Bootstrapped Multinomial Logistic Regression on Apnea Detection Using ECG Data

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1 ICACSIS 2010 ISSN: Bootstrappd Multinomial Logistic Rgrssion on Apna Dtction Using ECG Data Hadaiq R Sanabila, Mohamad Ivan Fanany, Wisnu Jatmiko, and Aniati Murni Arimurthy Laboratory of Pattrn Rcognition, Imag Procssing, and Contnt Basd Imag Rtrival Faculty of Computr Scinc, Univrsitas Indonsia hadaiq.rolis@ui.ac.id, ivan@cs.ui.ac.id, wisnuj@cs.ui.ac.id, aniati@cs.ui.ac.id Abstract In dsigning a classification systm, on of th most important considrations is how optimal th classifir will adapt and giv bst gnraliation whn it is givn data from unknown modl distribution. Unlik linar rgrssion, logistic rgrssion has no simpl formula to assss its gnraliation ability. In such cass, bootstrapping offrs an advantag ovr analytical mthods thanks to its simplicity. This papr prsnts an analysis of bootstrappd multinomial logistic rgrssion applid on apna dtction using ECG data. W xamin multinomial logistic rgrssion to dtct or rcogni multi-class apna catgoris (havy, middl, halthy). W show that for gnrally complx and highly unstructurd mdical data such as ECG for apna dtction, bootstrapping givs mor maningful assssmnt to dtct ovr-fitting than k-fold cross validation. Th bootstrapping also givs highr classification accuracy prdiction ovr k-fold cross validation for th sam training data proportion. N I. INTRODUCTION owdays statistical mthods has bcom a vry powrful tool for supporting mdical dcisions. Doctors can b hlpd by statistical modls to intrprt corrctly so many data and to support thir dcisions. Evn furthr, du to th charactristic of mdical data and hug numbr of variabls to b considrd, rsarchs to automat th dcision support systm that can b prformd by machin (.g., dtction apna symptoms using computrs at hom [1], or warabl alarm clock that can dtct slp stags [2] ) is continuously prolifrating. Of cours, although th statistical modls ar vry powrful for doctors and computrs ar gtting fastr, th modls and th computrs cannot substitut doctors' viwpoint. Many of th mdical problms ar rlatd to qustions of classification and prdiction, many tims with only two catgoris (disas or not disas, for instanc). In thos cass, th us of classical tchniqus has to b rstrictd to som spcific mthods such as logistic rgrssion or similar. Whn w ar daling with multi-catgoris classifications usually w prfr to us nwr tools such as nural ntworks which do not rquir such rstrictiv hypothsis. In addition, our prfrnc to such nwr This work is supportd by Comptnc-Basd Rsarch Grant Univrsity of Indonsia tools is also du th fact that mdical data ar gnrally complx and hav lack of structur. Howvr, according to a study [3] which compard logistic rgrssion and nural ntworks, svral points should b rmarkd: For data that was usd to build th modl, som of th nural ntworks can b considrd bttr, but for data that was usd to validat th modl non of thm ar bttr. Th nural ntworks modls that can b considrd bttr in building data, actually nds a gratr numbr of inputs. Doctors usually prfr to us logistic rgrssion which includs lss variabls and hav an asy maning in th modl. Prdiction can b don with a simpl quation in logistic rgrssion, whras th ncssity of computing tool in nural ntwork can dlay th diagnos for th doctors. Hnc, [3] rcommnds to us logistic rgrssion for mdical data. Rcntly, [4] also us multinomial logistic rgrssion to xamin th influnc of ag, body mass indx (BMI), gndr, smoking, and social charactristics on apna hypoapna indx (AHI). Cross validation is a tchniqu for assssing how th rsults of a statistical analysis will gnrali to an indpndnt data st. It is mainly usd in sttings whr th goal is prdiction, and on wants to stimats how accuratly a prdictiv modl will prform in practic. On round of cross validation involvs partitioning a sampl of data into complmntary substs, prforming th analysis on on subst (calld th training st), and validating th analysis on th othr subst ovr th rounds. In this papr, w try to asss and stimat how accuratly th multinomial logistic rgrssion classifir will prform in practic in trms of classification accuracy and gnraliation ability by analying classification of ECG data sampls to automatically dtct th disordrd brathing during slp (apna). W will show that bootstrapping cross validation mthod is prfrrd than k-fold cross validation for th valuation and assssmnt of this data sampls. II. SLEEP APNEA Slp disordr is a mdical disordr in slp of a 181

