Correlation investigations between HbA1c and blood glucose indicators on type 1 diabetic Hungarian children

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1 Coelation investigations between HbA1c and blood glucose indicatos on tye 1 diabetic Hungaian childen T. Feenci *, A. Köne ** and L. Kovács * * Óbuda Univesity, John von Neumann Faculty of Infomatics, Physiological Contol Gou, Budaest, Hungay ** Semmelweis Univesity, 1 st Deatment of Paediatics, Budaest, Hungay. feenci.tamas@hd.uni-obuda.hu, kone.anna@med.semmelweis-univ.hu, kovacs.levente@nik.uni-obuda.hu Abstact Technological advancements in diabetes has imoved teatment ossibilities. The big amount of data obtained fom continuous glucose measuement (CGM) devices gave new investigation esectives of blood glucose vaiation and othe aametes connected to diabetic teatment. The aim of the ae is to investigate the elationshi between age, duation of diabetes and sex of the atient with blood glucose levels measued with continuous glucose monito. Blood glucose level was chaacteized with the elative time sent in hye- and hyoglycaemia, cental tendency (mean and median) and disesion (standad deviation and intequatile ange). These aametes wee measued on n=58 Hungaian childen suffeing fom tye 1 diabetes mellitus. The childen wee ooly contolled, with non-blinded continuous glucose monito efomed to otimize theay. The univaiate association between the afoementioned aametes was investigated with scattelots (with non-aametic smoothing), linea and Seaman-ρ coelation coefficients. Multivaiate stuctue was investigated with canonical coelation analysis. It was found that age and duation of diabetes was not significantly associated with any descito of blood glucose, but hemoglobin A1c (HbA1c) was ositively associated with time sent in hyeglycaemia (but not with hyoglycaemia), with cental tendency and with disesion. The association with disesion is likely a suious elationshi induced by the cental tendency (as a confounde). We obseved that the associations of the descitos with HbA1c ae nonmonotone, with a beak in the ositive coelation at 10%. We hyothesize that this is caused by the oo comliance of the atients, i.e. those in wose state inceasingly cheat duing CGM measuements, that is, they ay moe attention to thei blood glucose levels than what is usually done when no CGM measuement is esent; theefoe beaking the exected ositive, monotone association. I. INTRODUCTION The nomal blood glucose concentation level in the human body vaies in a naow ange (4-6 mmol/l). If fo some eason the human body is unable to contol the nomal glucose-insulin inteaction (e.g. the glucose concentation level is constantly out of the above mentioned ange), diabetes is diagnosed. The newest statistics of the Wold Health Oganization (WHO) edict that the diabetes oulation will be doubled in the next 20 yeas (fom 2010 to 2030) [1], which alams diabetic societies to eseach moe intensively this disease. New technological imovements in diabetes eesented secially by continuous glucose monitoing (CGM) techniques allows a moe ecise follow-u of the blood glucose changes in the human body. By thei 5 minutes measuement time (288 measuements in one day) CGM ossibilities have diect effect on shot tem monitoing, but questions aised also on long tem effects. The most imotant indicato in this sense is eesented by Hemoglobin A1c (HbA1c) that eflects the aveage glucose level of a atient ove 120 days (the life cycle of hemoglobin) [2]. Coelation of HbA1c and blood glucose is well known, but CGM ossibilities oened new hoizons in this investigation [3]-[5]. The aim of the cuent ae is connected to this toic and analysis elationshi between age, duation of diabetes and sex of the atient with blood glucose levels on tye 1 diabetes Hungaian childen. The ae is stuctued as follows. Section II esents the backgound of ou measuements and the consideed aametes, but also the statistical aaatus to be used. Section III highlights the esults obtained that ae discussed in Section IV. The ae ends with conclusions. II. MATERIALS AND METHODS A. Patient Data Investigated Hungaian childen (n=58), suffeing fom tye 1 diabetes mellitus (DM) wee selected as a convenience samle fom the 1 st Deatment of Paediatics of Semmelweis Univesity (Budaest, Hungay) database, with continuous glucose monitoing (CGM) measuement data between July 2009 and Febuay Patients wee ooly contolled, with CGM efomed to otimize theay. CGM measuements wee nonblinded to the atients. CGM ecodings wee electonically ocessed and the following aametes wee extacted fom the time seies of blood glucose (BG) measuements: Time sent in hyeglycemia and hyoglycemia elative to the whole length of the ecoding (hyoglycaemia was defined as BG < 3.9 mmol/l, hyeglycaemia was defined as BG > 10 mmol/l) in [%]. Cental tendency of BG levels (quantified with mean and median BG) in [mmol/l].

