Research Article Delay in the Detrended Fluctuation ...downloads.hindawi.com/journals/jdr/2016/9361958.pdfResearch Article Delay in the Detrended Fluctuation Analysis Crossover Point

Research ArticleDelay in the Detrended Fluctuation Analysis Crossover Point asa Risk Factor for Type 2 Diabetes Mellitus

Manuel Varela1 Luis Vigil1 Carmen Rodriguez1

Borja Vargas2 and Rafael Garciacutea-Carretero1

1Servicio de Medicina Interna Hospital Universitario de Mostoles Rio Jucar sn Mostoles 28935 Madrid Spain2European University of Madrid Villaviciosa de Odon Spain

Correspondence should be addressed to Manuel Varela manuelvarelasaludmadridorg

Received 3 February 2016 Revised 11 April 2016 Accepted 27 April 2016

Academic Editor Janet H Southerland

Copyright copy 2016 Manuel Varela et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Detrended FluctuationAnalysis (DFA)measures the complexity of a glucose time series obtained bymeans of aContinuousGlucoseMonitoring System (CGMS) and has proven to be a sensitive marker of glucoregulatory dysfunction Furthermore some authorshave observed a crossover point in the DFA signalling a change of dynamics arguably dependent on the beta-insular function Weinvestigate whether the characteristics of this crossover point have any influence on the risk of developing type 2 diabetes mellitus(T2DM) To this endwe recruited 206 patients at increased risk of T2DM(because of obesity essential hypertension or a first-degreerelative with T2DM) A CGMS time series was obtained from which the DFA and the crossover point were calculated Patientswere then followed up every 6 months for a mean of 175 months controlling for the appearance of T2DM diagnostic criteria Thetime to crossover point was a significant predictor risk of developing T2DM even after adjusting for other variables The angle ofthe crossover was not predictive by itself but became significantly protective when the model also considered the crossover pointIn summary both a delay and a blunting of the crossover point predict the development of T2DM

1 Introduction

Glycaemic variability is considered a risk factor for dia-betic complications over and above raw glycaemic levels(as measured through fasting blood glucose or glycosylatedhaemoglobin) [1ndash3] However there is still controversy aboutwhich metric should be used to assess these dynamic aspects[4] Conventional statistics (standard deviation coefficientof variability) have the pitfall of considering every measureas independent thus overlooking an essential part of thetime series its sequentiality Mean Amplitude of GlycaemicExcursions (MAGE) takes sequentiality into account butfixes an arbitrary threshold of ldquosignificantrdquo excursions thusoverlooking the fine-grain regulation

Complexity analysis of glucose time series measuredby means of Detrended Fluctuation Analysis (DFA) hasemerged as a useful alternative and is increasingly being usedas a standard to measure glucose dynamics especially in

diabetic patients [5ndash15] In all of these papers there is a con-sistent correlation between loss of complexity (ie increasedDFA) and glucoregulatory dysfunction

Ogata et al [9] have also described a crossover pointin DFA located approximately in the 2-hour time windowFurthermore they observed a decrease in long-range neg-ative correlations (ie decreased complexity in large timewindows) in patients with diabetes [11] Although DFA hasmainly been used in patients with diabetes several paperssuggest that there is a progressive fall in complexity (ieincrease in DFA) as a patient walks his way from healththrough the prediabetes states to full-blown type 2 diabetesmellitus (T2DM) [6 9ndash12 15ndash17]

The present study intends to analyse the characteristicsof the DFA crossover point in a population with high riskof becoming diabetic and to find out if these character-istics may have any influence on the risk of developingT2DM

Hindawi Publishing CorporationJournal of Diabetes ResearchVolume 2016 Article ID 9361958 6 pageshttpdxdoiorg10115520169361958

2 Journal of Diabetes Research

2 Methods

21 Patients A sample of 262 patients from the InternalMedicine Outpatient Clinic and the Vascular Risk Unit ofthe University Hospital of Mostoles were selected based onan assumed increased risk of developing T2DM The maincharacteristics of this sample have been published previously[12] The inclusion criteria were an HbA1c gt 5 and lt65and any of the following