2 prson or animal. It can b classifid into dyssomnias (charactrid by ithr hyprsomnolnc or insomnia) and parasomnias (charactrid by abnormal and unnatural movmnts in slp). Slp disordr intrfrs with normal physical, mntal and motional functioning. On catgory of dyssomnias is slp apna. Th slp apna is dfind as abnormal paus of airflow during slp, prvnting air from ntring th lungs and causs an obstruction. Th typs of slp apna ar cntral slp apna (CSA), obstructiv slp apna (OSA), and mixd slp apna (both cntral slp apna and obstructiv slp apna). CSA occurs whn th brain dos not snd th ordr signal to th muscls to tak a brath so thr is no muscular ffort to tak a brath. OSA happns whn th brain snds th instruction signal to th muscls and th muscls mak an ffort to tak a brath but thy ar unsuccssful bcaus th airway bcoms obstructd and prvnts an adquat flow of air. Mixd slp apna, occurs whn both cntral slp apna and obstructiv slp apna ar occurrd. Slp disordr is rlatd to a risn risk of cardiovascular illnss, strok, high blood prssur, arrhythmias, diabts, and slp dprivd driving accidnts [1-4]. Slp apna prson also hav a 30% highr risk of hart attack or prmatur dath than thos unaffctd [5]. Th symptoms of slp apna may includ daytim fatigu & slpinss, insomnia, poor concntration, mmory problms, anxity, irritability, hadachs, and impdimnt prforming work dutis. Gnrally, slp disordr is diagnosd using polysomnogram. It rcords minimum up to twlv channls: thr channls for EEG (Elctroncphalography), on or two channls for quantify airflow, on channl for chin muscl ton, on or mor channls for lg movmnt, two for y motion, on for hart rat, on for oxygn intnsity, and on for ach blts which masurs chst wall movmnt and uppr abdominal wall movmnt. Th polysomnographic diagnos mthod is rlativly costly and du to th darth of diagnos tic slp laboratoris, th slp apna is widly undrdiagnosd [6]. In addition, polysomnogram dos not provid a sound prov that slp apna as indirct of vidnc of airflow masurmnt and rspiratory movmnt that is usd to valuat th disordrd brathing. Thrfor w want to provid a rliabl idntification of disordrd brathing with fwr and simplr masurmnt using ECG III. LOGISTIC REGRESSION A. Logistic Rgrssion Logistic rgrssion is on of th rgrssion mthods which is usd to prdict th probability of dichotomous vnt. It is usd whn th dpndnt variabl is a dichotomy and th indpndnt variabls ar of any typ. Usually, logistic rgrssion is usd to prdict a dpndnt variabl on th basis of continuous and catgorical indpndnts. It is also usd to dtrmin th ffct of th si of th indpndnt variabls on th dpndnt. Odd ratios ar usd to clarify th impact of prdictor variabls. Logistic rgrssion us logistic function as a modl. Logistic function is usful bcaus it can tak as an input any valu from ngativ infinity to positiv infinity, whras th output is confind to valus btwn 0 and 1. Th formula of logistic function is dscribd blow: f( ) 1 (1) Th variabl dfins as β 0 +β 1 x 1 + β 2 x β k x k, whr β 0, β 1,, β k calld th intrcpt and th x 1, x 2,, x k calld as cofficint. Th cofficint dscribs th proportions of that risk factor, a positiv cofficint mans that th variabl incras th probability of outcom and vic vrsa. odds(v )= (2) 1 whr = β 0 +β 1 x 1 + β 2 x β k x k. Logistic rgrssion is a suitabl way of dscribing th rlationship btwn indpndnt variabls and a binary rspons variabl, xprssd as a probability that has dichotomous vnts. B. Multinomial Logistic Rgrssion Multinomial logistic rgrssion is th gnraliation of logistic rgrssion which allowing mor than two outcoms vnts. Multinomial logistic rgrssion usd whn th dpndnt variabls cannot b ordrd in any maningful way. Its modl assums that data in ach indpndnt variabl has a singl valu for ach cas. Multinomial logistic rgrssion slcts on of dpndnt variabl as th confrontation catgory and assums that th dpndnt variabl cannot b prfctly prdictd from th indpndnt variabls. Multinomial logistic rgrssion compars multipl groups through a combination of binary logistic rgrssions. Th modls of multinomial logistic rgrssion ar Xi j Pr() yi j J Xi j (3) 1 and j 1 X i j Pr()0 yi J ' X i j 1 j 1 (4) whr for th i th individual, y i is th outcom vnt and X i is a vctor of xplanatory/indpndnt variabls. Th paramtrs β j ar typically approximatd by maximum a postriori (MAP) which is an xtnsion of maximum liklihood using rgulariation of th wight to prvnt morbid 182

