Detecting important electrocardiogram characteristics for the diagnosis of Fabry disease via statistics and machine learning techniques

Uni e sidade do Minho Escola de Engenha ia Ana Ri a Sousa Mou a De ec ing impo an elec oca diog am cha ac e is ics o he diagnosis o Fab y disease ia s a is ics and machine lea ning echniques Ma ch o 2022 UMinho | 2022 Ana Mou a De ec ing impo an elec oca diog am cha ac e is ics o he diagnosis o Fab y disease ia s a is ics and machine lea nings echniques Ana Ri a Sousa Mou a De ec ing impo an elec oca diog am cha ac e is ics o he diagnosis o Fab y disease ia s a is ics and machine lea ning echniques Mas e ’s disse a ion In eg a ed Mas e ’s in Biomedical Enginee ing Medical elec onics Wo k elabo a ed unde he supe ision o P o . D . Es ela Bicho (Supe iso ) D . Flo a Fe ei a (Co-supe iso ) Uni e sidade do Minho Escola de Engenha ia Ma ch o 2022 DIREITOS DE AUTOR E CONDIÇÕES DE UTILIZAÇÃO DO TRABALHO POR TERCEIROS Es e é um abalho académico que pode se u ilizado po e cei os desde que espei adas as eg as e boas p á icas in e nacionalmen e acei es, no que conce ne aos di ei os de au o e di ei os conexos. Assim, o p esen e abalho pode se u ilizado nos e mos p e is os na licença abaixo indicada. Caso o u ilizado necessi e de pe missão pa a pode aze um uso do abalho em condições não p e is as no licenciamen o indicado, de e á con ac a o au o , a a és do Reposi ó iUM da Uni e sidade do Minho. Licença concedida aos u ilizado es des e abalho A ibuição-NãoCome cial-SemDe i ações CC BY-NC-ND h ps://c ea i ecommons.o g/licenses/by-nc-nd/4.0/ ii 0.1 Ag adecimen os Tenho que ag adece a algumas pessoas, pelo apoio que me p opo ciona am, de di e sas o mas, du an e a minha disse ação e odo o meu pe cu so académico. Em p imei o luga , ag adeço à p o esso a Es ela Bicho po me e acei e nes e p oje o e pela sua disponibilidade e à Dou o a Flo a Fe ei a pela ajuda e o ien ação du an e oda a disse ação, pela con i- ança, pela disponibilidade e pelos conhecimen os que me ansmi iu. Ag adeço ambém ao Dou o Miguel Gago e à Dou o a Olga Aze edo, po e em lançado o desa io, o necido os dados e ajudado nas ques ões clínicas que su gi am nes e abalho, sem eles es a disse ação não se ia possí el. Aos meus pais e ao meu i mão pelos es o ços que ize am pa a me possibili a em es a opo unidade, po me apoia em e que e em semp e o melho pa a a minha ida. Sem eles não inha conseguido chega aqui. Ob igada po udo Mãe. Um g ande ob igada a odos os meus amigos e amilia es, que du an e es es anos da minha ida, es ando pe o ou longe, me acompanha am e incen i a am, em especial à Bá ba a, à Helena, à Ma iana, ao Nuno e à p ima Ca olina. Ao meu a ilhado po aleg a os meus dias e à minha mad inha. Não podia deixa de ag adece ao meu namo ado, Tiago, que du an e a minha disse ação e du an e o cu so, que pe co emos jun os, es e e semp e p esen e pa a me ajuda , mo i a e acima de udo a u a . Es a conquis a ambém é um pouco ua. iii STATEMENT OF INTEGRITY I he eby decla e ha ing conduc ed his academic wo k wi h in eg i y. I con i m ha I ha e no used plagia ism o any o m o undue use o in o ma ion o alsi ica ion o esul s along he p ocess leading o i s elabo a ion. I u he decla e ha I ha e ully acknowledged he Code o E hical Conduc o he Uni e si y o Minho. i 0.2 Resumo Tí ulo: De eção de ca ac e ís icas do elec oca diog ama impo an es pa a o diagnós ico da doença de Fab y u ilizando es a ís ica e écnicas de machine lea ning. A doença de Fab y (DF) é uma doença gené ica a a de depósi o lisossômico que a e a a qualidade de ida e pode mesmo le a à mo e p ema u a. O diagnós ico ainda a dio eduz a e iciência da e apia de eposição enzimá ica. Assim, é ex emamen e impo an e iden i ica bioma cado es que possam auxilia no diagnós ico p ecoce da DF. Apesa dos p og essos nos úl imos anos, a DF con inua a se mal comp een- dida. Des a o ma, es a disse ação e e como obje i o iden i ica ca ac e ís icas de elec oca diog ama (ECG) impo an es pa a o diagnós ico da DF, mais especi icamen e, pa a di e encia os pacien es de DF com e sem lesões da ma é ia b anca, e es es de pacien es com mioca diopa ia hipe ó ica sa comé ica. Pa a es e im, o am desen ol idos e aplicados modelos es a ís icos e de machine lea ning (ML). Quinze ca ac e ís icas de ECG o am a aliadas usando di e sos mé odos de in e ência es a ís ica, sob e udo pa a iden i ica di e enças signi ica i as en e os g upos endo em con a o sexo e a idade. Dois mé odos de seleção de a ibu os o am aplicados, um baseado nos alo es do a o de in lação da a iância (VIF), e uma eliminação ecu si a de a ibu os usando logis ic eg ession,suppo ec o machine (SVM) linea e andom o es como classi icado es. Depois, a aliou-se a pe o mance de cinco algo i mos de ML -logis ic eg ession, SVM com unção de base adial (RBF), andom o es ek-nea es neighbo (KNN) - a dis ingui os di e en es g upos, pa a iden i ica o melho modelo pa a cada p oblema de classi icação. A idade e elou se signi ica i amen e di e en e en e os g upos e es a elacionada com as a iá eis de ECG. Após subdi idi em ês aixas e á ias, algumas ca ac e ís icas e ela am-se impo an es pa a dis ingui os g upos, não sendo a e adas pela idade. Com base nas ca ac e ís icas de ECG selecionadas, os esul ados mos a am boa axa de ace o, com os melho es esul ados a a ia de 80% a 85%, ob idos usando SVM RBF, andom o es e KNN. Es as descobe as demons am o po encial das écnicas de ML baseadas em ca ac e ís icas de ECG como e amen a complemen a ao diagnós ico da DF, com e sem lesões da ma é ia b anca, o que pode se ú il pa a eduzi a demo a no diagnós ico. Pala as-cha e: Classi icação, Doença de Fab y, Ele oca diog ama, Es a ís ica, Machine Lea ning. 0.3 Abs ac Ti le: De ec ing impo an elec oca diog am cha ac e is ics o he diagnosis o Fab y disease ia s a is ics and machine lea ning echniques. Fab y disease (FD) is a a e gene ic lysosomal s o age diso de ha a ec s li e quali y and may e en lead o p ema u e dea h. The mean delay be ween he onse o symp oms and he diagnosis is s ill e y high, educing enzyme eplacemen he apy’s e iciency. The e o e, i is ex emely impo an o iden i y bioma ke s ha could assis in he ea ly diagnosis o FD. Despi e all he p og ess in ecen yea s, FD emains misunde s ood. Thus, his disse a ion aimed o iden i y impo an elec oca diog am (ECG) cha - ac e is ics o diagnosing FD, and mo e speci ically, o di e en ia e FD wi h whi e ma e lesions (WMLs) om FD wi hou WMLs pa ien s and hese om pa ien s wi h sa come ic hype ophic ca diomyopa hy. To his end, s a is ics and machine lea ning (ML) models ha e been de eloped and applied. Fi een ECG a iables we e e alua ed using se e al s a is ical in e ence me hods mainly o iden i y signi ican di e ences be ween g oups, conside ing sex and age. Two ea u e selec ion me hods we e ap- plied, one based on a iance in la ion ac o (VIF) alues, and a ecu si e ea u e elimina ion using logis ic eg ession, linea suppo ec o machine (SVM), and andom o es classi ie s. Then, he pe o mance o i e ML algo i hms - logis ic eg ession, linea SVM, adial basis unc ion (RBF) SVM, andom o es , and K-nea es neighbo (KNN) - a dis inguishing he di e en g oups we e e alua ed o iden i y he bes model o each classi ica ion p oblem. Age was ound o be signi ican ly di e en be ween g oups and o be ela ed o he ECG a iables alues. A e subdi ision in o h ee ca ego ies by age, some ECG cha ac e is ics we e iden i ied as impo an o dis inguish he g oups and una ec ed by age. Based on selec ed ECG cha ac e is ics, he esul s showed good classi ica ion accu acies, wi h he bes sco es anging om 80% o 85%, ob ained using RBF SVM, andom o es , o KNN. These indings demons a e he po en ial o ML echniques based on ECG cha ac e is ics as a com- plemen a y ool o diagnosing FD wi h o wi hou WMLs ha could be use ul o educe he diagnosis delay. Keywo ds: Classi ica ion, Elec oca diog am, Fab y Disease, Machine Lea ning, S a is ics. i Con en s 0.1 Ag adecimen os ................................... iii 0.2 Resumo ....................................... 0.3 Abs ac ........................................ i Lis o Figu es xi Lis o Tables xii Ac onyms x i I : In oduc ion and S a e o he A 1 1 In oduc ion 2 1.1 Mo i a ion ...................................... 2 1.2 Goals......................................... 3 1.3 Disse a ionS uc u e................................. 3 2 Fab y disease and hype ophic ca diomyopa hy disease 5 2.1 Fab yDisease .................................... 5 2.1.1 Desc ip ion.................................. 6 2.1.2 Pheno ype and Clinical Mani es a ions . . . . . . . . . . . . . . . . . . . . 6 2.1.3 Diagnosis .................................. 8 2.1.4 T ea men .................................. 8 2.2 Hype ophic Ca diomyopa hy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 ii 31 S a is ically non-signi ican logis ic eg ession esul s o HCM and FD wi h WMLs g oups wi hagesabo e59..................................114 32 Hype pa ame e s alues/s a us pe machine lea ning model and classi ica ion p oblem o pa ien s aged be ween 40 and 59 (inclusi e) . . . . . . . . . . . . . . . . . . . . 115 33 Accu acy alues pe machine lea ning model and classi ica ion p oblem o pa ien s aged be ween 40 and 59 (inclusi e) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 34 Hype pa ame e s alues/s a us pe machine lea ning model and numbe o ea u es o HCM and FD wi hou WMLs pa ien s aged 40 o 59 (inclusi e) . . . . . . . . . . . . . 117 35 Hype pa ame e s alues/s a us pe machine lea ning model and numbe o ea u es o HCM and FD wi h WMLs pa ien s aged 40 o 59 (inclusi e) . . . . . . . . . . . . . . . 118 36 Hype pa ame e s alues/s a us pe machine lea ning model and numbe o ea u es o FD wi h WMLs and FD wi hou WMLs pa ien s aged 40 o 59 (inclusi e) . . . . . . . . 119 37 Hype pa ame e s alues/s a us pe machine lea ning model and classi ica ion p oblem o pa ien sagedabo e59 ..............................120 38 Accu acy alues pe machine lea ning model and classi ica ion p oblem o pa ien s aged abo e59.......................................120 39 Hype pa ame e s alues/s a us pe machine lea ning model and numbe o ea u es o HCM and FD wi h WMLs pa ien s aged abo e 59 . . . . . . . . . . . . . . . . . . . . 