(i) essential hypertension(ii) BMI ge 30Kgm2(iii) a first-degree relative with a diagnosis of T2DM

Patients were excluded if they had a diagnosis of DM or wereon drugs that could interfere with glucose regulation (egglucocorticoids)

After an interview physical exam and routine biochem-ical tests a 3-day glucometry was performed by meansof a Continuous Glucose Monitoring System device (iProMedtronicMiniMed Northridge CAUSA)The glucometrywas obtained in an ambulatory setting while the patientfollowed his normal life with no special dietary restrictionsThe patient was thereafter followed up every 6 months with aclinical visit and routine biochemical tests The present studyis an interim analysis on the projectrsquos third year

The main outcome was a diagnosis of T2DM (basal gly-caemia ge 70mmolL glycosylated haemoglobin (HbA1c) ge65 or starting on antidiabetic drugs)

22 DFA and Crossover From the glucometry obtained atadmission a clean 24-hour-long time series was selectedfor each patient Whenever possible the selected 24-hoursequence started at 0800 AM the day after the deviceinsertion to avoid the stressful hours in the hospital If therewere missing values these were obtained by interpolationas long as the missing string was lt3 consecutive values Ifthere were three or more consecutive missing values another24-hour period was selected If no adequate 24-hour periodwas found the time series was considered unsuitable anddiscarded

Each selected series was thus composed of 288 consecu-tive measures of interstitial glucose sampled every 51015840

Each time series was submitted to Detrended FluctuationAnalysis without previous integration A full description ofDFA may be consulted in [18] A brief description can befound in [12] and a basic introductory video is available athttpwwwcomplexity-at-the-bedsideorgcomplexitytuto-rials

In essence DFA estimates the degree of long-rangecorrelationswithin a signal analysing how the time series andits linear regression diverge as the ldquotime windowrdquo consideredincreases (Figure 1) Metaphorically one could consider thelinear regression of each time window as a ldquomaprdquo of a certainldquoterritoryrdquo As the time windows increase the regressionrsquosfitness deteriorates and thus the ldquomap-to-territory gaprdquoincreases The rate at which this gap increases reflects howthe informational content of the time series is distributedA high-complexity time series will have comparatively more

information encoded in the small windows Conversely low-complexity time series will have more information encodedin the large time windows and therefore the ldquomap-to-territory gaprdquo will be increasing at a steady pace well intolarger time windows

Specifically we submitted the time series (without pre-treatment by integration) to detrending with a windowingsequence of 3 4 6 8 9 12 16 18 24 32 36 48 72 96 144and 288 points (corresponding to time windows of 151015840 201015840301015840 401015840 451015840 601015840 801015840 901015840 1201015840 1601015840 1801015840 2401015840 3601015840 48010158407201015840 and 14401015840)

For each time window a ldquomap-to-territory gaprdquo wascalculated

119865119899 = radic1

119873

119873

sum

119896=1

[119910 (119896) minus 119910119899(119896)]2

(1)

A log(119865119899) sim log(time window) was drawn for each glucome-try with 16 points (the aforementioned time windows)

Next a set of pairs of linear regressions was built forseveral combinations of points (ie points 1ndash4 for the firstlimb and 5ndash16 for the second then 1ndash5 and 6ndash16 then 1ndash6 and7ndash16 etc until 1ndash11 and 12ndash16) (Figure 2)

A combined weighted 1198772 was obtained for each pairof regression lines and the best-fit pair was selected asthe best representation of the time series The abscissa ofthe intersection of both limbs expressed in minutes wasconsidered the crossover point and the angle was from thedifference between the slopes of the two limbs The slope ofthe first and second limb was assumed to be the DFA for theshort and long time windows respectively

23 Statistical Analysis Comparison between admitted andexcluded patients was performed by means of 119905-test (forquantitative variables) or Chi-square test (for qualitativevariables)

The effect of the various variables was analysed bymeans of a multivariate Cox proportional hazard survivalanalysis The statistical analysis was performed in R (R(httpwwwr-projectorg)) Significance was set at two-tailed 119901 lt 005 although 119901 lt 010 were also displayed