2 Disesion of BG levels (quantified with standad deviation and intequatile ange of BG) in [mmol/l]. In addition to these, the following aametes wee extacted fo each atient fom the electonic ecods of the hosital infomation system: Sex [male/female], Age [yeas], Time since onset of diabetes [yeas], HbA1C [%] at the time of the CGM measuement. Simle descitive statistics of these aametes fo the whole samle ae esented in Table I. B. Statistical Analysis As aleady discussed, ou aim was to analyze the connection between age, time since onset of diabetes, HbA1c and the aleady intoduced descitos of the CGM measuements. Fist, we efomed this analysis aiwise (i.e. we analyzed the connection between evey ossible (altogethe 3 6 = 18 ais). As evey vaiable was quantitative, measued on scale, this was essentially a question of coelation, which was investigated with gahical (scattelot) and analytical (calculation of coelation coefficients) methods. To allow fo the ossible non-linea elationshis, we calculated the Seaman-ρ coelation coefficient (a ank coelation coefficient that measues monotone connections geneally, not only linea connections [6]) in addition to the taditional (Peason-) linea coelation coefficient [7]. Also to facilitate the detection of non-linea connections, we lotted the LOWESS-estimatos [8] fo the nonaametic egession between the investigated vaiables on the scattelots. 95% confidence intevals fo the egession will be also shown. To efom a moe subtle analysis that incooates the intenal multivaiate stuctue of the two data sets, we also efomed a Canonical Coelation Analysis (CCA). TABLE I. MOST IMPORTANT DESCRIPTIVE STATISTICS OF THE INVESTIGATED PARAMETERS IN MEAN (MEDIAN) ± SD (IQR) [MIN-MAX] FORMAT Paamete Sex Descitive statistics 37 female, 21 male Age 12,3 (12,5) ± 3,7 (5,8) [4 18] Duation of DM 5,03 (4) ± 3,53 (5,75) [0 18] HbA1c 8,6 (8,2) ± 1,5 (1,8) [ ] Ratio of hyegly. 32,0 (30,8) ± 17,0 (21,4) [ ] Ratio of hyogly. 1,10 (0,50) ± 1,40 (1,30) [ ] Mean BG 8,85 (8,85) ± 1,28 (1,47) [ ] Median BG 8,47 (8,40) ± 1,42 (1,88) [ ] BG standad dev. 2,76 (2,81) ± 0,59 (0,62) [ ] BG IQR 3,84 (3,90) ± 1,00 (1,05) [ ] CCA aims to fom linea combinations (called canonical vaiables) of the vaiables in two sets of data (in this case: descitos of the BG measuements on the one hand, and age, duation of DM and HbA1c on the othe hand) such that the coelation of the fomed linea comosites will be maximal [9]. (Futhe combinations can be fomed by imosing a estiction that evey canonical vaiable is uncoelated with the evious canonical vaiables.) By insecting the coefficients of these linea combinations, it is ossible to daw conclusions on the common factos behind the two sets of data [10]. To actically achieve this, usually the coelation between the oiginal vaiables and the canonical vaiables (the socalled loadings) ae visualized (tyically fo the fist two canonical coelations) by lotting each oiginal vaiable as a oint on a two-dimensional lane, with the loadings being the coodinates. To test the significance of the canonical coelations, we calculated the classical F-aoximation of the Wilks- Λ test statistic [11], which ovides sequential test fo each canonical coelation. Dawback of this aoach is its asymtotical natue (i.e. eithe a ioi known multivaiate nomality is needed o lage samle so that cental limit theoem becomes effective). To mitigate this, we also calculated the significance fo the