121 xi Ac onyms ANOVA Analysis o a iance. AUC A ea unde cu e. ECG Elec oca diog am. ERT Enzyme eplacemen he apy. FD Fab y disease. GLA Galac osidase alpha. HCM Hype ophic ca diomyopa hy. HR Hea a e. HRV Hea a e a iabili y. KNN K-nea es neighbo . LOOCV Lea e-one-ou c oss- alida ion. LR Logis ic eg ession. LVH Le en icula hype ophy. ML Machine lea ning. x MRI Magne ic esonance imaging. OR Odds a io. RBF Radial basis unc ion. RF Random o es . RFE Recu si e ea u e elimina ion. SVM Suppo ec o machine. VIF Va iance in la ion ac o . WMLs Whi e ma e lesions. x i Pa I : In oduc ion and S a e o he A 1 Chap e 1 In oduc ion This Chap e p esen s he mo i a ion o his disse a ion as well as i s goals. Finally, a desc ip ion o how he disse a ion is s uc u ed is p esen ed. 1.1 Mo i a ion Fab y disease (FD) is a a e gene ic disease ha a ec s li e quali y and may lead o p ema u e dea h. The e a e ea men s o his disease, like Enzyme eplacemen he apy (ERT) [1] [2]. Al hough his ea men has shown good esul s, i may no be able o s abilize disease mani es a ions i i is al eady in an ad anced s age, so i is essen ial o begin ERT as ea ly as possible [1]. The mean delay be ween he symp om onse and diagnosis is a ound 14.7 and 15.1 yea s in male and emale pa ien s, espec i ely [3]. The e o e, i is ex emely impo an o ind bioma ke s ha could assis in an ea ly diagnosis o Fab y disease. Despi e all he p og ess in ecen yea s, FD emains misunde s ood. The e is e idence ha speci ic ca dio ascula , neu ological, and ce eb o ascula mani es a ions may be cha ac e is ics o his disease [4]. Hence, i is impo an o iden i y signi ican elec oca diog am (ECG) cha ac e is ics o diagnosing FD, and di e en ia e FD wi h whi e ma e lesions (WMLs) om FD wi hou WMLs pa ien s. In his disse a ion, 24-hou ECG da a (Hol e ) is used since Elec oca diog am (ECG) is a medical 2 exam ha is usually pe o med o diagnose and ollow pa ien s wi h ca diac diseases, like FD [5]. The coho o pa ien s may ha e o no ha e whi e ma e lesions. Pa ien s wi h Hype ophic Ca diomyopa hy a e also included in he s udy because his disease has simila i ies in ca diac mani es a ions o hose ound in FD, mainly le en icula hype ophy. S a is ics and machine lea ning models a e de eloped and applied o ex ac and selec impo an in o ma ion om clinical da a o unde s and be e and achie e a mo e accu a e disease p edic ion [6]. 1.2 Goals The main goal o his disse a ion is o de ec impo an elec oca diog am cha ac e is ics o he diagnosis o Fab y disease, using o ha s a is ics and machine lea ning me hods. Mo e p ecisely, he objec i es o his disse a ion a e: • De ec impo an ECG cha ac e is ics o di e en ia e FD pa ien s wi h whi e ma e lesions (WMLs) om FD pa ien s wi hou WMLs, and hese wo g oups om pa ien s wi h sa come ic hype ophic ca diomyopa hy (HCM); • In es iga e which physical cha ac e is ics, like age and sex, a e co ela ed wi h ECG cha ac e is ics and, he e o e, could impac he classi ica ion esul s; • Implemen and e alua e he pe o mance o di e en Machine Lea ning models on he di e en ia- ion be ween he g oups o pa ien s. 1.3 Disse a ion S uc u e This disse a ion is di ided in o h ee Pa s and, in u n, hese Pa s a e di ided in o Chap e s, hen Sec ions and Subsec ions. 3 The i s Pa (Pa I) is deno ed “In oduc ion and S a e o A ”, which, as indica ed by he name, includes an in oduc ion whe e he mo i a ion, goals and s uc u e (cu en subsec ion) o his disse a ion a e p esen ed. I also includes a Chap e ela i e o Fab y and Hype ophic Ca diomyopha y diseases, in which, o each disease, a desc ip ion, i s pheno ype and clinical mani es a ions, how i is diagnosed, and possible ea men s, a e p esen ed. The alue o elec oca diog am (ECG) cha ac e is ics as da a o classi ica ion is also explo ed in his pa , mainly h ough s udies ha ha e al eady used ECG cha ac e is ics o diagnose and dis inguish diseases. Machine lea ning diagnosis alue is also explained and se e al s udies ha use ECG-based machine lea ning models o classi ica ion p oblems a e also p esen ed. In Pa II he ma e ials and me hods a e delinea ed. The s udy da a is i s p esen ed, ollowed by he desc ip ion o he adop ed me hodology o pe o med s a is ical analysis and a summa ized explana ion o he di e en implemen ed s a is ical me hods. Las in his pa , he adop ed machine lea ning me hod- ology and a b ie explana ion o he di e en me hods and concep s inco po a ed in his me hodology, a e p esen ed. The las Pa o his disse a ion (Pa III) inco po a es he s a is ical esul s and machine lea ning esul s Chap e s. Thus, he esul s ob ained om he applica ion o he s a is ical and machine lea ning me hods, espec i ely, a e p esen ed and discussed in hese Chap e s. In his Pa he e is also a Chap e dedica ed o he conclusion o he disse a ion as well as i limi a ions and u u e wo k. The Appendices can be ound in he las pages o his disse a ion. These include an appendix ha is ela i e o he s a is ical analysis and ano he one ha is ela i e o some esul s ob ained using machine lea ning echniques. The con en o he appendices is in e media e esul s, ha is, esul s ha we e necessa y o each he inal esul s and conclusions. 4 Chap e 2 Fab y disease and hype ophic ca diomyopa hy disease Since he main goal o his s udy is o de ec impo an elec oca diog am cha ac e is ics o suppo and assis in an ea ly diagnosis o Fab y disease, i is essen ial o p esen a desc ip ion o his disease, i s pheno ype and clinical mani es a ions, how o diagnose i , and possible ea men s. Thus, his is he ocus o he i s sec ion o his chap e . Fab y is no he only disease add essed in his chap e , Hype ophic Ca diomyopa hy is also desc ibed in he second sec ion. This disease is included in his s udy due o he simila i ies in he ca diac mani es a ions o hese wo diseases, mainly le en icula hype ophy (LVH), which is no mally (40-60% o cases) caused by Sa come ic Hype ophic Ca diomyopa hy, howe e , in abou 5-10% o cases, unexplained LVH can be caused by o he non-gene ic o a e gene ic diso de s, such as Fab y [7]. 2.1 Fab y Disease This sec ion includes a desc ip ion o Fab y disease, i s pheno ype and clinical mani es a ions (wi h a desc ip ion o Whi e Ma e Lesions), how i is diagnosed and he possible ea men s. 5 2.1.1 Desc ip ion Fab y disease (FD), i s ecognized as a sys emic ascula disease, is an X-ch omosome-linked lysoso- mal s o age diso de caused by mu a ions in he galac osidase alpha (GLA) gene, ha esul in a de icien o e en absen ac i i y o he enzyme alpha-galac osidase A (α-GAL A). This de icien ac i i y leads o lyso- somal accumula ion o globo iaosylce amide (Gb3) and o he ela ed glycosphingolipids, since α-GAL A is esponsible o ca alyzing he hyd olysis o glycosphingolipids and pa icipa es in hei deg ada ion in he lysosome. Gb3 can accumula e in cells and o gans, o example, body luids, ascula endo helial cells, pe i helial, smoo h-muscle cells o blood essels, ca diomyocy es, ca diac conduc ion issue, and al ula ib oblas s. Fab y disease a ec s a small pe cen age o he popula ion, and so, i is conside ed a a e disease [1] [4] [8] [9]. 2.1.2 Pheno ype and Clinical Mani es a ions The mu a ions in he GLA can cause a p ac ically null enzyma ic ac i i y o can lead o esidual enzy- ma ic ac i i y (REA). The i s case is ela ed o se e e and ea ly onse classical pheno ypes ha de elop in childhood o adolescence, like ac opa es hesias (bu ning, ingling, o p ickling sensa ions o numbness in he ex emi ies), neu opa hic pain, hypohyd osis (dec eased swea ing), hea , cold and exe cise in ole - ance, co nea e icilla a (who l-like pa e n o golden b own o g ay deposi s in he in e io in e palpebal po ion o he co nea), angioke a omas ( ascula lesions in he skin and mucous memb anes), gas oin- es inal symp oms and p o einu ia (high p o eins concen a ion in he u ine); in adul hood, pa ien s also expe ience senso ineu al dea ness and ca diac, enal and ce eb o ascula mani es a ions. The second case is associa ed wi h a enua ed and la e-onse pheno ypes such as hose indica ed o adul hood and he pheno ype may be in luenced by he pa icipa ion o an o gan, such as he kidneys o he hea [4] [10]. Some o he ca diac mani es a ions in FD a e le en icula hype ophy (LVH) (unexplained by ab- no mal ca diac loading condi ions), which is he mos common, palpi a ions and a hy hmias, exe ional dyspnoea (pe son eels sho o b ea h du ing exe cise), small- essel co ona y disease (condi ion in which 6 he walls o he small a e ies in he hea a e no wo king p ope ly), and e en hea ailu e. The e o e, his disease leads o p ema u e dea h, being ca diac complica ions one o he mos common causes [1] [4] [9]. I has been p o ed ha symp oms occu ea lie in males han in emales, including ca diac symp oms like le en icula hype ophy and ha he disease mani es s in a mode a e way in women [1]. A s udy including Fab y pa ien s wi h p.F113L mu a ion epo ed whi e ma e lesions (WMLs) as a common mani es a ion ha inc eases wi h age and becomes a uni e sal inding abo e 70 yea s old (in bo h sexes). Howe e , due o he highe p e alence o WMLs in young pa ien s wi hou o he como bidi ies, WMLs seem o be caused by FD, p obably mainly by Gb3 deposi s in mic oglial cells and as ocy es, and no by age o o he condi ions. A simila conclusion was ound in a la ge coho o p.N215S pa ien s, di e ing only in he appea ing age, which is ea ly be o e 30 yea s old in he p.F113L mu a ion and be o e 40 yea s in his coho [4]. Whi e Ma e Lesions The exchange o in o ma ion and communica ion be ween di e en a eas o he g ay ma e is ca ied ou by a ne wo k o ne e ibe s denomina ed whi e ma e (WM). The Whi e ma e is loca ed below g ay ma e in he b ain co e ing almos hal o i and is supe icial o g ay ma e in he spinal co d. The neu al ne wo ks a e o med by ne e ibe s called axons ha a e he ex ensions o ne e cells (neu ons). The axons a e su ounded by a ype o shea h, he myelin, ha allows elec ical impulses o ansmi quickly and e icien ly along he ne e cells. Since myelin is composed o p o ein and a y subs ances i is esponsible o he whi e colo in he whi e ma e [11] [12] [13]. Whi e ma e lesions (WMLs) a e a consequence o ce eb al small essel disease (CSVD) on he b ain pa enchyma, along wi h lacuna in a c s, ce eb al mic obleeds and enla ged pe i ascula spaces. The e m CSVD inco po a es all he pa hological p ocesses o he ce eb al small essels and i is he mos common cause o ascula cogni i e impai men and demen ia. Whi e ma e lesions a e also called eukoa aiosis o whi e ma e hype in ensi ies being he las one mo e o a desc ip i e exp ession used on magne ic esonance imaging (MRI) since hese lesions a e bes seen as hype in ensi ies on T2 weigh ed and FLAIR (Fluid-a enua ed in e sion eco e y) sequences o MRI. Non- ascula condi ions may also lead o WMLs, o example, any change in chemical composi ion, damage, o ischemia o myelina ed ibe s. Demen ia, 7 he depola iza ion and epola iza ion o hea muscle (ca dio) allowing he iden i ica ion and loca ion o pa hology. This elec ical ac i i y (elec o) is small and is