3 Results

Of the 262 patients initially included 40were finally excludedbecause we were not able to obtain a suitable glucometry15 patients had no follow-up visits and one patient wasexcluded because she started on high-dose glucocorticoidsdue to a facial palsy Except for a slightly lower diastolicblood pressure (739mmHg versus 781mmHg 119901 = 001)there were no major differences between admitted andexcluded patients regarding anthropometric physical examor analytical parameters Thus exclusion did not seem tocarry any bias

The 206 patients finally included were followed up for amean of 18 months (IQR 15) (Table 1) There were 18 events(T2DM new diagnoses) for an incidence of 582 cases1000patients-year

Journal of Diabetes Research 3

Time

70

80

90

100

110

Glu

c

(a)Time

70

80

90

100

110

Glu

c

(b)

Time

70

80

90

100

110

Glu

c

(c)

minus1

0

1

2

log(Fn)

2 3 4 51

log(time window)

(d)

Figure 1 DFA analyses how the time series (the ldquoterritoryrdquo) and its representation through linear regression (the ldquomaprdquo) diverge as the timewindow considered increases (a) (b) and (c) display this ldquoterritory versus map gaprdquo (grey area) with three different time windows (a) One-hour time window (12 points in each regression line) (b) Six-hour time window (36 points in each regression line) (c) Twenty-four-hourtime window (288 points in the regression line) The complete windowing sequence used was 3 4 6 8 9 12 16 18 24 32 36 48 72 96 144and 288 points (corresponding to time windows of 151015840 201015840 301015840 401015840 451015840 601015840 801015840 901015840 1201015840 1601015840 1801015840 2401015840 3601015840 4801015840 7201015840 and 14401015840) (d)plots the log(ldquomap-to-territory gaprdquo) versus log(time window)The slope of a regression line through this set of points (not shown) would bethe DFA of the time series (not considering the crossover)

The median to the crossover point was 114min (IQR647min) and themedian angle between the first limb (smalltime windows before the crossover point) and the secondlimb (large time windows) was 064 radians (IQR 017 rad)

In a Cox proportional hazard ratio model the crossoverpoint was a significant risk factor for the development ofT2DM (120573 = 0015 119901 lt 0001) This implied a hazard rateof 153 for every 30-minute delay in crossover These resultsdid not change significantly when adjusting for other relevantvariables whether anthropometric (gender age body massindex and waist circumference) clinical (blood pressure andfirst-degree relatives with diabetes) or analytical (HbA1cinsulin mean glucose glucose standard deviation MAGE

HOMA or global DFA)When adjusting for basal glycaemiathe effect of crossover did not attain significance although itpersisted as a trend (119901 = 008)

The crossover angle had no significant influence on thedevelopment of T2DM when considered alone (120573 = minus243119901 = 015) but became significantly protective when themodel considered also the crossover point (120573 = minus4172 119901 =0005) Similarly neither the DFA of the first nor the secondlimb (before and after the crossover) alone had significantinfluence on the hazard rate of developing T2DM (dfa1 120573 =minus0475 119901 = 0735 dfa2 120573 = 1452 119901 = 0279) but they bothbecame significant when adjusting for the crossover point(dfa1 120573 = 4876 119901 = 0018 dfa2 120573 = 4050 119901 lt 0001)


Table 1 Patients characteristics

History and physical examAge (years) (median IQR) 61 (13)Gender (FM) 101105Smoking habit () 23 (11)Relatives with T2DM () 55 (28)Systolic BP (mmHg) (median IQR) 1335 (1925)Diastolic BP (mmHg) (mean SD) 782 (90)BMI (Kgm2) (median IQR) 30 (6)Abdominal perimeter (cm) (mean SD)

Men 1045 (101)Women 992 (121)

Complementary testsBasal glycaemia (mmolL) (mean SD) 556 (062)HbA1c () (median IQR) 576 (03)IFG () 105 (51)HbA1c ge 383mmolmol () 129 (66)HDL-cholesterol (median IQR)

Men 135 (035)Women 150 (032)