Wilks-Λ test statistic based on emutation test [12]. C. Pogams Used Statistical analysis and visualization was efomed unde the R statistical envionment, vesion [13]. Canonical coelation analysis was efomed using the CCA libay [14] and CCP libay [15]. The R scit develoed fo this uose is available at the coesonding autho on equest. III. RESULTS Scattelots fom the aiwise analyses ae shown on : Figue 1 (hye- and hyoglycaemia) Figue 2 (cental tendency of BG) Figue 3 (disesion of BG). The (asymmetic) coelation matices between the two sets of vaiables ae shown on: Table II (Peason linea coelation coefficient) Table III. (Seaman-ρ coelation coefficient) with -values fo the null hyothesis of no coelation. Canonical coelations between the two sets of vaiables wee ρ1=0.5593, ρ2= and ρ3= Unfotunately, -value fo the Wilks-Λ was (asymtotical), (emutation test) even fo the fist canonical coelation, so we wee not able to detect any significant canonical coelation. In the light of these, we used the aleady descibed gahical method uely descitively, i.e. to efom a visualization of the data, the esult of which is shown on Figue 4.

3 TABLE II. ASYMMETRIC CORRELATION MATRIX OF THE INVESTIGATED PARAMETERS (LINEAR CORRELATION COEFFICIENT WITH SIGNIFICANCE) Ratio of hyegly. Age DM length HbA1C -0,05-0,07 0,19 0,6938 0,6215 0,1547 Ratio of hyoglyc. Mean BG Median BG BG std. deviation BG IQR 0,00 0,04-0,13 0,9723 0,7613 0,3284-0,05-0,03 0,17 0,7322 0,8308 0,2142-0,06-0,01 0,11 0,6624 0,9225 0,4166 0,08-0,17 0,36 0,5391 0,2090 0,0049 0,10-0,08 0,42 0,4776 0,5719 0,0012 Figue 2. Scattelots with LOWESS-estimatos (dashed line) and 95% confidence intevals (shaded in gey) fo the cental tendency of BG (mean and median BG) vs. age, time since onset of DM and HbA1c. TABLE III. ASYMMETRIC CORRELATION MATRIX OF THE INVESTIGATED PARAMETERS (SPEARMAN-Ρ CORRELATION COEFFICIENT WITH SIGNIFICANCE) Figue 1. Scattelots with LOWESS-estimatos (dashed line) and 95% confidence intevals (shaded in gey) fo the time sent in hyeand hyoglycaemia vs. age, time since onset of DM and HbA1c. Ratio of hyegly. Ratio of hyoglyc. Mean BG Median BG BG std. deviation BG IQR Age DM length HbA1C ρ 0,02-0,07 0,14 0,9026 0,6152 0,3074 ρ 0,02 0,08-0,06 0,8675 0,5272 0,6580 ρ 0,04-0,03 0,11 0,7935 0,8112 0,3951 ρ 0,00-0,02 0,04 0,9915 0,9031 0,7561 ρ 0,05-0,17 0,23 0,7229 0,2125 0,0880 ρ 0,08-0,06 0,32 0,5643 0,6567 0,0138

4 Figue 4. Visualization of the esults of CCA: loadings fo diffeent investigated vaiables. Figue 3. Scattelots with LOWESS-estimatos (dashed line) and 95% confidence intevals (shaded in gey) fo the disesion of BG (SD and IQR of BG) vs. age, time since onset of DM and HbA1c. As fa as the cental tendency is concened, oughly the same can be said about age and duation of DM, with the excetion that both exhibit an initial deceasing hase (no matte whethe mean o median is used to chaacteize cental tendency), which seems to be moe significant fo age. Hee HbA1c again shows a clea ositive association both fo mean and median. The aadoxical non-monote egion aound 10% shows u again. The disesion of BG shows no association with age and duation of DM (neithe fo standad deviation, no fo intequatile ange). Howeve, with HbA1c thee is a clea ositive association (both fo standad deviation and intequatile ange). The aadoxical temoay tendchange aound 10% can be obseved again. Results of analytical investigations (i.e. the coelation