de ec ed by con ac elec odes placed on di e en pa s o pa ien ’s ches and limb [23] [24]. The ECG may be composed o 12 leads which p o ides iews o he hea in bo h on al and ho izon al planes, hus ob aining eco ds in di e en o ien a ions and pe spec i es. The e a e wo ypes o leads: he limb leads ha iew he hea in on al plane and he p eco dial leads o ches leads ha iew he hea in ho izon al plane. The i s one is composed by he leads I, II and III, called he s anda d leads and he ones ha o m he Ei ho en’s iangle, and also by h ee augmen ed limb leads, aVR, aVL and aVF. The second one, he p eco dial leads a e V1, V2, V3, V4, V5 and V6 [25] [26]. The e ical axis o an ECG eco d is ol age and he ho izon al is ime, he e o e, measu emen s in ho izon al axis indica e he o e all hea a e, egula i y, and he ime in e als du ing elec ical ac i a ion. In e ical axis, measu emen s indica e he ol age ha is measu ed in he su ace and ha ep esen he “summa ion” o he elec ical ac i a ion o all he ca diac cells [27]. In e p e a ion o ECG may de ec many ca diac abno mali ies, some only by a single ECG eco d and o he s by se ial eco ding o e ime [27]. Reco ds o hea ’s ac i i y du ing 24 o 48 hou s, o e en mo e, a e a chi ed by a po able de ice called Hol e moni o [28]. Elec oca diog am cha ac e is ics, such as in e als, ampli udes, and a es, can be ob ained by in e - p e ing he ECG. The e a e al eady se e al elec oca diog aphic indings obse ed in Fab y disease pa ien s. A sho PR in e al, signs o LVH, T wa e in e sion, b adyca dia, and a ial ib illa ion a e examples o hese elec- oca diog aphic indings [8] [10]. Sho ening o QRS wid h and inc eased QTc du a ion a e also iden i ied in some s udies [29] [30]. As p e iously desc ibed, pa ien s wi h HCM also exhibi elec oca diog aphic abno mali ies, o exam- ple, signs o en icula hype ophy wi h inc eased p eco dial ol ages, and non-speci ic ST segmen and T-wa e abno mali ies, deep in e io and/o la e al Q-wa es (sugges i e o a hype ophied sep al depo- la iza ion), P-wa e abno mali ies (sugges i e o le a ial enla gemen ), and T-wa e in e sions [18] [20] [21]. This p o es ha Fab y disease and HCM pa ien s do, in ac , show elec oca diog aphic abno mali ies. Also, he e is a huge need o iden i y o he causes o LVH besides sa come ic HCM and elec oca diog aphy 14 is one o he i s s eps when e alua ing hese pa ien s. The e o e, elec oca diog am could be an impo an ool o dis inguish and diagnose hese diseases. Some s udies al eady ied o iden i y ECG cha ac e is ics o dis inguish be ween FD and HCM, which is he case o Junqua e al. [5] and Namda e al [31]. Junqua e al. [5] aimed o assess he diagnos ic alue o elec oca diog aphic sco es o LVH in Fab y disease pa ien s and also he diagnos ic alue o Fab y disease o a model combining elec oca diog aphic and echoca diog aphic c i e ia. Junqua e al. e alua ed se e al ECG cha ac e is ics o 61 Fab y disease pa ien s and 59 pa ien s wi h sa come ic HCM. These cha ac e is ics we e hea a e (bpm), co ec ed PQ (ms), QRS du a ion (ms), co ec ed QT (ms), RBBB, LBBB, Le an e io hemiblock, Le pos e io hemiblock, p e-exci a ion, pa hologic Q wa e, a ial ib illa ion, and LVH indexes (Co nell ol age index (mm), Gubne index (mm), Sokolow—Lyon ol age index (mm), Romhil —Es es sco e, Sokolow—Lyon p od- uc (mm.ms), and Co nell p oduc (mm.ms)). A uni a ia e analysis was pe o med, using S uden ’s - es o con inuous a iables and Fishe es o chi-squa ed es o quali a i e a iables. Among he cha ac- e is ics, QRS du a ion was signi ican ly highe and RBBB mo e equen in he Fab y g oup. The LVH indexes, Gubne index and Sokolow—Lyon p oduc , we e also highe in his g oup (Fab y pa ien s). As o he emaining ECG cha ac e is ics, Junqua e al. did no ind signi ican di e ences be ween FD and HCM pa ien s. A mul i a iable analysis, wi h he elec oca diog am and echoca diog am a iables ha p esen ed a p- alue ≤0.01 in he uni a ia e analysis, was pe o med. Among he ECG a iables, only RBBB and Sokolow—Lyon p oduc we e independen ly associa ed wi h Fab y disease. I is impo an o men ion ha Junqua e al. ound ha age was signi ican ly di e en be ween FD and HCM g oups, being Fab y pa ien s olde han HCM pa ien s [5]. The aim o he s udy o Namda e al. [31] was o in es iga e he alue o common ECG pa ame e s in he diagnosis o pa ien s wi h Fab y disease (FD), amyloidosis, hype ensi e hea disease (HHD), ao ic s enosis (AS), and nonobs uc i e hype ophic ca diomyopa hy (HC). These ECG pa ame e s include es - ing hea a e (bea s/min), P-wa e du a ion (ms), P wa e co ec ed o hea a e (ms), PQ in e al (ms), co ec ed PQ in e al (ms), PQ in e al < 120 ms, PQ in e al minus P-wa e du a ion in lead II (ms), QRS du a ion (ms), Sokolow–Lyon index (mV, le en icula hype ophy and igh en icula hype ophy), maximum peak o end o T wa e (ms), co ec ed QT mean in e al (ms), and co ec ed QT dispe sion (ms). I should be no ed ha , in his s udy, g oups we e ma ched o age and le en icula muscle 15 mass index so ha i would no in luence ECG pa ame e s. Namda e al. compa ed he con inuous a i- ables wi h analysis o a iance o epea ed measu emen s and pos hoc analysis wi h Fishe ’s p obable leas -signi ican di e ences es and/o S uden ’s - es . As o ca ego ical a iables, hese we e compa ed using Fishe ’s exac es . The s udy included 94 pa ien s, being 17 diagnosed wi h FD, 20 wi h HHD, 17 wi h amyloidosis, 20 wi h AS, and 20 wi h HC. In he FD g oup, PQ in e al, co ec ed PQ in e al, and PQ in e al minus P-wa e du a ion in lead II a iables we e signi ican ly sho e . These wo las cha ac e - is ics led o he highes diagnos ic pe o mance o he diagnosis o FD, wi h cu -o alues o 114 ms and 40 ms, speci ici y o 90% and 99%, AUC o 0.90 and 0.94, espec i ely, and sensi i i y o 82% on bo h. Howe e , Namda e al. ealised ha he combina ion o no mal co ec QT in e al (i.e., < 440 ms) and sho PQ in e al minus P-wa e du a ion in lead II (i.e., < 40 ms) ga e a be e diagnos ic pe o mance o he diagnosis o FD, wi h speci ici y o 99% and sensi i i y o 100%. Should be no ed ha none o he HC pa ien s ul illed hese wo c i e ia [31]. As p e iously men ioned, WMLs a e a mani es a ion in FD pa ien s, and simila o he s udies ha aimed o dis inguish FD om HCM pa ien s, he e is also s udies ha aimed o dis inguish FD pa ien s wi h WMLs om FD pa ien s wi hou WMLs, based on elec oca diog am cha ac e is ics, which is he case o B aga (2021) [32]. B aga (2021) [32] e alua ed ECG cha ac e is ics o 114 FD pa ien s, in which 61 ha e WMLs and 53 do no ha e WMLs. These ECG cha ac e is ics include hea a e a iables (HR Min, HR Mean, HR Max), HRV a iables (ASDNN 5, SDANN 5, SDNN, RMSSD), QT analysis a iables (QT Min, QT Mean, QT Max, QTc Min, QTc Mean, QTc Max, QTc ≥450). and a sup a en icula ec opy a iable (Longes R-R). B aga (2021) iden i ied ha 6 ECG cha ac e is ics, HR Max, QT Min, QT Mean, QT Max, QTc Mean, and QTc ≥450, we e signi ican ly di e en be ween he wo g oups. Age was also signi ican ly di e en be ween he g oups, wi h FD wi h WMLs being olde han FD wi hou WMLs pa ien s. These compa ison o con inuous a iable was done wi h - es and Mann Whi ney U Tes , o no mally and non-no mally dis ibu ed a iables, espec i ely. Then, B aga (2021) pe o med a uni a ia e logis ic eg ession analysis o e alua e he associa ion be ween each ECG a iable and he p esence o WMLs and ealised ha HR Max, QT Min, QT Mean, QTc Mean, and QTc ≥450 a iables p esen ed a signi ican associa ion wi h he p esence o WMLs. Howe e , when adjus ed by age, none o he ECG a iables p esen ed a signi ican associa ion wi h he p esence o WMLs. Due o he signi ican di e ence in he age o he wo g oups, B aga (2021) di ided he pa ien s in o age 16 classes, and epea ed he uni a ia e and mul i a iable analysis in he age class o [40,60[ ( he only class wi h simila numbe o pa ien s in each g oup) ha did no p esen signi ican di e ences on pa ien s’ age o sex. Two a iables, o HRV, we e signi ican ly associa ed wi h he p esence o WMLs, SDANN 5 and SDNN a iables. When adjus ed o age o sex, hese wo a iables emained associa ed wi h he p esence o WMLs [32]. Ano he ele an s udy, Galluzzi e al. [33], also uses ECG da a, mo e speci ically, HRV da a o pa ien s wi h and wi hou WMLs. Howe e , in his s udy, pa ien s ha e mild cogni i e impai men (MCI) ins ead o FD. Thus, he aim o his s udy was o e alua e he independen associa ion o HRV wi h WMLs in pa ien s wi h mild cogni i e impai men (MCI). Galluzzi e al. used 24-hou ECG eco dings o 82 MCI pa ien s, in which 32 p esen WMLs, o calcula e HRV a iables. In ime domain, s anda d de ia ion o he RR in e als, s anda d de ia ion o he 5-minu e mean alues o RRs o each 5-minu e in e al, a e age o s anda d de ia ions o RR o each 5-minu e in e al, and he RMSSD we e calcula ed. As o equency domain, low equency (LF) 0.04 – 0.15 Hz, HF 0.15 – 0.40 Hz, and low high- equency a io we e calcula ed. The di e ences be ween MCI wi h and wi hou WMLs g oups we e assessed using - es and Mann-Whi ney o no mally dis ibu ed and non-no mally dis ibu ed con inuous a iables, espec i ely, and chi-squa e o ca ego ical a iables. Galluzzi e al. also e alua ed he associa ion be ween each HRV index and WMLs (ARWMC, age- ela ed whi e ma e changes, scale o al sco e, om magne ic esonance imaging) h ough linea eg ession models, and he po en ial o HRV indices o p edic he ex en o WMLs wi h a s epwise mul iple eg ession model. In his s udy, age was signi ican ly di e en be ween he wo g oups, pa ien s wi h WMLs being olde han hose wi hou WMLs. Di e ences we e also ound in RMSSD and LF ha we e educed in MCI pa ien s wi h WMLs. Galluzzi e al. ound ha RMSSD, LF, and HF we e in e sely associa ed wi h he ex en o WMLs in he unadjus ed models, howe e , in he adjus ed models, RMSSD was he only a iable ha emained in e sely associa ed. As o he s epwise esul s, hese showed ha RMSSD and age we e signi ican p edic o s o WMLs [33]. In conclusion, all he p esen ed s udies demons a e ha ECG cha ac e is ics a e al eady used as da a o diagnose and o dis inguish diseases and/o mani es a ions, which is he case o Fab y disease and Whi e Ma e Lesions, and ini ially p omising esul s ha e been achie ed. 17 3.2 ECG-based machine lea ning algo i hms o classi ica ion Machine lea ning (ML) is a b anch o compu a ional algo i hms ha a e in ended o ep oduce human in elligence by being able o de ec meaning ul pa e ns in da a e en i he da ase s a e complex and la ge [34]. A co ec diagnosis o a disease o condi ion is a complex p ocess since a lo o symp oms a e non- speci ic and a iable among pa ien s, some diagnos ic es s a e no egula ly done and a e expensi e, and i equi es a huge human e o , as well as ime. Also, physicians a e usually suscep ible o cogni i e bias du ing he diagnosis s age, being mo e biased o diseases o condi ions ha hey ha e al eady diagnosed in he pas and, he e o e, a e mo e amilia wi h. Due o he p e alence o a e diseases, he e is a highe p obabili y ha physicians ha e cogni i e bias du ing he diagnosis s age o hese diseases [35] [36] [37]. Machine lea ning is use ul o medical diagnosis since wi h unbiased and balanced da ase s, ML algo i hms a e able o a enua e he cogni i e bias p oblem and, hus, p oduce highe accu acy. Machine lea ning has been applied o a a ie y o medical diagnosis p oblems, o example, b eas cance , diabe es, cance issues, and hy oid [35] [37]. Simila o wha is p oposed in his s udy, se e al s udies ha e also applied classi ica ion supe ised ML algo i hms o ECG da a, which is he case o Hija i e al. [6], Vigie e al. [38], Munla e al. [39], and B aga (2021) [32]. Wha is p oposed by each o hese s udies, as well as he main me hods and esul s, a e now going o be b ie ly explained. Hija i e al.