Triglycerides (mmolL) (median IQR) 0125 (071)EPI-GFR (mLmin173m2) (mean SD) 930 (95)Insulin (mlUL) (median IQR) 117 (95)HOMA-index (median IQR) 306 (227)Albuminuria (mggr creatinine) (median IQR) 278 (615)Number of ATP-III MS defining criteria (median IQR) 2 (1)Number of patients complying with the ATP-III MS definition (ge3 criteria) 100 (49)

GlucometryMedian glucose of the time series (median IRQ) 544 (089)Median SD of the time series (median IRQ) 081 (041)CV () glucose time series (median IQR) 142 (67)MAGE (mgdL) (median IQR) 365 (229)DFA (whole time series) (mean SD) 090 (009)

CrossoverTime to crossover (min) (mean IQR) 1140 (647)Crossover angle (rad) (mean IQR) 064 (017)DFA first limb (mean IQR) 153 (023)DFA second limb (mean IQR) 036 (024)T2DM type 2 diabetes mellitus BP blood pressure BMI body mass index IFG impaired fasting glucose (basal glucose ge 100mgdL) EPI-GFR estimatedglomerular filtration rate (EPI-creatinine equation) HOMA homeostasis model assessment MS metabolic syndrome CV coefficient variationMAGEmeanaverage glucose excursions DFA Detrended Fluctuation AnalysisMean and standard deviation for normally distributed variables and median and interquartile range for nonnormally distributed variables

4 Discussion

DFA analyses how the correlation between successive pointsevolve as the time-window considered increases Followingthe conventional homeostatic paradigm a healthy physio-logical system should promptly detect trends and unleashmechanisms to correct them Therefore it is reasonable toexpect a deterioration in the fit of the regression line as thetime windows increase Furthermore one would expect thatas the physiological system becomes old or dysfunctional itsresponse will become ldquosluggishrdquo and the decorrelation willbe slower This loss of sharpness (ie loss of complexity)is displayed as an increase in DFA Indeed there is ample

evidence relating diabetesmellituswith an increase in glucosetime seriesrsquo DFA [6 7 9ndash12 16]

An important advantage of DFA with respect to otherconventional dynamic metrics (ie coefficient of variabilityor MAGE) is that it considers the time series as a whole notas a set of independent measurements (as with the coefficientof variability) nor does it make any assumptions on theldquosignificancerdquo of each glycaemic excursion (as with MAGE)

Glucoregulation is a rather asymmetric system whilethere are at least four main counterregulatory hormonalsystems in charge of fighting hypoglycaemia (glucagonalpha-sympathomimetics glucocorticoids and growthhormone) there is only one strictly antihyperglycaemic


minus1

0

1

2

log(Fn)

2 3 4 51

log(time window)

Figure 2 To calculate the crossover point a set of pairs of linearregression lines are built with several combinations of points points1ndash4 for the first limb and 5 16 for the second then 1 5 and 6 16then 1 6 and 1 16 and so on until 1 11 and 12 16 A combined 1198772is calculated for each pair of regression lines and the best-fit pairis assumed to be the best representation of the time series In thisfigure the shade of the regression lines represents the goodness offit (darker grey better fit) The best fit is represented by a solid lineThe abscissa of the intersection between both limbs is the crossoverpoint (represented as log(number of measurements per window))To obtain the time (in minutes) for a value 119909 crossover (minutes) =119890(5sdot119909)

hormone namely insulinThis has obvious evolutionary jus-tifications (short-term hypoglycaemia is far more dangerousthan hyperglycaemia) butmay cause significant differences inthe counterregulatory dynamics While the hyperglycaemicdrift may be a swift multisystem driven reaction theantihyperglycaemic push is mainly a one-man job and maytherefore havemore abrupt characteristics Arguably thismayexplain the dynamic change underlying the crossover pointdescribed by Ogata et al [9] If this were the case it wouldbe reasonable to expect a progressive delay (and fading) ofthis dynamic change as the beta-function deteriorates longbefore its failure allows for the diagnosis of diabetes