coefficients) cooboate the above findings. Linea coelation coefficients ae insignificant with the excetion of BG standad deviation and BG intequatile ange vs. HbA1c. This comes as no suise given the fact that even in instances wee association was obseved on the scattelots, it was mostly non-linea, save fo this two. The alication of Seaman-ρ coelation coefficients yields simila esults (albeit the significance is wose even fo these two cases, which can be exlained by lowe owe of the moe geneal estimato and the elatively lage numbe of outlies). Note, that now we efomed 18 hyothesis testings in aallel (fo each coelation coefficient), so esults can not be comaed to the taditional theshold of 5% due to the multile comaisons situation [16]. Howeve, significant coelations esecially fo the linea coelation coefficient had a magnitude smalle - values, so the labeling of these as significant association is justified, even in the light of the multile comaisons situation. Canonical coelation analysis confims the association of HbA1c with SD and IQR of BG measuements (i.e. the disesion of BG), but also eveals a close connection to the atio sent in hyeglycaemia and the indicatos of the cental tendency of BG. It is vey inteesting to note that this henomenon was aleady seen to some extent on the scattelots, but was not aeciable fom the coelation coefficients. The age and duation of DM shows some association with the time sent in hye- and hyoglycaemia, and also with the indicatos of the cental tendency of BG, but not with the indicatos of the disesion of BG measuements. Fom these esults, the ositive association between the indicatos of the cental tendency of blood glucose and HbA1c is long known, even quantitatively [17]-[19]. The ositive association between the indicatos of the disesion and HbA1c, howeve, might be suising, given the hysiological mechanism govening the foming of HbA1c (which is elated to the level of BG not its disesion). This can be easily exlained by noting that the coelation coefficient between mean BG and BG standad deviation is 0.56, suggesting that the association between disesion and HbA1C is simly a suious elationshi induced by the cental tendency of BG (as a confounde).

5 The exlanation fo the seemingly aadoxical behavio of the association of HbA1C with the vaious descitos of BG is ossibly the oo comliance of the investigated childen. The motivation to cheat duing the CGMmeasuements (i.e. to ay close attention to BG levels than it is usually done by the childen) is highe fo those having wose metabolic state (as evidenced by HbA1C highe than 10%). Also, thee is not only a motivation, but also a ossibility fo this, given that the measuements wee non-blinded fo the childen. Hence, we hyothesize that childen above 10% HbA1c stat to inceasingly cheat duing CGM measuement, beaking the association between HbA1c and the mean (o median) glucose duing CGM. IV. CONCLUSION Ou esults confimed the well-known ositive association of HbA1c with the indicatos of the cental tendency of blood glucose (mean, median), and demonstated that hyeglycaemia (but not hyoglycaemia) is also ositively associated with HbA1C. The ositive association of HbA1C with the indicatos of the disesion of blood glucose is likely a suious elationshi induced by the mean blood glucose (as a confounde). The elationshi between HbA1c and the indicatos of the cental tendency of blood glucose ae non-linea, which is likely