[6] a emp ed o iden i y pa ien s a isk o Long QT Synd ome (LQTS) symp oms, by aining ML algo i hms wi h inpu a iables ex ac ed om aw ECG da a. The pu pose was o a classi ie o be able o ou pu “symp oms expec ed” o “no symp oms expec ed” based on some measu emen s om an ECG. Hija i e al. conside ed ha QT and RR in e als we e he mos ele an ma ke s o hei s udy and used 24-hou ECG eco ds o 434 pa ien s wi h he mos common LQTS geno ypes. Then, hey implemen ed se e al classi ica ion algo i hms, such as k-nea es neighbo s, linea SVM, RBF SVM, andom o es , and AdaBoos , using sciki -lea n (Py hon lib a y) [40]. Finally, hey de e mined he classi ie s’ accu acy by lea ing 30% o he samples o es ing and 70% o aining, and doing he p ocess o selec ion o aining da a, aining and es ing 50 imes o each classi ie , hen calcula ing he a e age esul . In conclusion, 18 he classi ie ha pe o med be e , in he es phase, in he Hija i e al. s udy, was he RBF SVM classi ie wi h abou 70% accu acy, and he andom o es classi ie achie ed he second-bes accu acy [6]. Vigie e al. [38] aimed o c ea e and e alua e a machine lea ning model able o disc imina e be- ween cance pa ien s and heal hy con ols based on 5-min ECG eco dings. They selec ed 12 hea a e a iabili y (HRV) ea u es, which we e hen educed o he op 5 (SDNN, RMSSD, pNN50%, HRV iangu- la index, and SD1) wi h ecu si e ea u e elimina ion (RFE). These ea u es we e hen used as inpu o h ee di e en machine lea ning algo i hms: linea disc imina ion analysis (LDA), andom o es , and nai e bayes. An ensemble model based on he s acking me hod, which comp ised he p edic ions o he h ee base classi ie s, was also implemen ed. The s udy included 77 cance pa ien s (b eas , p os a e, lung, colo ec al, and panc ea ic cance s) and 57 heal hy con ols, 40% o he da ase was used o es ing and he emaining 60% o aining, wi h a en old c oss alida ion. Vigie e al. concluded ha among he h ee base ML algo i hms, andom o es was he one ha pe o med bes du ing he aining e alua ion, wi h an accu acy o 85%. The ensemble model pe o med be e han all base classi ie s, wi h an accu acy o 0.929 in he aining phase and 0.865 in he es phase [38]. A s udy, pe o med by Munla e al. [39], in es iga ed s ess le el de ec ion o a d i e du ing a eal wo d d i ing expe imen , based on hea a e a iabili y (HRV) analysis. Munla e al. pe o med di e en HRV analyses, in ime, equency, non-linea , and ime- equency. The ea u es ex ac ed om hese anal- yses we e used, sepa a ely, as inpu da a o h ee ML algo i hms, k-nea es neighbo (KNN), adial basis unc ion (RBF) and suppo ec o machine wi h linea and RBF ke nels, in o de o classi y da a in o wo physiological s a es o he d i e , highly s essed o no mal. The SVM wi h RBF ke nel was he model ha p esen ed he bes esul s, wi h a co ec p edic ion a e o 83.33% bo h wi h ime and non-linea pa am- e e s, and 66.66% wi h equency, poinca e (a non-linea analysis) and STFT (a ime- equency analysis me hod) pa ame e s [39]. One o he objec i es o a s udy pe o med by B aga (2021) was o e alua e he e ec i eness o ma- chine lea ning me hods o disc imina e Fab y disease (FD) pa ien s wi h whi e ma e lesions (WMLs) om Fab y disease pa ien s wi hou whi e ma e lesions based on ECG da a. Fo his, B aga (2021) used 48 Fab y disease pa ien s, whe e 23 ha e WMLs and 25 do no ha e WMLs. A e pe o ming wo ea u e selec ion me hods, one being a il e me hod ha selec ed he 10 mos signi ican ea u es no co ela ed (using Mann Whi ney U Tes and a |ρ|<0.80) and he o he ecu si e ea u e elimina ion (RFE), B aga 19 (2021) ended up wi h 4 elec oca diog am ea u es, which we e hea a e mean and maximum, QT max- imum, and SDANN 5. Using hese 4 ea u es and SDANN 5 ea u e alone, i e classi ica ion algo i hms, logis ic eg ession (LR), SVM linea Ke nel, SVM RBF ke nel, andom o es (RF), and k-nea es neigh- bo s (KNN), we e applied, in o de o iden i y he op imal combina ion o ea u es and he classi ica ion model wi h he bes pe o mance. In he case o he 4- ea u e combina ion, he model ha ga e he high- es alida ion accu acy, 79.72%±1.40%, was RF, ollowed by KNN wi h a alida ion accu acy equal o 77.75%±1.57%. Howe e , using only he SDANN 5 ea u e, he model ha ga e he highes alida ion accu acy was SVM linea ke nel wi h 74.53%±0.67%, ollowed by LR wi h 74.52%±0.72%. To no e ha o e alua e he models’ pe o mance a 5- old c oss alida ion was used [32]. All hese s udies a e examples o he medical diagnosis powe o machine lea ning, in his case, mo e speci ically, when i is applied o ECG da a, since hey show se e al machine lea ning algo i hms ha lead o high classi ica ion pe o mances (mos abo e 70%). 20 Pa II : Ma e ials and Me hods 21 Chap e 4 S udy da a This chap e in oduces he sample o indi iduals included in his s udy and some o hei demog aphic cha ac e is ics. The e alua ed a iables and hei no mal e e ence ange o alues acco ding o age and/o sex a e also p esen ed in his chap e . 4.1 S udy Sample The s udy sample included Fab y disease (FD) pa ien s and Sa come ic Hype ophic ca diomyopa- hy (HCM) pa ien s om he Ca diology and Neu ology Depa men s o Hospi al Senho a da Oli ei a in Guima ães ci y, Po ugal. This s udy e ospec i ely en olled 114 pa ien s wi h FD (GLA gene mu a ion c.337T>C (p.F113L)), in which 61 (53.51%) ha e WMLs and 53 (46.49%) do no , and also 39 pa ien s wi h Sa come ic HCM. The pa ien s’ ages ange be ween 19-91 yea s inclusi e (Table 1). While he pe cen ages o emales in he FD wi h WMLs g oup and he FD wi hou WMLs a e 62,3% and 60,4% espec i ely, in he HCM g oup i is only 33,3%. 22 Table 1: Demog aphic cha ac e is ics o he s udy sample HCM (n=39) FD wi h WMLs (n=61) FD wi hou WMLs (n=53) Sex (Female numbe ) 13 38 32 Age ([Minimum, Maximum] yea s) [21, 87] [20, 91] [19, 71] Since Hol e a iable measu es a y ac oss age and sex [41] and age is he s onges known isk ac o o he onse o WMLs [42] [43], he pa ien s we e subg ouped in o h ee age classes: age 19-39 yea s, age 40-59 yea s, and age > 59 yea s (Table 2). The numbe o FD pa ien s wi h WMLs and HCM pa ien s in age class 19–39 yea s is e y low, wi h 8 and 4 pa ien s, espec i ely. Thus, his age class was no included in his s udy. Fu he mo e, as he e a e only 3 FD pa ien s wi hou WMLs olde han 59 yea s, his subg oup o pa ien s was also excluded. Table 2: Pa ien s coun pe g oup and age class Age Class HCM FD wi h WMLs FD wi hou WMLs Pa ien s (Females) Pa ien s (Females) Pa ien s (Females) [19,39] 4 (1) 8 (6) 25 (14) [40,59] 16 (6) 23 (13) 25 (17) [60,91] 19 (6) 30 (19) 3 (1) 4.2 24-Hou Hol e As men ioned in Sec ion 3.1, an Elec oca diog am (ECG) is an exam ha eco ds he po en ial changes a skin su ace ha esul om he depola iza ion and epola iza ion o he hea muscle, hus, allowing he iden i ica ion and loca ion o pa hologies. The e o e, a single ECG o a eco ding o e ime (24 o 48 hou s) achie ed by a Hol e moni o , a e powe ul exams since hey can de ec many ca diac abno mali ies [23] [27]. 23 a iances. Welch es has he ad an age o keeping ype I e o a e despi e he e oscedas ic a iances [51] [52] [53]. • Null hypo hesis (H0): All g oup means in he popula ion a e equal. • Al e na i e hypo hesis (H1): A leas one g oup mean in he popula ion di e s om he o he s. To apply he Welch-ANOVA es , a unc ion om he pingouin lib a y [47], he welch_ano a() unc ion, was used. And, as explained, his es was applied o he a iables ha ha e a no mal dis ibu ion (e al- ua ed p e iously by Shapi o es ) bu do no ha e homogenei y o a iances (e alua ed by Le ene’s es ) . K uskal-Wallis Tes The K uskal-Wallis es is he nonpa ame ic equi alen o he one-way ANOVA and so i is used o de e mine whe he mo e han wo independen samples ha e a di e en dis ibu ion [51]. • Null hypo hesis (H0): Popula ion median o all g oups a e equal. • Al e na i e hypo hesis (H1): Popula ion median o all g oups a e no equal. The ejec ion o he null hypo hesis (signi ican es ) and he e o e he accep ance o he al e na i e hypo hesis, means ha a leas one o he samples is di e en om he o he samples. Like in one-way ANOVA, K uskal-Wallis also does no iden i y whe e he di e ence occu s nei he how many occu . We do no ejec he null hypo hesis when he es is non-signi ican and, so, we conclude ha all sample dis ibu ions a e equal. Since his es is he nonpa ame ic equi alen o he one-way ANOVA es , i was only pe o med on he a iables which we e no no mally dis ibu ed (e alua ed p e iously by Shapi o-Wilk es ). One mo e ime, he es s a is ic and p- alue we e ob ained, bu his ime wi h he k uskal() unc ion om he scipy.s a s module [45]. 