Our findings of a delay in the crossover point and ablunting of the angle between both limbs as prognostic factorsfor the development of T2DM in patients at increased risk arecongruent with this hypothesis Arguably this may representboth a delay and a dampening of the insulin kick-in andmay reveal an early dysfunction of glucoregulation Thisshould be further confirmed by means of conventional beta-function examination However our model has significantadvantages over other experimental evaluations of beta-function it may be applied in real-life situations rather thanin the laboratory it is much simpler and it displays thefunctioning of the glucoregulatory system as a whole not asthe specific response to a certain glycaemic load or insulininfusion

We may be starting to have drugs available that can delayor prevent the evolution toT2DMin subjects at risk [19ndash23] Itwill be crucial to identify those patients whowould eventually

GlycaemiaIntegrated glycaemia

Time (24 hours)minus800

minus400

0

200

Inte

grat

ed g

lyca

emia

80

100

120

140

Gly

caem

ia

Figure 3 Glycaemia (solid line left axis) and integrated glycaemia(dashed line right axis) Generally before proceeding to thedetrending process mentioned in Figure 1 most authors preprocessthe time series through integration 119910(119896) = sum119896

119894=1(119866119894minus 119866mean) where

119910(119896) is the integrated value 119866119894is each individual measurement and

119866mean is the mean of the series The resulting integrated time seriescomplies with the conventional random-walk model and thus iseasier to interpret However this standardization comes at the priceof a significant smoothing of the time-series profile thus arguablyloosing significant information

walk all their way to diabetes in order to better target thera-peutic interventions Classic variables (basal glycaemia oralglucose tolerance test and HbA1c) are probably insufficientand it is not through fine-tuning thresholds that this problemwill be solved Arguably glucodynamic techniques studyinghow glucose levels fluctuate in time may afford a fresh newinsight into this problem

It should be mentioned that contrary to most studieswith DFA in glycaemia we have not preprocessed the timeseries through integration before performing the sliding-windows fluctuation analysis This arguably takes us out ofthe conventional random-walk model and the standard 15threshold of ldquobrownrdquo noise (integrated random series) DFAcannot be applied Our model is therefore only a tool tocompare different time series (within similar series lengthand time windows) However integrating the time serieserases important information (eg Figure 3 displays thesame time series with and without pretreatment throughintegration) and we believe that preserving this informationis worth the loss of standardization caused by omitting theconversion to a random-walk model DFA measures thecomplexity of a time series by evaluating how the ldquomap-territory gaprdquo enlarges (ie how the linear regression andthe curve diverge) as the time window increases and thusprovides a usefulmeasure of the seriesrsquo entropy even omittingthe random-walk model

We have run the same analysis before treating the timeseries through integration and although the same tendenciespersist the crossover effects are much less obvious and oftendo not reach statistical significance

41 Study Limitations Oral glucose tolerance tests were notperformed and thus neither Impaired Glucose Tolerance norinsulin response to OGTT could be analysed


The notion that a delay in crossover represents a damp-ening of beta-function is only a hypothesis and needs confir-mation through conventional experimental tests

5 Conclusions

The characteristics of the crossover phenomenon have pre-dictive value for the development of T2DM in patients atrisk and may provide a sensitive and easy way to explore theearliest signs of glucoregulatory failure

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

The present study was supported by Grant 1100811 from theFondo de Investigacion Sanitaria Ministerio de Sanidad yConsumo Spain and FEDER (Fondo Europeo de DesarrolloRegional)

References

[1] A Ceriello K Esposito L Piconi et al ldquoOscillating glucose ismore deleterious to endothelial function and oxidative stressthan mean glucose in normal and type 2 diabetic patientsrdquoDiabetes vol 57 no 5 pp 1349ndash1354 2008

[2] LMonnier EMas C Ginet et al ldquoActivation of oxidative stressby acute glucose fluctuations compared with sustained chronichyperglycemia in patients with type 2 diabetesrdquo The Journal ofthe AmericanMedical Association vol 295 no 14 pp 1681ndash16872006

[3] M Muggeo G Zoppini E Bonora et al ldquoFasting plasmaglucose variability predicts 10-year survival of type 2 diabeticpatients the Verona Diabetes Studyrdquo Diabetes Care vol 23 no1 pp 45ndash50 2000

[4] R M Bergenstal ldquoGlycemic variability and diabetes compli-cations does it matter simply put there are better glycemicmarkersrdquo Diabetes Care vol 38 no 8 pp 1615ndash1621 2015