3 solutions. Th solution is typically found using and itrativ procdur such as itrativly r -wightd last squars (IRLS) or, mor commonly ths days, a quasi-nwton mthod such as th limitd mmory Broydn-Fltchr-Goldfarb-Shanno(L-BFGS) mthod. Multinomial logistic rgrssion dos not mak any assumption of normality, linarity, and homognity of varianc for th indpndnt variabls. Bcaus it dos not impos ths rquirmnts, it is prfrrd to discriminant analysis whn th data dos not satisfy ths assumptions. IV. CROSS VALIDATION Cross validation is important in guarding against tsting hypothss suggstd by th data, spcially whr furthr sampls ar haardous, costly or impossibl to collct. In linar rgrssion whr th training man-squard-rror (MSE) undrstimats th validation MSE, cross validation is not practically usful. In most othr rgrssion procdurs lik logistic rgrssion, howvr, no simpl formula to mak such adjustmnt. Cross validation is a gnrally applicabl way to prdict th prformanc of a modl on a validation st using computation in plac of mathmatical analysis. Thr ar svral typs of cross validation: (1) K-fold cross validation, (2) Lav-on-out or Jack-knif cross validation, (3) Rpatd random sub-sampling or bootstrapping. In this study, w compar bootstrapping to K-fold cross validation. A. K-fold K-fold cross validation is on cross validation mthod which divid datast into k datasts and th holdout mthod is itratd k tims. Th cross - validation K-Fold is th data rsultd from th obsrvation of th mntiond sub-groups to b K which dnots th numbr of sub-groups. A subgroup of data is usd for validation and tsting and th rst sub-group K 1 is for training procss. Th mntiond procss is rpatd for K tims with ach sub-group usd on tim only. Th rsult of such calculation is th man valu to gt th final valu. Th advantag of this mthod is that all obsrvd data is usd ithr in training or tsting procss. Th conductd xprimnt uss 3, 5, 10, 15, and 20 folds cross validation. B. Rpatd Random Sub-sampling (Bootstrapping) Bootstrapping is on of th r-sampling mthods usd to masur th proprtis of stimator from th distribution approximation sampl. This mthod stimats th rror of th mdian by raffling th sampl with rplacmnt from original data and stimat th standard rror of th original mdian from th obsrvd variabl. Bootstrapping is a rliabl altrnativ to dduct basd on paramtric assumptions whn thos assumptions ar in doubt or paramtric dduction is rquirs vry complicatd formulas for th standard rror calculation. In [17], Adr t al. (2008) suggsts to mploy bootstrapping for th following condition: Whn th thortical distribution of a statistic is complicatd or unknown Whn th sampl si is insufficint for straightforward statistical infrnc Whn powr calculations hav to b prformd, and a small pilot sampl is availabl V.EXPERIMENTAL SETUP Th databas usd in this xprimnt was obtaind from PhysioNt [6]. It is rcordd from 35 prsons containing singl ECG signal of approximatly 8 hours obsrvation which dividd into on-minut sgmnts. Th ECG signals wr xtractd from rcordd polysomnogram masurmnt. Each sgmnt annotatd basd on 3 classifications that is Apna (A), Bordrlin/mild apna (B), and Normal (N). Th total numbr of sgmnts classifid in this mannr was with (61.6%) annotatd as normal, 252 (1.5%) annotatd as mild apna and 6240 (36.9%) annotatd as apna. Th faturs usd in this xprimnt was xtractd from ECG signal using QRS dtctor program [7][8]. Th considrd faturs wr: Man of RR-intrval, Standard dviation RR-intrval, Th NN50 masur (variant 1), dfind as th numbr of pairs of adjacnt RR-intrvals whr th first RR-intrval xcds th scond RR-intrval by mor than 50 ms, NN50 masur (variant 2), dfind as th numbr of pairs of adjacnt RR-intrvals whr th scond RR-intrval xcds th first RR-intrval by mor than 50 ms, Two pnn50 masurs, dfind as ach NN50 masur dividd by th total numbr of RRintrvals, th SDSD masurs, dfind as th standard dviation of th diffrncs btwn adjacnt RR-intrvals, RMSSD masur, dfind as th squar root of th man of th sum of th squars of diffrncs btwn adjacnt RR-intrvals, Mdian of RR-intrval, Intr-quartil rang, dfind as diffrnc btwn 75th and 25th prcntils of th RRintrval valu distribution, Man absolut dviation valus, dfind as man of absolut valus obtaind by th subtraction of th man RR-intrval valus from all th RR-intrval valus in an poch. Ths fatur us as an attributs into our multinomial logistic rgrssion classifir. 183