30 Unpai ed - es The unpai ed - es is also known as independen - es and i is a s a is ical hypo hesis es used o es whe he he means o wo g oups a e equal, when he e is wo independen (un ela ed) g oups and one nume ical o o dinal a iable o in e es . This es makes some assump ions, such as ha he a iable o in e es is no mally dis ibu ed in each g oup and ha he e is homogenei y o a iances ( he a iances o he wo g oups a e equal) [49] [51]. • Null hypo hesis (H0): The popula ion means in he wo g oups a e equal. • Al e na i e hypo hesis (H1): The popula ion means in he wo g oups a e no equal. So, when we ejec he null hypo hesis (signi ican es , wi h p < 0.05) ha indica es ha he e is su icien e idence ha he popula ion means in he wo g oups a e di e en , and so, he dis ibu ions a e no equal. Howe e , i we do no ejec he null hypo hesis, (non-signi ican es , wi h p > 0.05) hen i indica es ha he popula ion means in he wo g oups a e equal. The Py hon unc ion used o his es was es _ind() om he s a smodels lib a y [46], s a s.weigh s a s module. Due o es assump ions, his unc ion was only applied o he a iables ha p esen ed a no mal dis ibu ion ( e i ied by Shapi o-Wilk es ) and homogenei y o a iances ( e i ied by Le ene’s es ). Mann Whi ney U Tes The Mann-Whi ney is he non-pa ame ic equi alen o he unpai ed - es . This es was named o Hen y Mann and Donald Whi ney, al hough i is some imes called he Wilcoxon-Mann-Whi ney es , om F ank Wilcoxon, who also de eloped a a ia ion o he es o Wilcoxon’s ank sum es . This es is a s a is ical signi icance es used o de e mine whe he wo independen samples we e d awn om a popula ion wi h he same dis ibu ion [49] [51]. • Null hypo hesis (H0): Sample dis ibu ions a e equal. • Al e na i e hypo hesis (H1): Sample dis ibu ions a e no equal. So, i we do no ejec he null hypo hesis (p > 0.05) i means ha bo h samples we e d awn om a popula ion wi h he same dis ibu ion. On he o he hand, we conclude ha sample dis ibu ions a e no 31 equal when we ejec he null hypo hesis and ha happens when he es is signi ican (p < 0.05). This es was applied h ough he mannwhi neyu() unc ion om he s a s module o he scipy lib a y [45]. Since his es is he non-pa ame ic equi alen o he unpai ed - es , i was only applied o hose a iables which we e no no mally dis ibu ed (e alua ed p e iously by he Shapi o-Wilk es ). Pos Hoc Tes s Pos hoc es s, also e e ed o as a pos e io i o unplanned es s, o e en mul iple compa ison es s, a e s a is ical es s ha a e applied a e a signi ican F es . As explained, he p e ious es s, i.e, one-way ANOVA, Welch ANOVA and K uskal-Wallis only indica e ha he e is a signi ican means di e ence be ween he g oups, hey do no indica e in which g oups pai o pai s ha di e ence occu s. To o e come his, pos hoc es s allow compa isons be ween a pai o g oup means in o de o speci y which o he pai s o means a e s a is ically signi ican ly di e en om each o he . This is almos simila o aking e e y pai o g oups and pe o ming a - es on each pai , howe e , pai wise compa isons ha e an ad an age, hey con ol he amilywise e o by co ec ing he le el o signi icance o each es , so ha he o e all Type I e o a e ac oss all compa isons emains a 0.05 [50] [54] [55]. The Tukey es uses pai wise pos hoc es ing o de e mine which o h ee o mo e sample means a e signi ican ly di e en a e ob aining a signi ican ANOVA F- es . Thus, his es is an ANOVA pos hoc es , which is usually known as Tukey’s HSD (Hones ly Signi ican Di e ence), howe e , he Tukey HSD is only used when he samples sizes o he g oups a e equal. This es was modi ied by K ame , so ha i could be used in cases whe e he samples sizes o he g oups a e no equal and i is called he Tukey-K ame me hod [56] [57] [58]. Then, his es was only applied on he a iables ha ga e a signi ican one-way ANOVA, h ough he pai wise_ ukey() unc ion om he pingouin lib a y [47]. This unc ion applies he pai wise Tukey HSD pos hoc es , howe e , i he samples sizes a e no equal, i au oma ically uses he Tukey-K ame me hod. The Games-Howell es is an ex ension o he Tukey-K ame es and is app op ia e in cases wi h unequal a iances as well as unequal sample sizes. The es con ols he ype I e o o he whole compa ison and also main ains he de aul signi icance le el e en when he size o he sample is di e en . Howe e , his es may be oo libe al o small sample sizes and he e o e should only be used in sample sizes g ea e han i e [56] [59]. Since his es is indica ed o cases wi h unequal a iances, Games- 32 Howell is he pos hoc es o Welch ANOVA, and, he e o e, is applied only in he a iables ha had a signi ican esul in Welch ANOVA es . The Py hon unc ion used o his es was pai wise_gameshowell() om he pingouin lib a y [47]. The e is also Dunn’s es which is a pos hoc pai wise es o mul iple compa isons o mean ank sums. This es is he app op ia e p ocedu e a e a signi ican K uskal-Wallis es [60]. Fo Dunn’s es , he Py hon unc ion used was pos hoc_dunn() om he sciki -pos hocs package [40]. 5.2.4 Di e ences be ween independen samples: quali a i e da a Chi-Squa ed Tes Chi-squa ed es , also known as Pea son’s Chi-squa ed es , named o Ka l Pea son, is a s a is ical hypo hesis es o de e mine whe he he e is a ela ionship be ween wo ca ego ical a iables ( ac o s), mo e speci ically, whe he he p opo ions o indi iduals who possess a ce ain cha ac e is ic a e he same in he independen g oups. This da a can be ep esen ed in a x c con ingency able, wi h ows and c columns, in which o each cell we calcula e he expec ed equencies, hen, de e mine whe he he di ision o he g oups, called he obse ed equencies, ma ches he expec ed equencies. The esul is a es s a is ic ha has a Chi-Squa ed dis ibu ion, denomina ed o he G eek lowe case le e chi (χ) [49] [50] [51]. • Null hypo hesis (H0): The e is no associa ion be ween he ca ego ies o one ac o and he ca ego ies o he o he ac o in he popula ion. • Al e na i e hypo hesis (H1): The wo ac o s a e associa ed in he popula ion. So, i he es is signi ican (p < 0.05) we should ejec he null hypo hesis and accep he al e na i e one, ha he wo ac o s a e associa ed in he popula ion. On he o he hand, i he es is non-signi ican (p > 0.05), we should no ejec he null hypo hesis, so, he e is no associa ion be ween he ca ego ies o one ac o and he ca ego ies o he o he ac o in he popula ion, ha is, hey a e independen . 33 The Py hon unc ion used o Chi-Squa ed es was chi2_con ingency() om he scipy lib a y [45], s a s module. This unc ion was applied o de e mine whe he he e was a ela ionship be ween Sex (Female o Male) and g oup, a e he acquisi ion o he 3x2 con ingency able wi h hese p opo ions. Fishe ’s Exac es Fishe ’s exac es is no mally used when he e a e wo independen g oups and we a e in e es ed in whe he he p opo ions o indi iduals who ha e a cha ac e is ic a e he same in bo h g oups. This es should be applied in small samples (whe e he expec ed equencies a e small) since i was designed o o e come a p oblem wi h hese samples which is ha he sampling dis ibu ion o he chi-squa e s a is ic di e subs an ially om a chi-squa e dis ibu ion. In ac , Fishe ’s exac es is mos ly a way o compu ing he exac p obabili y o he chi-squa e s a is ic, ins ead o a es [49] [50]. This es can also be used as pos hoc es by applying a 2x2 Fishe ’s exac es o each o he pai wise compa isons, bu hen co ec o mul iple compa isons using o example he Bon e oni co ec ion (used o con ol he amilywise e o a e) [58]. • Null hypo hesis (H0): he p opo ions o indi iduals wi h he cha ac e is ic a e equal in he wo g oups in he popula ion. • Al e na i e hypo hesis (H1): hese popula ion p opo ions a e no equal. Iden ically o o he hypo hesis es s, when he Fishe ’s exac es is non-signi ican (p > 0.05), we mus no ejec he null hypo hesis, and in his case ha means ha he p opo ions o indi iduals wi h he cha ac e is ic a e equal in he wo g oups in he popula ion. On he o he hand, i he es is signi ican (p < 0.05) we should ejec he null hypo hesis and accep he al e na i e one, which indica es ha hese popula ion p opo ions a e no equal. This es was applied o e alua e whe he he p opo ions o emale and male indi iduals (sex a iable) a e he same in wo g oups. Tha way, he Py hon unc ion ishe _exac () om he scipy lib ab y [45], s a s module was used, a e ob aining he 2x2 con ingency able. When used as pos hoc es , he unc ion mul iple es s() om s a smodel lib ab y, s a s.mul i es module, was also applied. This unc ion akes he p alues ob ained in he Fishe ’s exac es as a gumen and, he “me hod” a gumen equal o “bon e oni”. 34 5.3 Logis ic Reg ession Analysis Logis ic eg ession is used when he ou come/dependen a iable (Y) is ca ego ical and he e is one o mo e p edic o /explana o y/independen a iables (X) ha a e con inuous o ca ego ical. When he ou come a iable has only wo possible ca ego ical ou comes, his eg ession is known as bina y logis ic eg ession. When we analyze he ela ionship be ween one independen a iable and one dependen a iable, we o en call i uni a ia e analysis. When we analyze he ela ionship be ween wo o mo e independen a iables and one ou come a iable (dependen ) we call i a mul i a iable analysis. In he case o ela ionships o se e al p edic o s wi h wo o mo e ou come/dependen a iables a he same ime, i is called a mul i a ia e analysis [49] [50] [61] [62]. The unc ion used o exp ess he ela ionship be ween he p edic o a iables and he bina y ou come a iable is he logis ic, his is why i is called logis ic eg ession. The logis ic eg ession equa ion enables he de e mina ion o which explana o y a iables in luence he ou come and, using an indi idual´s alues o he explana o y a iables, e alua e he p obabili y ha he indi idual will ha e a pa icula ou come. A mul i a iable logis ic eg ession model ( wo o mo e explana o y a iables) is exp essed as [49] [50] [61]: logi (p) = a+b1x1+b2x2+... +bkxk(5.1) Whe e, logi (p) = ln p 1−p(5.2) In hese equa ions: • xiis he i h explana o y a iable (i=1,2,3,...,k); •pis a binomial p opo ion; •ais he es ima ed cons an e m; •b1,b2, . . . , bka e he es ima ed logis ic eg ession coe icien s. 35 In a logis ic eg ession model, he odds a io (OR) is a measu e o associa ion be ween an explana o y a iable and he ou come. The OR ep esen s he odds ha an ou come will occu gi en a pa icula explana o y a iable, compa ed o he odds o he ou come occu ing in he absence o ha p edic o a iable. The OR is ob ained by he exponen ial o a coe icien . Fo example, exp(b1) is he es ima ed odds o an ou come o (x1+ 1) ela i e o he es ima ed odds o an ou come o x1, while adjus ing o all o he x’s in he equa ion. The e o e, using he exp(b1) example, i means ha when he e is a one uni change in he x1and he o he explana o y a iables a e held cons an , he odds o Y = 1 change by exp(b1) uni s. When he odds a io alue is abo e one his indica es an inc eased odds o ha ing he ou come linked o Y= 1, on he o he hand, i he odds a io alue is below one, hen i indica es a dec eased odds o ha ing he ou come linked o Y= 1, as he pa icula explana o y a iable inc eases by one uni [49] [61]. I is possible o ob ain a Wald es s a is ic o each explana o y a iable [49]: • Null hypo hesis (H0): The ele an logis ic eg ession coe icien is ze o. • Al e na i e hypo hesis (H1): The ele an logis ic eg ession coe icien is di e en om ze o. I is also possible o e alua e all explana o y a iables and hei e ec on he ou come, o example wi h chi-squa e o co a ia es [49]: • Null hypo hesis (H0): All he logis ic eg ession coe icien s in he model a e ze o. • Al e na i e hypo hesis (H1): A leas one logis ic eg ession coe icien is di e en om ze o. Fo each Hol e a iable, a uni a ia e logis ic eg ession analysis, assuming he Hol e a iable as he explo a o y a iable and he p esence o one o he diseases as he ou come, was pe o med, using he Logi () unc ion om he s a smodels lib a y [46], disc e e.disc e e_model module. As he associa ion o a Hol e a iable wi h he p esence o a disease could be a ec ed by Sex and Age di e ences [63] [64], o each Hol e a iable, wo mul i a iable logis ic eg ession analyses we e also pe o med: 1) Age and Hol e a iable as explana o y a iables; and 2) Sex and Hol e a iable as explana o y a iables. These logis ic eg ession models ha e also been applied h ough he Logi () unc ion. 36 Chap e 6 The implemen ed Machine Lea ning me hods This chap e inco po a es a desc ip ion o he di e en s eps ha we e applied o ou da a in o de o achie e he inal classi ica ion machine lea ning models. The main s eps a e p esen ed in he lowcha o Figu e 1. As can be seen, he me hodology is di ided in o wo di e en phases: ea u e selec ion and classi ica ion. Figu e 1: Me hodology machine lea ning-based lowcha . 