[5] R Brunner G Adelsmayr H Herkner C Madl and UHolzinger ldquoGlycemic variability and glucose complexity incritically ill patients a retrospective analysis of continuousglucose monitoring datardquo Critical Care vol 16 no 5 articleR175 2012

[6] J Churruca L Vigil E Luna J Ruiz-Galiana and M VarelaldquoThe route to diabetes loss of complexity in the glycemicprofile from health through the metabolic syndrome to type 2diabetesrdquo Diabetes Metabolic Syndrome and Obesity vol 1 pp3ndash11 2008

[7] K-D Kohnert P Heinke L Vogt P Augstein and ESalzsieder ldquoDeclining 120573-cell function is associated with thelack of long-range negative correlation in glucose dynamicsand increased glycemic variability a retrospective analysis inpatients with type 2 diabetesrdquo Journal of Clinical and Transla-tional Endocrinology vol 1 no 4 pp 192ndash199 2014

[8] K Lundelin L Vigil S Bua I Gomez-Mestre T Honrubiaand M Varela ldquoDifferences in complexity of glycemic profile

in survivors and nonsurvivors in an intensive care unit a pilotstudyrdquo Critical Care Medicine vol 38 no 3 pp 849ndash854 2010

[9] HOgata K Tokuyama SNagasaka et al ldquoLong-range negativecorrelation of glucose dynamics in humans and its break-down in diabetes mellitusrdquo American Journal of PhysiologymdashRegulatory Integrative and Comparative Physiology vol 291 no6 pp R1638ndashR1643 2006

[10] H Ogata K Tokuyama S Nagasaka et al ldquoLong-range corre-lated glucose fluctuations in diabetesrdquo Methods of Informationin Medicine vol 46 no 2 pp 222ndash226 2007

[11] H Ogata K Tokuyama S Nagasaka et al ldquoThe lack of long-range negative correlations in glucose dynamics is associatedwith worse glucose control in patients with diabetes mellitusrdquoMetabolism Clinical and Experimental vol 61 no 7 pp 1041ndash1050 2012

[12] M Varela C Rodriguez L Vigil E Cirugeda A Colas and BVargas ldquoGlucose series complexity at the threshold of diabetesrdquoJournal of Diabetes vol 7 no 2 pp 287ndash293 2015

[13] L Vigil E Condes M Varela et al ldquoGlucose series complexityin hypertensive patientsrdquo Journal of the American Society ofHypertension vol 8 no 9 pp 630ndash636 2014

[14] N Yamamoto Y Kubo K Ishizawa et al ldquoDetrended fluc-tuation analysis is considered to be useful as a new indicatorfor short-term glucose complexityrdquo Diabetes Technology andTherapeutics vol 12 no 10 pp 775ndash783 2010

[15] L Crenier M Lytrivi A Van Dalem B Keymeulen and BCorvilain ldquoGlucose complexity estimates insulin resistance ineither nondiabetic individuals or in type 1 diabetesrdquoThe Journalof Clinical EndocrinologyampMetabolism vol 101 no 4 pp 1490ndash1497 2016

[16] J-L Chen P-F Chen andH-MWang ldquoDecreased complexityof glucose dynamics in diabetes evidence from multiscaleentropy analysis of continuous glucose monitoring systemdatardquo American Journal of PhysiologymdashRegulatory IntegrativeandComparative Physiology vol 307 no 2 pp R179ndashR183 2014

[17] M D Costa T Henriques M N Munshi A R Segal and A LGoldberger ldquoDynamical glucometry use of multiscale entropyanalysis in diabetesrdquo Chaos vol 24 no 3 p 033139 2014

[18] C-K Peng S Havlin H E Stanley and A L GoldbergerldquoQuantification of scaling exponents and crossover phenomenain nonstationary heartbeat time seriesrdquo Chaos vol 5 no 1 pp82ndash87 1995

[19] M Bergman ldquoPathophysiology of prediabetes and treatmentimplications for the prevention of type 2 diabetes mellitusrdquoEndocrine vol 43 no 3 pp 504ndash513 2013

