015.1993.10509930
D'Agostino RB, Belanger A, D'Agostino RBJ. A Suggestion for Using Powerful and Informative Tests of Normality,The American Statistician 1990; 44(4): 316-21. DOI: https://doi.org/10.1080/00031305.1990.10475751
Wilhelmsson A. Garch Forecasting Performance under Different Distribution Assumptions. Journal of Forecasting 2006; 25: 561-278. http://dx.doi.org/10.1002/for.1009 DOI: https://doi.org/10.1002/for.1009
Patton AJ. Volatility forecast comparison using imperfect volatility proxies. Journal of Econometrics 2011; 160(1): 246-56. http://dx.doi.org/10.1016/j.jeconom.2010.03.034 DOI: https://doi.org/10.1016/j.jeconom.2010.03.034
Iscoe KE, Davey RJ, Fournier PA. Increasing the Low-Glucose Alarm of a Continuous Glucose Monitoring System Prevents Exercise-Induced Hypoglycemia Without Triggering Any False Alarms. Diabetes Care 2011; 34(6): e109. http://dx.doi.org/10.2337/dc10-2243 DOI: https://doi.org/10.2337/dc10-2243
Skladnev VN, Tarnavskii S, McGregor T, Ghevondian N, Gourlay S, Jones TW. Hypoglycemia alarm enhancement
using data fusion. Journal of Diabetes Science and Technology 2010; 4(1): 34-40. http://dx.doi.org/10.1177/193229681000400105 DOI: https://doi.org/10.1177/193229681000400105
Skladnev VN, Ghevondian N, Tarnavskii S, Paramalingam N, Jones TW. Clinical evaluation of a noninvasive alarm system for nocturnal hypoglycemia. Journal of diabetes science and technology 2010; 4(1): 67-74. http://dx.doi.org/10.1177/193229681000400109 DOI: https://doi.org/10.1177/193229681000400109
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