37 Fi s , da a we e submi ed o a il e supe ised ea u e selec ion me hod. The goal was o de e mine i he e was any mul icollinea i y be ween he independen a iables in his s udy. This was done by de e mining he a iance in la ion ac o (VIF) alues and he highly co ela ed a iables (which ha e a g ea VIF alue) we e excluded om he se h ough a s epwise p ocedu e. Then, o each o he 3 machine lea ning algo i hms (logis ic eg ession (LR), suppo ec o machines wi h linea ke nel (linea SVM), and andom o es (RF)), he hype pa ame e s alues/s a us ha adjus ed be e o he da a (highe accu acy), we e disco e ed. This is called hype pa ame e uning and was done wi h a g id sea ch s a egy using he s anda dized da a o ain he models and lea e-one-ou c oss- alida ion (LOOCV) o e alua e he pe o mance o he models. A e he hype pa ame e s uning each o he imp o ed models was used in a second ea u e selec ion me hod. This ime a w appe ea u e selec ion me hod was pe o med, he ecu si e ea u e elimina ion (RFE), o disco e which numbe and combina ion o ea u es lead o be e classi ica ion pe o mances. The jus desc ibed p ocedu es a e pa o he ea u e selec ion phase. Now ha ea u es a e selec ed, he classi ica ion phase akes place. Each o he ea u e combina ions was used o ain 5 di e en machine lea ning models: logis ic eg ession (LR), SVM wi h linea ke nel (linea SVM), SVM wi h adial basis unc ion (RBF) ke nel (RBF SVM), andom o es (RF), and k-nea es neighbo s (KNN). Since he da a ha is used in hese models is no he o iginal da a, he hype pa ame e s uning p ocedu e, desc ibed p e iously, is also applied in he classi ica ion phase. This way, he inal classi ica ion models a e achie ed. The desc ibed me hodology is applied o h ee dis inc bina y classi ica ion p oblems. In one p oblem he classes indica e whe he an FD pa ien has WMLs (class 1) o no (class 0), he o he whe he a pa ien has FD wi h WMLs (class 1) o has HCM (class 0), and he las , whe he a pa ien has FD wi hou WMLs (class 1) o has HCM (class 0). 38 6.1 C oss- alida ion When we a e building a machine lea ning model, we a e in e es ed in e alua ing i s pe o mance, mainly, in disco e ing how well he model pe o ms on unseen da a. O e i ing is he mos common p oblem in applied machine lea ning and i leads o models wi h poo pe o mance. O e i ing happens when a model is oo adjus ed o he aining da a, ha is, when he model ac ually lea ns oo much o he de ail and noise o he aining da a. This esul s in a model wi h poo pe o mance because he model in e p e s he lea ned noise as concep s and, wi h new da a, hese concep s do no exis , so, he model’s pe o mance on he new da a is nega i ely a ec ed. This is a huge p oblem because his is he pe o mance ha we a e mos in e es ed in, no he aining pe o mance [65] [66]. To o e come his p oblem we can use c oss- alida ion o es ima e he model’s pe o mance on unseen da a. In c oss- alida ion, he aining da ase is spli in o ain se and alida ion se , in di e en ways (di e en obse a ions in each se , each ime) using some s a egy and hen, mul iple i e a ions o each model on hese di e en spli s a e buil [65] [66]. The e a e se e al c oss- alida ion s a egies ha di e only in he way ha he ini ial ain se is di ided in o he ain se and alida ion se . In his s udy lea e-one-ou c oss- alida ion (LOOCV) is he used s a egy since se e al s udies de end i s use o e alua e he pe o mance o a classi ica ion model when he sample size is small, which is ou case. In LOOCV, he alida ion se includes only an obse a ion (in ou case, a pa ien ), and he emaining obse a ions, n-1 (being n he sample size), a e pa o he ain se , hus, his s a egy pe o ms n i e a ions o each model [65] [66] [67] [68]. The sciki -lea n [40] lib a y has a Lea eOneOu class ha was used in his s udy o apply he lea e- one-ou c oss- alida ion. As p e iously men ioned, his c oss- alida ion s a egy is inco po a ed in he hype pa ame e uning p ocess, which will now be explained. 39 speci ic, his ou pu a iable is ca ego ical, in ac , is dicho omous, since i is ei he ha ing o no ha ing a condi ion/disease. So, as explained, his is a classi ica ion p oblem, and, he e o e, he models applied o ou da a a e logis ic eg ession, suppo ec o machine, andom o es , and also K-nea es neighbo s. 6.4.1 Logis ic Reg ession Logis ic eg ession was al eady desc ibed in Sec ion 5.3 whe e i was used o exp ess he ela ionship be ween he p edic o a iables and he bina y ou come a iable. This ime we a e using logis ic eg ession as a p edic i e model. Howe e , he logis ic eg ession unc ion is he same in bo h si ua ions, he only di e ence is ha when using logis ic eg ession as a p edic i e model, we wan o calcula e he p obabili y o he de aul class ( he i s class), and, he e o e, we use Equa ion 6.2, which is equi alen o Equa ion 5.2 (in oduced in Sec ion 5.3) [65] [66]. p(x) = ea+b1x1+b2x2+...+bkxk 1 + ea+b1x1+b2x2+...+bkxk (6.2) The logis ic eg ession coe icien s (b1,b2, ..., bk) a e es ima ed om he aining da a using maximum- likelihood es ima ion (common lea ning algo i hm). A e es ima ing hese coe icien s, hey a e used in he equa ion, as well as he inpu ec o x (x1,x2, ..., xk), o calcula e he p obabili y (p(x)) [65] [66]. Then, he p obabili y p edic ion is ans o med in o a bina y alue/ class (0 o 1) [65] [66]: p edic ion =     0,i p(x)<0.5 1,i p(x)≥0.5 (6.3) I is impo an o no ice ha , when he e a e highly co ela ed inpu s, he likelihood es ima ion p ocess can ail o con e ge and he logis ic eg ession model can o e i . The e o e, i is impo an o emo e highly co ela ed inpu s be o e applying he logis ic eg ession [65] [66]. In his s udy, he logis ic eg ession model was c ea ed using he Logis icReg ession sciki -lea n’s class [40]. 46 6.4.2 Suppo Vec o Machines The suppo ec o machine (SVM) model is a supe ised machine lea ning algo i hm ha inds a hype plane, in a mul idimensional space, ha is able o sepa a e he aining da a by labels/class. Fo example, i we ha e wo known labels and wo inpu a iables ( ea u es), hen, his o ms a wo-dimensional space. In his case, he selec ed hype plane, o sepa a e he poin s in he space by hei class, is a line. The pe pendicula dis ance be ween he line and he closes poin s is known as he ma gin. The maximal- ma gin hype plane is he name gi en o he op imal hype plane, he one ha sepa a es he classes wi h he la ges ma gin. The closes poin s a e, in ac , he only ele an poin s o de ine he hype plane and o cons uc he classi ie . These poin s a e called he suppo ec o s. Figu e 2 illus a es a possible wo-dimensional space si ua ion wi h he espec i e hype plane, suppo ec o s, and ma gin [65] [73]. A e disco e ing he hype plane, he equa ion ha de ines i can be used o make p edic ions, by inse ing he inpu alues in o he equa ion. The label o he new inpu a iable is indica ed by whe he he poin is abo e o below he hype plane (easie o unde s and when he hype plane is a line) [65] [73]. Figu e 2: Example o suppo machine classi ica ion esul s [73]. Howe e , he maximal-ma gin classi ie is a hypo he ical classi ie , since eal da a may no be pe ec ly 47 sepa a ed by a hype plane. So, in eal si ua ions, he ma gin is no maximized, and some poin s o he aining da a a e allowed o iola e he sepa a ing line. The amoun o iola ion o he ma gin ha is allowed is de ined by he pa ame e C, being ha la ge C alues indica e ha mo e iola ions o he hype plane a e allowed. Thus, C pa ame e also in luences he numbe o suppo ec o s used by he model [65] [73]. In p ac ice, he SVM algo i hm is implemen ed using a ke nel. This ke nel can be linea , polynomial o adial. In his s udy, linea and adial ke nels we e used. The linea ke nel uses he do -p oduc and de ines he simila i y be ween new da a and he suppo ec o s. The adial ke nel can c ea e complex egions and, o his ke nel, a gamma pa ame e should be speci ied o he algo i hm [65] [73]. We ob ained SVM classi ie using he SVC class om sciki -lea n lib a y [40] and se he ke nel pa- ame e o “linea ” o “ b ” acco ding o he desi ed model. 6.4.3 Random Fo es Random Fo es is an ensemble me hod based on bagging (boo s ap agg ega ing) whe e independen classi ica ion o eg ession un-p uned decision ees a e agg ega ed (using majo i y o e o classi ica ion o a e aging o eg ession) o p oduce a mo e accu a e classi ica ion [65] [74] [75]. The e o e, i s , le ’s unde s and wha a e decision ees and how hey wo k. Decision ees, o CART (classi ica ion and eg ession ees), as indica ed by he name, a e inspi ed in he o dina y ee s uc u e, which is composed o a oo and nodes ( he posi ions whe e he b anches di ide), b anches, and lea es. Simila ly, a decision ee is o med om nodes ha a e ep esen ed by ci cles and he b anches ha a e ep esen ed by he segmen s ha connec he nodes. The decision ee s a s in he oo node, mo es downwa d and ends in he lea node and no mally is d awn om le o igh . Each in e nal node (a node ha is no a lea node) can ha e wo o mo e b anches. A node ep esen s a ce ain cha ac e is ic and he b anches ep esen a ange o alues. The desc ibed decision ee s uc u e can be obse ed in Figu e 3 [65] [74] [75]. 