[20] M Lilly andMGodwin ldquoTreating prediabetes withmetforminsystematic review and meta-analysisrdquo Canadian Family Physi-cian vol 55 no 4 pp 363ndash369 2009

[21] S K Malin R Gerber S R Chipkin and B Braun ldquoIndepen-dent and combined effects of exercise training and metforminon insulin sensitivity in individuals with prediabetesrdquo DiabetesCare vol 35 no 1 pp 131ndash136 2012

[22] O J Phung W L Baker V Tongbram A Bhardwaj andC I Coleman ldquoOral antidiabetic drugs and regression fromprediabetes to normoglycemia a meta-analysisrdquo Annals ofPharmacotherapy vol 46 no 4 pp 469ndash476 2012

[23] R E Ratner and A Sathasivam ldquoTreatment recommendationsfor prediabetesrdquoMedical Clinics of North America vol 95 no 2pp 385ndash395 2011

Submit your manuscripts athttpwwwhindawicom

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Evidence-Based Complementary and Alternative Medicine

Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom


2 Methods

21 Patients A sample of 262 patients from the InternalMedicine Outpatient Clinic and the Vascular Risk Unit ofthe University Hospital of Mostoles were selected based onan assumed increased risk of developing T2DM The maincharacteristics of this sample have been published previously[12] The inclusion criteria were an HbA1c gt 5 and lt65and any of the following

(i) essential hypertension(ii) BMI ge 30Kgm2(iii) a first-degree relative with a diagnosis of T2DM

Patients were excluded if they had a diagnosis of DM or wereon drugs that could interfere with glucose regulation (egglucocorticoids)

After an interview physical exam and routine biochem-ical tests a 3-day glucometry was performed by meansof a Continuous Glucose Monitoring System device (iProMedtronicMiniMed Northridge CAUSA)The glucometrywas obtained in an ambulatory setting while the patientfollowed his normal life with no special dietary restrictionsThe patient was thereafter followed up every 6 months with aclinical visit and routine biochemical tests The present studyis an interim analysis on the projectrsquos third year

The main outcome was a diagnosis of T2DM (basal gly-caemia ge 70mmolL glycosylated haemoglobin (HbA1c) ge65 or starting on antidiabetic drugs)

22 DFA and Crossover From the glucometry obtained atadmission a clean 24-hour-long time series was selectedfor each patient Whenever possible the selected 24-hoursequence started at 0800 AM the day after the deviceinsertion to avoid the stressful hours in the hospital If therewere missing values these were obtained by interpolationas long as the missing string was lt3 consecutive values Ifthere were three or more consecutive missing values another24-hour period was selected If no adequate 24-hour periodwas found the time series was considered unsuitable anddiscarded

Each selected series was thus composed of 288 consecu-tive measures of interstitial glucose sampled every 51015840

Each time series was submitted to Detrended FluctuationAnalysis without previous integration A full description ofDFA may be consulted in [18] A brief description can befound in [12] and a basic introductory video is available athttpwwwcomplexity-at-the-bedsideorgcomplexitytuto-rials

In essence DFA estimates the degree of long-rangecorrelationswithin a signal analysing how the time series andits linear regression diverge as the ldquotime windowrdquo consideredincreases (Figure 1) Metaphorically one could consider thelinear regression of each time window as a ldquomaprdquo of a certainldquoterritoryrdquo As the time windows increase the regressionrsquosfitness deteriorates and thus the ldquomap-to-territory gaprdquoincreases The rate at which this gap increases reflects howthe informational content of the time series is distributedA high-complexity time series will have comparatively more

information encoded in the small windows Conversely low-complexity time series will have more information encodedin the large time windows and therefore the ldquomap-to-territory gaprdquo will be increasing at a steady pace well intolarger time windows

Specifically we submitted the time series (without pre-treatment by integration) to detrending with a windowingsequence of 3 4 6 8 9 12 16 18 24 32 36 48 72 96 144and 288 points (corresponding to time windows of 151015840 201015840301015840 401015840 451015840 601015840 801015840 901015840 1201015840 1601015840 1801015840 2401015840 3601015840 48010158407201015840 and 14401015840)