4 W conductd xprimnts to obtain optimal cross validation for dtcting apna slp disordr. As prformanc valuation w us classification accuracy (CA), or confusion matrix. A. K-fold K-fold cross validation is on of th cross validation mthod which divid datast into k datasts and th holdout mthod is itratd k tims. Th cross - validation K-Fold is th data rsultd from th obsrvation of th mntiond sub-groups to b K which dnots th numbr of sub-groups. A subgroup of data is usd for validation and tsting and th rst sub-group K 1 is for training procss. Th mntiond procss is rpatd for K tims with ach sub-group usd on tim only. Th yild of such calculation is th man valu to gt th final valu. Th illustration of k-fold cross validation dpictd on th figur 1. Th advantag of this mthod is that all obsrvd data is usd ithr in training or tsting procss. Th xprimnt conductd us 3, 5, 10, 15, and 20 folds cross validation. B. Rpatd Random Sub-sampling (Bootstrapping) In th bootstrapping, th data was split into two groups, training and tsting data with particular composition. Th data compositions ar constructd by drawing from th original data randomly. Thn, n- prcnt of th data usd as training data and th rmaining usd as tsting data. Th xprimnts usd 50, 60, 70, 80 and 90 prcnt of data as training data. A. K-fold VI. RESULT AND ANALYSIS Th xprimntal rsult using various cross validation shows that highr fold givs a bttr accuracy rsult. Th xprimntal rsult of k-fold cross validation dpictd on th Figur 2. Th highst classification accuracy was obtaind for th 15 and 20 folds. Th lowst classification accuracy obtaind on th 3-fold cross validation. In k-fold cross validation, th data sparatd in k groups. Th mor groups formd th numbr of training and tsting data ar gtting significantly diffrnt. This would rsults in th condition whr th xprimnt us larg numbr of data for training whil for tsting th systm uss fwr data. Confusion matrix could b us for furthr analysis. Th confusion matrix rsult of this xprimnt dpictd on Figur 4. Basd on confusion matrix, class B always obtains constant rcognition in all k- fold xprimnts. It mans that th rcognition of class B could not b nhancd in any fold lction in cross validation. But for class A and N, it can b sn that th classification accuracy incrass whn highr k-fold is slctd. But for th 15 and 20 folds th classification accuracy ar saturatd. Th corrct prdiction of class A in 15 fold is highr than 20-fold. Manwhil, in th class N th corrct prdiction of 20-fold is highr than 20-fold. It can b occurs bcaus for th composition of training and tsting data in 15 fold is th bst and fittst paramtr optimiation of ach attributs for logistic rgrssion in class A. Manwhil for th class B, it can b happns bcaus th composition of training and tsting data in 20 fold is th bst and fittst paramtr optimiation of ach attributs for logistic rgrssion. Fig 1 th illustration of k-fold cross validation Confusion matrix could b us for furthr analysis. Th confusion matrix of this xprimnts dpictd on fig 4. Basd on confusion matrix, th class B always obtains constant rcognition in any k-fold xprimnts. It mans that th rcognition of class B could not nhancd in any fold lction in cross validation. But for class A and N, it can b sn that th classification accuracy is incrasd whn highr numbr of k is slctd. But for th 15 and 20 folds w obtaind th sam classification accuracy. It can b analyd using confusion matrix. TABLE I THE CONFUSION MATRIX OF 3 (A), 5(B), 10 (C), 15 (D), 20 (E) FOLD CROSS VALIDATION Basd on th confusion matrix, th corrct prdiction of class A in 15 fold is highr than 20 fold. Manwhil, in th class N th corrct prdiction of 20 fold is highr than 15 fold. Hnc, th composition of training and tsting data in 15-fold is th bst suitd to paramtr optimiation of ach attribut for logistic rgrssion in class A. Manwhil for th class B, th composition of training and tsting data in 20 fold is th bst. 184