48 Figu e 3: Decision ee s uc u e [76]. P edic ions can be made by isi ing he ee and pe o ming he es s included in he oo and in e nal nodes, and, when a lea node is eached, he p edic ed label co esponds o he epo ed class [65] [74] [75]. To build a decision ee, a g eedy app oach ( he e y bes spli poin is chosen in each ime) is used o di ide he inpu space, called ecu si e bina y spli ing. In his p ocedu e all he alues a e lined up and hen, using a cos unc ion, di e en spli poin s a e ied and es ed. The spli ha p esen s he lowes cos is he chosen one. Fo classi ica ions p oblems, he cos unc ion used is he Gini, which indica es how pu e he lea nodes a e. Gini cos (G) is calcula ed as shown in Equa ion 6.4, whe e ˆpkis he ac ion o aining ins ances wi h class K in he ec angle o in e es [65] [74] [75]. G= n X k=1 ˆpk(1 −ˆpk)(6.4) Thus, a node ha has all he aining ins ances o he same class (pe ec class pu i y), has a G = 0. On he o he hand, G eaches i s maximum alue (G = 0.5) when he e is a 50-50 spli o classes (ˆpk=1 2) [65] [74] [75]. The ecu si e bina y spli ing equi es a s opping p ocedu e o know when i should s op spli ing. This s opping p ocedu e can be limi ing he minimum le el o impu i y o spli a node o he minimum numbe o samples pe node. In he second p ocedu e, i he coun o aining ins ances is less han he minimum, hen, he spli is no accep ed and he espec i e node is aken as a inal lea node [65] [74] [75]. Howe e , igo ous s opping c i e ia can lead o unde i ing ees. To sol e his p oblem, p uning 49 c i e ia is used ins ead. So, be e pe o mances can be achie ed by aining an un es ic ed ee and hen p uning i using o ha , o example, he weakes link p uning p ocedu e on which a lea ning pa ame e (alpha) is used o weigh whe he nodes can be emo ed based on he size o he sub- ee [65] [74] [75]. Al hough decision ees p esen desi able p ope ies and success, hei disc e e na u e in ol es high a iance in p edic ions. As p e iously explained, andom o es is an ensemble me hod, and hese ype o me hods allow he cons uc ion o models ha p oduce be e p edic ions by agg ega ing he p edic ions o a se o indi idual classi ie s. Random o es is based on bagging which is a p ocedu e ha educes he a iance o algo i hms ha ha e high a iance, like decision ees [65] [74] [75]. As p e iously explained, decision ees a e g eedy. When dealing wi h mul iple decision ees, hese ees can ha e s uc u al simila i ies and, so, highly co ela ed p edic ions. The ensemble me hods a e mo e accu a e i he p edic ions om he sub- ees a e weakly co ela ed, ideally, unco ela ed. Thus, in andom o es , he sub- ees lea n in a way ha hei p edic ions ha e less co ela ion. In decision ees (o CART) he lea ning algo i hm, when selec ing a spli poin , is allowed o look o all a iables and all hei alues o selec he mos op imal spli -poin . Howe e , in andom o es , he lea ning algo i hm sea ch is limi ed o a andom sample o ea u es. The numbe o ea u es ha can be sea ched a each spli poin mus be speci ied as a pa ame e o he algo i hm [65] [74] [75]. In Py hon, andom o es model was implemen ed h ough he RandomFo es Classi ie class, om he sciki -lea n lib a y [40]. 6.4.4 K-Nea es Neighbo s In he K-nea es neighbo s (KNN) algo i hm, no lea ning is in ac necessa y, all he p ocedu e o KNN is made when a p edic ion is equi ed. The only model in KNN is s o ing he en i e aining da ase . So, KNN s o es he aining da ase and makes a p edic ion o a new da a poin by sea ching, in he en i e da ase , o he K mos simila ins ances, called he neighbo s. A dis ance measu e is used o ind ou which K ins ances, in he aining da ase , a e mos simila o he new inpu . Euclidean dis ance is he mos common dis ance measu e o eal- alued inpu a iables and i is he measu e used in his s udy. Howe e , he e a e o he dis ance measu es like Hamming dis ance and Manha an dis ance [65]. 50 The Euclidean dis ance is calcula ed as he squa e oo o he sum o he squa ed di e ences be ween a poin a and poin b ac oss all inpu a ibu es i, as p esen ed in Equa ion 6.5 [65]. EuclideanDis ance(a, b) = u u n X i=1 (ai−bi)2(6.5) Fo classi ica ion p oblems, he class o he new inpu poin can be p edic ed by de e mining, om among he K mos simila ins ances, he class wi h highe equency. Thus, o a new inpu ins ance, we de e mine he K mos simila ins ances and, hen, o his se , we calcula e he no malized equency o samples ha belong o each class, as exempli ied in Equa ion 6.6 [65]. p(class = 0) = coun (class = 0) coun (class = 0) + coun (class = 1) (6.6) This algo i hm is mo e indica ed o lowe dimensional da a, so i can bene i om ea u e selec ion o educe he dimensions o he inpu ea u e space [65]. The KNN e sion o classi ica ion p oblems was achie ed wi h he KNeighbo sClassi ie () class om he sciki -lea n lib a y [40]. 6.5 Pe o mance Me ics To e alua e a model’s pe o mance some pe o mance me ics a e measu ed in he alida ion phase, such as accu acy, sensi i i y, speci ici y, and a ea unde cu e (AUC). To be e comp ehend hese me ics, i s , we should unde s and wha is a con usion ma ix. So, a con usion ma ix is no a me ic bu is a way o e alua e a classi ica ion model since i s ep esen a ion can be used o delinea e se e al me ics. This ep esen a ion is ob ained by compa ing he p edic ed labels, ha we e gi en by he classi ie , wi h he ue labels, ha a e al eady known. A ypical con usion ma ix o a bina y classi ica ion p oblem is p esen ed in Figu e 4, whe e p designa es he posi i e class and n designa es he nega i e class and whe e he columns ep esen he p edic ed labels and he ows he ue labels. To no e ha he con usion ma ix can also be ep esen ed wi h he p edic ed labels in he ows and 51 he ue labels in he columns. As can be seen, he compa ison be ween p edic ed and ue labels leads o ou di e en e ms: ue nega i e, alse nega i e, alse posi i e, and, ue posi i e [66]. • T ue Posi i e (TP): To al coun s o when he ue label is posi i e and he p edic ed label is posi i e. • T ue Nega i e (TN): To al coun s o when he ue label is nega i e and he p edic ed label is nega i e. • False Posi i e (FP): To al coun s o when he ue label is nega i e and he p edic ed label is posi i e. • False Nega i e (FN): To al coun s o when he ue label is posi i e and he p edic ed label is nega i e. Figu e 4: Con usion Ma ix s uc u e [66]. Thus, om he con usion ma ix, i is possible o ob ain he desi ed me ics. Fi s , he accu acy, his me ic is one o he mos popula o e alua e a classi ie pe o mance and i is de ined as he p opo ion o co ec p edic ions o he model, since, as illus a ed in Equa ion 6.7, i is he numbe o co ec p edic ions ( ue) o e he o al amoun o p edic ions (equal o he sample size) [66]. Accu acy =T P +TN TP +TN +F P +F N (6.7) Sensi i i y, also known as ecall, is a measu e o iden i y he pe cen age o ele an da a poin s. Sen- si i i y is calcula ed as p esen ed in Equa ion 6.8 and i is de ined as he numbe o cases o he posi i e class ha we e co ec ly p edic ed [66]. 52 Sensi i i y =T P TP +FN (6.8) Speci ici y, in u n, is de ined as he numbe o cases o he nega i e class ha we e co ec ly p edic ed and is measu ed as p esen ed in Equa ion 6.9 [77]. Speci ici y =TN FP +TN (6.9) The ecei e ope a ing cha ac e is ic (ROC) cu e is also an impo an isual ool o in e p e classi i- ca ion models ha is ob ained by plo ing he ue posi i e a e (TPR), which is equal o sensi i i y, e sus he alse posi i e a e (FPR), which is equal o 1 - speci ici y. So, each p edic ion esul , ob ained om he con usion ma ix, akes one poin in he ROC space, which is be ween (0,0) and (1,1). An illus a ion o a ROC cu e is p esen ed in Figu e 5. In his igu e, we can see a diagonal line, which co esponds o he ROC cu e o a classi ie ha does a andom guess. An ideal model would esul in a ROC cu e a he (0,1) poin , howe e , his is no ealis ic, so, as close is he ROC cu e o his poin , which is si ua ed in he op le co ne o he g aph, he be e is he classi ie [66] [77]. Figu e 5: Example o ROC cu e and AUC [78]. In o de o compa e models, a me ic is calcula ed om he ROC cu e, which is called a ea unde cu e (AUC). The ROC cu e illus a ed in Figu e 5 has he espec i e a ea unde cu e, which is he g ay- colo ed a ea. This me ic can be calcula ed by in eg a ing he a eas unde he s eps o he ROC cu e. So, i ROC cu e is ob ained by connec ing he poin s {(x1,y1), (x2,y2), ..., (xm,ym)}, whe e x1= 0 and 53 xm= 1, hen, AUC is es ima ed as p esen ed in Equa ion 6.10. Since his me ic ep esen s he a ea unde he ROC cu e, i s alue will always be be ween 0 and 1. An ideal classi ie would esul in a uni AUC alue, and, due o he diagonal ROC cu e, a ealis ic classi ie has an AUC alue abo e 0.5 (a ea unde he diagonal). Thus, wi h he AUC i is possible o compa e models, and gene ally, he bes model is he one ha p esen s he highe AUC alue [66] [77]. AUC =1 2 m−1 X i=1 (xi+1 −xi)·(yi+yi+1)(6.10) In his s udy, hese me ics (accu acy, sensi i i y, speci ici y, and AUC) we e calcula ed du ing he hype pa ame e uning p ocess o enable he selec ion o he bes hype pa ame e alue/s a us, howe e , he decision elied on he accu acy, and, in case o ies, on he AUC. These pe o mance me ics we e ob ained, in Py hon and using sciki -lea n [40], in di e en ways. The accu acy was ob ained by accessing he mean o he alida ion esul s p oduced by he accu acy_sco e() unc ion. The AUC was ob ained applying he auc() unc ion o he FPR and TPR alues gi en by he oc_- cu e() unc ion. As o he sensi i i y and speci ici y, i s , he TP, TN, FP, and FN alues we e ob ained o each c oss- alida ion i e a ion by compa ing he ue and p edic ed labels, and hen, hese wo me ics we e de e mined using he o mulas p e iously p esen ed in Equa ion 6.8 and 6.9, espec i ely. 54 Pa III : Resul s, Discussion, Conclusion, and Fu u e Wo k 55 Table 8: S a is ically signi ican logis ic eg ession esul s o HCM and FD wi h WMLs g oups Va iables Uni a ia e logis ic eg es- sion Mul i a iable logis ic e- g ession - Adjus ed o age Mul i a iable logis ic e- g ession - Adjus ed o sex OR (95% C.I) p- alue OR (95% C.I) p- alue OR (95% C.I) p- alue HR Min 1.09 (1.02 - 1.16) 0.0097 1.09 (1.02 - 1.17) 0.0087 1.08 (1.01 - 1.16) 0.0222 Age - - 0.99 (0.96 - 1.02) 0.3878 - - Sex - - - - 2.97 (1.24 - 7.09) 0.0142 HR Mean 1.09 (1.04 - 1.15) 0.0009 1.09 (1.04 - 1.15) 0.0011 1.09 (1.03 - 1.15) 0.0013 Age - - 1.00 (0.97 - 1.03) 0.9738 - - Sex - - - - 3.32 (1.35 - 8.20) 0.0092 HR Max 1.02 (1.00 - 1.05) 0.0441 1.03 (1.00 - 1.05) 0.0591 1.03 (1.00 - 1.05) 0.0355 Age - - 1.00 (0.97 - 1.03) 0.9148 - - Sex - - - - 3.53 (1.48 - 8.42) 0.0045 QT Min 0.98 (0.97 - 0.99) 0.0068 0.98 (0.97 - 1.00) 0.0086 0.98 (0.97 - 1.00) 0.0392 Age - - 1.00 (0.97 - 1.03) 0.8283 - - Sex - - - - 2.57 (1.06 - 6.23) 0.0363 QT Mean 0.98 (0.96 - 0.99) 0.0004 0.98 (0.96 - 0.99) 0.0005 0.98 (0.96 - 0.99) 0.0004 Age - - 1.01 (0.98 - 1.04) 0.6271 - - Sex - - - - 3.69 (1.45 - 9.38) 0.0061 QT Max 0.99 (0.99 - 1.00) 0.0013 0.99 (0.99 - 1.00) 0.0015 0.99 (0.98 - 1.00) 0.0006 Age - - 1.00 (0.98 - 1.04) 0.7507 - - Sex - - - - 4.81 (1.79 - 12.95) 0.0019 QTc Max 0.99 (0.99 - 1.00) 0.0270 0.99 (0.99 - 1.00) 0.0340 0.99 (0.99 - 1.00) 0.0058 Age - - 1.00 (0.97 - 1.03) 0.8252 - - Sex - - - - 5.02 (1.90 - 13.26) 0.0012 62 Table 9: S a is ically signi ican logis ic eg ession