For each time window a ldquomap-to-territory gaprdquo wascalculated

119865119899 = radic1

119873

119873

sum

119896=1

[119910 (119896) minus 119910119899(119896)]2

(1)

A log(119865119899) sim log(time window) was drawn for each glucome-try with 16 points (the aforementioned time windows)

Next a set of pairs of linear regressions was built forseveral combinations of points (ie points 1ndash4 for the firstlimb and 5ndash16 for the second then 1ndash5 and 6ndash16 then 1ndash6 and7ndash16 etc until 1ndash11 and 12ndash16) (Figure 2)

A combined weighted 1198772 was obtained for each pairof regression lines and the best-fit pair was selected asthe best representation of the time series The abscissa ofthe intersection of both limbs expressed in minutes wasconsidered the crossover point and the angle was from thedifference between the slopes of the two limbs The slope ofthe first and second limb was assumed to be the DFA for theshort and long time windows respectively

23 Statistical Analysis Comparison between admitted andexcluded patients was performed by means of 119905-test (forquantitative variables) or Chi-square test (for qualitativevariables)

The effect of the various variables was analysed bymeans of a multivariate Cox proportional hazard survivalanalysis The statistical analysis was performed in R (R(httpwwwr-projectorg)) Significance was set at two-tailed 119901 lt 005 although 119901 lt 010 were also displayed

3 Results

Of the 262 patients initially included 40were finally excludedbecause we were not able to obtain a suitable glucometry15 patients had no follow-up visits and one patient wasexcluded because she started on high-dose glucocorticoidsdue to a facial palsy Except for a slightly lower diastolicblood pressure (739mmHg versus 781mmHg 119901 = 001)there were no major differences between admitted andexcluded patients regarding anthropometric physical examor analytical parameters Thus exclusion did not seem tocarry any bias

The 206 patients finally included were followed up for amean of 18 months (IQR 15) (Table 1) There were 18 events(T2DM new diagnoses) for an incidence of 582 cases1000patients-year


Time

70

80

90

100

110

Glu

c

(a)Time

70

80

90

100

110

Glu

c

(b)

Time

70

80

90

100

110

Glu

c

(c)

minus1

0

1

2

log(Fn)

2 3 4 51

log(time window)

(d)









Men 1045 (101)Women 992 (121)


Men 135 (035)Women 150 (032)




4 Discussion






minus1

0

1

2

log(Fn)

2 3 4 51

log(time window)







minus400

0

200

Inte

grat

ed g

lyca

emia

80

100

120

140

Gly

caem

ia


119894=1(119866119894minus 119866mean) where









5 Conclusions


Competing Interests


Acknowledgments


References






























of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















Time

70

80

90

100

110

Glu

c

(a)Time

70

80

90

100

110

Glu

c

(b)

Time

70

80

90

100

110

Glu

c

(c)

minus1

0

1

2

log(Fn)

2 3 4 51

log(time window)

(d)









Men 1045 (101)Women 992 (121)


Men 135 (035)Women 150 (032)




4 Discussion






minus1

0

1

2

log(Fn)

2 3 4 51

log(time window)







minus400

0

200

Inte

grat

ed g

lyca

emia

80

100

120

140

Gly

caem

ia


119894=1(119866119894minus 119866mean) where









5 Conclusions


Competing Interests


Acknowledgments


References






























of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of



















Men 1045 (101)Women 992 (121)


Men 135 (035)Women 150 (032)




4 Discussion






minus1

0

1

2

log(Fn)

2 3 4 51

log(time window)







minus400

0

200

Inte

grat

ed g

lyca

emia

80

100

120

140

Gly

caem

ia


119894=1(119866119894minus 119866mean) where









5 Conclusions


Competing Interests


Acknowledgments


References






























of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















minus1

0

1

2

log(Fn)

2 3 4 51

log(time window)







minus400

0

200

Inte

grat

ed g

lyca

emia

80

100

120

140

Gly

caem

ia


119894=1(119866119894minus 119866mean) where









5 Conclusions


Competing Interests


Acknowledgments


References






























of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of


















5 Conclusions


Competing Interests


Acknowledgments


References






























of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of





















of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of
















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