5 B. Rpatd Random Sub-sampling (Bootstrapping) Bootstrapping xprimntal rsult shows as th prcntag of data usd for training is highr, th bttr accuracy rsult. Th xprimntal rsults of bootstrapping dpictd on th Figur 3. Th highst classification accuracy is obtaind whn 80 prcnt of data ar usd for training manwhil th lowst is obtaind whn 50 prcnt of data ar usd for training. Th mor data usd in training phas, it would b incras th prformanc of systm and vic vrsa. Th mor data training would giv bttr data rprsntation of th systm rsults in highr classification accuracy. Howvr for th 90 prcnt of data usd as data training has lowr classification accuracy than 80 prcnt of data usd as data training th mor data training would bring an ovr-fitting in rgrssion. Gnrally, incrasing th proportion of data usd for training aftr suitabl modl is found would only introduc an rror or nois rathr than a good data rprsntation. VII. CONCLUSION Cross validation is on of th validation mthods to prdict th fit of a modl to a prdiction validation st whn an obvious validation st is not availabl. On of th cross validation typ is k-fold cross validation. Basd on th xprimntal rsult, th highr numbrs of fold in k-fold cross validation would incras th classification accuracy vn slightly. But aftr an optimal k is obtaind, incrasing th proportion of training data (by incrasing k) will not giv any diffrnc. On th othr hand, th bootstrapping xprimntal rsults show that up to crtain proportion, th highr n-prcnt data ar usd for training might incrass th classification accuracy. But aftr this crtain proportion is found, w can s that th classifir will b dgradd du to ovr-fitting btwn th data and th modl to b stimatd. In addition, compard to k-fold cross validation, bootstrapping giv a highr accuracy prdiction bcaus it givs a mor accurat data prsntation by introducing randomnss in slcting th training and tsting data. VIII. FURTHER WORKS Th apna disordr dtction systm is continuously bcoming an intrsting rsarch topic that draws many attntions and mor applications in th futur. With th advancd of tchnology, many disass could b dtctd and tratd arly. Othr approachs can b studid furthr to incras th classification accuracy such as by using mor prcis faturs in ECG that contains th most information and by using othr polysomnogram channls. In th futur, w ar planning to xamin logistic rgrssion not only to dtct apna but also slp stags. Fig 2 Th classifir accuracy in ach fold lction Fig 3 th classifir accuracy in ach n-prcnt data usd as data training REFERENCES [1] Yilma B, Asyali MH, Arikan E, Ytkin S, Ogn F. Slp stag and obstructiv apnaic poch classification using singl-lad ECG.Biomd Eng Onlin Aug 19;9(1):39. [2] [3] Escano LME, Sai GS, Lornt FJL, Frnando AB, Ugarria JMV, Logistic rgrssion vrsus nural ntworks for mdical data, Monografias dl Sminaro Matmatico Garcia d Galdano 33, , (2006). [4] Charokopos N., Lotsinidis M, Tsiamita M, Karkoulias K, Spiripoulos K., Slp Apna Syndrom in a Rfrral Population in Grc: Influnc of Social Factors, Lung (2007), 185: [5] Yan-fang S, Yu-ping W (August 2009). "Slp-disordrd brathing: impact on functional outcom of ischmic strok patints". Slp Mdicin 10 (7): doi: /j.slp PMID [6] [7] Bixlr EO, Vgontas AN, Lin HM, t al. (Novmbr 2008). "Blood prssur associatd with slp-disordrd brathing in a population sampl of childrn". Hyprtnsion 52 (5): doi: /hypertensionaha PMID [8] Lung RS (2009). "Slp-disordrd brathing: autonomic mchanisms and arrhythmias". Progrss in Cardiovascular Disass 51 (4): doi: /j.pcad PMID [9] Silvrbrg DS, Iaina A, Oksnbrg A (January 2002). "Trating obstructiv slp apna improvs ssntial hyprtnsion and lif". Amrican Family Physician 65 (2): PMID [10] Amrican Thoracic Socity (May 20, 2007). "Slp Apna Incrass Risk of Hart Attack or Dath by 30%". Prss rlas. Archivd from th original on Sptmbr 27, 2007 [11] P. d Chaal, R. Rilly, C. Hnghan, "Automatic Slp Apnoa Dtction Using Masurs of Amplitud and Hart Rat Variability from th Elctrocardiogram," icpr, vol. 1, 185

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