caused by the vaying comliance of the atients. We found no association between the duation of the diabetes and the age of the atient with any indicato of the blood glucose levels. Howeve, othe modeling techniques will be investigated simila to [20], [21], [22]. ACKNOWLEDGMENT Levente Kovács is suoted by the János Bolyai Reseach Scholashi of the Hungaian Academy of Sciences. REFERENCES [1] J. E. Shaw, R. A. Sicee and P. Z. Zimmet, Global Estimates of the Pevalence of Diabetes fo 2010 and 2030,. Diab Res Clin Pact, vol. 87,. 4-14, [2] D. LeRoith, S. I. Taylo and J. M. Olefsky, Diabetes Mellitus. A fundamental and clinical text, 3 d ed, Liincott Williams & Wilkins, [3] J. K. Nielsen, C. H. Gavholt, C. B. Djuhuus, D. Bandt, J. Becke, L. Heinemnn and J. S. Chistiansen, Continuous Subcutaneous Glucose Monitoing Shows a Close Coelation between Mean Glucose and Time Sent in Hyeglycemia and Hemoglobin A1c, J Diab Sci & Tech, vol. 1 (6), , [4] R. Mazze, The Futue of Self-Monitoed Blood Glucose:Mean Blood Glucose Vesus Glycosylated Hemoglobin, Diab Tech & Thea, vol. 10 (1),. S-93 S-101, [5] K. Sikais, The Coelation of Hemoglobin A1c to Blood Glucose, J Diab Sci & Tech, vol. 3 (3), , [6] M. Hollande and D. A. Wolfe, Nonaametic statistical methods, New Yok, Wiley, [7] P. Amitage, G. Bey and J. N. S. Matthews, Statistical Methods in Medical Reseach, 4 th ed, Blackwell, Malden, [8] W. S. Cleveland, E. Gosse and W. M. Shyu, Local egession models, in Statistical Models in S, J. M. Chambes and T. J. Hastie, Eds. Wadswoth & Books/Cole, [9] R. A. Johnson and D. W. Wichen, Alied Multivaiate Statistical Analysis, 6 th ed., Pentice Hall, [10] A. Shey and R. K. Henson, Conducting and Inteeting Canonical Coelation Analysis in Pesonality Reseach: A Use- Fiendly Pime, J Pesonality Assessment, vol. 84, , [11] T. W. Andeson, An Intoduction to Multivaiate Statistical Analysis, Wiley-Intescience, 3 d ed., [12] B. Efon and R. J. Tibshiani, An Intoduction to the Bootsta, Chaman & Hall, New Yok, [13] R Coe Team, R, A language and envionment fo statistical comuting, R Foundation fo Statistical Comuting, Vienna, Austia, [14] I. Gonzalez and S. Dejean, CCA: Canonical coelation analysis, R ackage vesion 1.2, [15] U. Menzel, CCP: Significance Tests fo Canonical Coelation Analysis (CCA), R ackage vesion 1.1, [16] R. G. Mille, Simultaneous Statistical Infeence, 2 nd ed, Singe, New Yok, [17] D. M. Nathan, J. Kuenen, R. Bog, H. Zheng, D. Schoenfeld and R. J. Heine, Tanslating the A1C Assay Into Estimated Aveage Glucose Values, Diabetes Ca, vol. 31, [18] K. Makis and L. Sanou, Is Thee a Relationshi between Mean Blood Glucose and Glycated Hemoglobin?, Jounal of Diabetes Science and Technology, vol. 5, [19] D. B. Sacks, Coelation between Hemoglobin A1c (HbA1c) and Aveage Blood Glucose: Can HbA1c Be Reoted as Estimated Blood Glucose Concentation?, Jounal of Diabetes Science and Technology, vol. 1, [20] I. B. Wilson and P. D. Cleay, Linking Clinical Vaiables With Health-Related Quality of Life. A Concetual Model of Patient Outcomes, Jounal of the Ameican Medical Association, vol.273(1), , [21] M. Badida, R. Kalikova, and E. Lumnitze, Modeling and the use of simulation methods fo the design of lighting systems, Acta Polytechnica Hungaica, vol. 8(2), , [22] K. C. Johnston, A. F. Connos J, D. P. Wagne, W. A. Knaus, X. Q. Wang and E. Clake Haley J, A Pedictive Risk Model fo Outcomes of Ischemic Stoke, Stoke, vol. 31,