Resul s o FD wi hou WMLs and FD wi h WMLs g oups Va iables Uni a ia e logis ic eg es- sion Mul i a iable logis ic e- g ession - Adjus ed o age Mul i a iable logis ic e- g ession - Adjus ed o sex OR (95% C.I) p- alue OR (95% C.I) p- alue OR (95% C.I) p- alue HR Max 0.95 (0.93 - 0.98) 0.0003 0.98 (0.95 - 1.01) 0.2405 0.95 (0.92 - 0.97) 0.0002 Age - - 1.06 (1.03 - 1.10) 0.0004 - - Sex - - - - 1.69 (0.72 - 3.96) 0.2251 QT Min 1.02 (1.01 - 1.03) 0.0068 1.02 (1.00 - 1.03) 0.0683 1.03 (1.01 - 1.04) 0.0025 Age - - 1.07 (1.04 - 1.10) < 0.0001 - - Sex - - - - 1.99 (0.82 - 4.85) 0.1283 QT Mean 1.02 (1.01 - 1.03) 0.0052 1.01 (0.99 - 1.02) 0.4081 1.02 (1.01 - 1.04) 0.0038 Age - - 1.07 (1.04 - 1.10) < 0.0001 - - Sex - - - - 1.46 (0.64 - 3.31) 0.3643 QTc Mean 1.02 (1.01 - 1.04) 0.0071 1.01 (0.99 - 1.03) 0.3947 1.02 (1.01 - 1.04) 0.0071 Age - - 1.07 (1.04 - 1.10) < 0.0001 - - Sex - - - - 1.11 (0.51 - 2.44) 0.7916 QTc > 450 1.02 (1.01 - 1.03) 0.0065 1.00 (0.99 - 1.02) 0.7636 1.02 (1.01 - 1.03) 0.0054 Age - - 1.07 (1.04 - 1.11) < 0.0001 - - Sex - - - - 1.33 (0.60 - 2.97) 0.4869 63 7.2 Resul s om pa ien s aged 40 o 59 yea s (inclusi e) The desc ip i e esul s o each Hol e a iable pe g oup (HCM, FD wi h WMLs and FD Wi hou WMLs) and compa a i e esul s, o his age class, a e p esen ed in Table 10. Once again, da a wi h a no mal dis ibu ion is p esen ed as mean ±s anda d de ia ion and da a wi h a non-no mal dis ibu ion is p e- sen ed as median (qua ile 1 - qua ile 3). The no mali y and he homogenei y o a iance es esul s can be consul ed in Table 26 o Appendix A. We can see ha , in con as o he esul s ob ained om he pa ien s o e 18 yea s old, o his subg oup o pa ien s, sex and age a iables we e no signi ican ly di e en be ween g oups (p > 0.0601). Howe e , g oup di e ences we e ound in some o he Hol e a iables, such as, HR Min, HR Mean, SDANN 5, SDNN, QT Mean, QT Max and, QTc > 450 (p < 0.0414). In he pa ien s aged 40 o 59 yea s (inclusi e), HCM pa ien s p esen ed highe QT Mean and QT Max compa ed wi h FD pa ien s, bo h wi h and wi hou WMLs (p < 0.0048) and also a highe QTc > 450 compa ed o FD wi h WMLs pa ien s (p = 0.0131). The FD wi hou WMLs pa ien s p esen ed a lowe SDNN compa ed wi h HCM and FD wi h WMLs pa ien s (p < 0.0171). The SDANN 5 a iable means in he FD wi h WMLs and FD wi hou WMLs g oups we e di e en (p = 0.0117), wi h a lowe alue in he FD pa ien s wi hou WMLs. Two di e ences be ween he HCM and FD wi hou WMLs g oups we e ound, in he HR Min and HR Max a iables (p < 0.0059), which we e bo h highe in he FD wi hou WMLs pa ien s. 64 Table 10: Va iables summa y and compa ison o means/medians be ween HCM, FD wi h WMLs and FD wi hou WMLs pa ien s aged 40 o 59 (inclusi e) Va iable HCM (n=16) FD w/ WMLs (n=23) FD w/o WMLs (n=25) P-Value -All g oups HCM s FD w/ WMLs HCM s FD w/o WMLs FD w/ WMLs s FD w/o WMLs Sex (Female numbe (%)) 6 (37.50) 13 (56.52) 17 (68.00) p = 0.1581 a- - - Age 54.50 (49.50 - 58.00) 50.61 ±5.17 49.00 ±5.67 p = 0.0601 d- - - HR Min 45.75 ±7.57 49.22 ±5.94 52.24 ±5.77 p = 0.0083 bp = 0.2188 ep = 0.0059 ep = 0.2306 e HR Mean 68.25 ±9.85 74.43 ±6.27 77.48 ±10.10 p = 0.0072 bp = 0.0885 ep = 0.0051 ep = 0.4641 e HR Max 118.00 ±20.79 125.65 ±10.06 128.84 ±16.92 p =0.1114 b- - - ASDNN 5 67.09 ±30.22 52.30 (48.05 - 65.10) 50.60 ±12.15 p = 0.0889 d- - - SDANN 5 124.36 ±39.24 133.18 ±33.67 106.11 ±23.05 p = 0.0141 bp = 0.6546 ep = 0.1765 ep = 0.0117 e SDNN 153.49 ±43.43 145.43 ±34.90 121.30 (111.10 - 137.20) p = 0.0129 dp = 0.6617 p = 0.0094 p = 0.0171 RMSSD 39.80 (34.00 - 96.58) 33.90 (28.20 - 40.25) 31.81 ±12.08 p = 0.0694 d- - - QT Min 313.44 ±23.35 306.39 ±21.52 295.76 ±28.50 p = 0.0809 b- - - QT Mean 412.00 (400.25 - 443.00) 392.61 ±26.28 385.00 (367.00 - 408.00) p = 0.0019 dp = 0.0048 p = 0.0007 p = 0.5520 QT Max 525.50 (491.75 - 633.25) 462.13 ±40.12 455.00 (424.00 - 489.00) p = 0.0016 dp = 0.0011 p = 0.0017 p = 0.8424 QTc Min 365.88 ±27.51 382.00 (376.00 - 399.50) 373.24 ±37.84 p = 0.1874 d- - - QTc Mean 447.25 ±23.31 431.74 ±17.35 430.00 (425.00 - 444.00) p = 0.0823 d- - - QTc Max 602.25 ±96.65 533.48 ±54.43 552.92 ±60.02 p = 0.0472 c- - - QTc > 450 29.50 (6.75 - 70.50) 7.00 (2.50 - 23.50) 9.00 (2.00 - 36.00) p = 0.0414 dp = 0.0131 p = 0.0633 p = 0.4607 Longes R-R 1.80 (1.40 - 2.33) 1.50 (1.35 - 1.75) 1.50 (1.30 - 1.60) p = 0.1504 d- - - I da a ha e a no mal dis ibu ion, hey a e ep esen ed as mean ±s anda d de ia ion. In case o a non-no mal dis ibu ion hey a e ep esen ed as median (qua ile1 −qua ile3). In e e y compa ison o means es αwas conside ed 0.05. aChi-Squa ed Tes bOne-Way ANOVA Tes . cWelch - ANOVA Tes . dK uskal-Wallis H Tes . eTukey HSD Tes as Pos hoc. Dunn’s Tes as Pos hoc. 65 Simila o wha was p esen ed o pa ien s aged abo e 18 yea s old, in Tables 11, 12 and, 13 a e he bina y logis ic esul s ha we e signi ican ly associa ed wi h g oup classi ica ion (HCM s FD wi hou WMLs, HCM s FD wi h WMLs, and FD wi hou WMLs s FD wi h WMLs) o he pa ien s aged 40 o 59 yea s. The esul s ha we e no signi ican ly associa ed a e p esen ed in Tables 27, 28 and 29 o Appendix A. Table 11 is ela i e o he ollowing wo ou comes: ha ing HCM (Y = 0) o ha ing FD wi hou WMLs (Y = 1) logis ic eg ession esul s. We can see ha 6 ou o 15 Hol e a iables we e signi ican ly associa ed wi h g oup membe ship, which we e, HR Min, HR Mean, ASDNN 5, SDNN, QT Mean and QT Max (p < 0.0425). When he model was adjus ed o age, his a iable was s a is ically signi ican only in he model wi h SDNN as Hol e a iable, and, in u n, his a iable emained signi ican ly associa ed wi h g oup membe ship (p = 0.0134). Only wo o he Hol e a iables emained signi ican ly associa ed wi h g oup membe ship when adjus ed o age, HR Min and QT Mean a iables (p < 0.0297). When adjus ed o sex, his a iable was no signi ican in all models and he 6 Hol e a iables emained signi ican ly associa ed wi h g oup membe ship (p < 0.0389). F om hese esul s we can see ha a highe HR Min and HR Mean lead o highe odds o ha ing FD wi hou WMLs a he han HCM (OR ≥1.10, 1.02 ≤95% CI ≤1.30), on he o he hand, an inc ease in ASDNN 5, SDNN, QT Mean and QT Max lead o dec eased odds o ha ing FD wi hou WMLs (OR ≤0.99, 0.92 ≤95% CI ≤1.00). Six a iables, HR Mean, QT Mean, QT Max, QTc Mean, QTc Max and QTc > 450, we e signi ican ly associa ed wi h g oup membe ship (p < 0.0331) when he wo possible ou comes we e: ha ing HCM (Y = 0) o ha ing FD wi h WMLs (Y = 1), as can be seen in Table 12. In he models adjus ed o age and o sex, bo h a iables we e no signi ican in all models and only one Hol e a iable was no longe signi ican , which was HR Mean a iable when adjus ed o age (p = 0.0602). Only he inc ease o he HR Mean a iable leads o inc eased odds o ha ing FD wi h WMLs a he han HCM (OR = 1.11, 95% CI= 1.01 - 1.21), when he emaining 5 Hol e a iables o QT analysis (QT Mean, QT Max, QTc Mean, QTc Max and QTc > 450) inc ease he odds o ha ing FD wi h WMLs dec ease (OR ≤0.99, 0.93 ≤95% CI ≤1.00). The esul s o when he dependen a iable has he ou comes: ha ing FD wi hou WMLs (Y = 0) o ha ing FD wi h WMLs (Y = 1), a e p esen ed in Table 13. In his case, only 2 ou o 15 Hol e a iables we e signi ican ly associa ed wi h g oup membe ship, SDANN 5 and SDNN (p < 0.0130), and hese a iables emained signi ican when he model was adjus ed bo h o age and sex (which we e no signi ican in all 66 models). A highe hea a e a iabili y (SDNN and SDANN 5 alues) lead o highe odds o ha ing WMLs wi hin FD pa ien s (OR = 1.03, 95% CI = 1.01 - 1.06 o SDNN and OR = 1.04, 95% CI = 1.01 – 1.07 o SDANN5). Table 11: S a is ically signi ican logis ic eg ession esul s o HCM and FD wi hou WMLs pa ien s aged 40 o 59 (inclusi e) Va iables Uni a ia e logis ic e- g ession Mul i a iable logis ic eg ession - Adjus ed o age Mul i a iable logis ic eg ession - Adjus ed o sex OR (95% C.I) p- alue OR (95% C.I) p- alue OR (95% C.I) p- alue HR Min 1.16 (1.04 - 1.30) 0.0088 1.14 (1.02 - 1.27) 0.0224 1.17 (1.04 - 1.31) 0.0113 Age - - 0.90 (0.79 - 1.03) 0.1210 - - Sex - - - - 3.57 (0.81 - 15.68) 0.0914 HR Mean 1.10 (1.02 - 1.18) 0.0126 1.08 (1.00 - 1.16) 0.0588 1.09 (1.01 - 1.17) 0.0191 Age - - 0.92 (0.80 - 1.05) 0.2314 - - Sex - - - - 3.11 (0.74 - 13.04) 0.1202 ASDNN 5 0.96 (0.92 - 1.00) 0.0425 0.96 (0.92 - 1.00) 0.0565 0.95 (0.91 - 1.00) 0.0389 Age - - 0.88 (0.77 - 1.00) 0.0498 - - Sex - - - - 4.49 (1.02 - 19.68) 0.0464 SDNN 0.97 (0.94 - 0.99) 0.0134 0.96 (0.94 - 0.99) 0.0134 0.96 (0.94 - 0.99) 0.0176 Age - - 0.86 (0.74 - 0.99) 0.0373 - - Sex - - - - 3.87 (0.84 - 17.71) 0.0815 QT Mean 0.97 (0.94 - 0.99) 0.0116 0.97 (0.94 - 1.00) 0.0297 0.97 (0.94 - 0.99) 0.0137 Age - - 0.92 (0.80 - 1.05) 0.2268 - - Sex - - - - 3.86 (0.86 - 17.40) 0.0784 QT Max 0.99 (0.98 - 1.00) 0.0162 0.99 (0.98 - 1.00) 0.0519 0.99 (0.98 - 1.00) 0.0182 Age - - 0.91 (0.80 - 1.04) 0.1693 - - Sex - - - - 4.10 (0.94 - 17.95) 0.0613 67 Table 12: S a is ically signi ican logis ic eg ession esul s o HCM and FD wi h WMLs pa ien s aged 40 o 59 (inclusi e) Va iables Uni a ia e logis ic e- g ession Mul i a iable logis ic eg ession - Adjus ed o age Mul i a iable logis ic eg ession - Adjus ed o sex OR (95% C.I) p- alue OR (95% C.I) p- alue OR (95% C.I) p- alue HR Mean 1.11 (1.01 - 1.21) 0.0331 1.10 (1.00 - 1.21) 0.0602 1.11 (1.01 - 1.22) 0.0304 Age - - 0.94 (0.82 - 1.08) 0.4036 - - Sex - - - - 2.50 (0.59 - 10.39) 0.2173 QT Mean 0.96 (0.94 - 0.99) 0.0125 0.96 (0.94 - 0.99) 0.0171 0.96 (0.93 - 0.99) 0.0112 Age - - 0.94 (0.81 - 1.08) 0.3702 - - Sex - - - - 3.16 (0.66 - 15.04) 0.1488 QT Max 0.97 (0.95 - 0.99) 0.0085 0.97 (0.95 - 0.99) 0.0093 0.97 (0.95 - 0.99) 0.0069 Age - - 0.94 (0.81 - 1.10) 0.4611 - - Sex - - - - 4.64 (0.73 - 29.62) 0.1045 QTc Mean 0.96 (0.93 - 1.00) 0.0329 0.96 (0.92 - 1.00) 0.0403 0.96 (0.93 - 1.00) 0.0300 Age - - 0.91 (0.79 - 1.05) 0.1906 - - Sex - - - - 2.47 (0.60 - 10.22) 0.2114 QTc Max 0.99 (0.98 - 1.00) 0.0173 0.99 (0.98 - 1.00) 0.0292 0.98 (0.97 - 1.00) 0.0101 Age - - 0.95 (0.82 - 1.09) 0.4466 - - Sex - - - - 5.28 (0.93 - 30.10) 0.0608 QTc > 450 0.97 (0.95 - 1.00) 0.0252 0.97 (0.95 - 1.00) 0.0312 0.97 (0.95 - 1.00) 0.0297 Age - - 0.91 (0.79 - 1.05) 0.2014 - - Sex - - - - 2.03 (0.50 - 8.27) 0.3241 Table 13: S a is ically signi ican logis ic eg ession esul s o FD wi hou WMLs and FD wi h WMLs pa ien s aged 40 o 59 (inclusi e) Va iables Uni a ia e logis ic e- g ession Mul i a iable logis ic eg ession - Adjus ed o age Mul i a iable logis ic eg ession - Adjus ed o sex OR (95% C.I) p- alue OR (95% C.I) p- alue OR (95% C.I) p- alue SDANN 5 1.04 (1.01 - 1.07) 0.0080 1.05 (1.01- 1.08) 0.0046 1.04 (1.01 - 1.07) 0.0064 Age - - 1.13 (0.99 - 1.28) 0.0733 - - Sex - - - - 0.42 (0.11 - 1.66) 0.2169 SDNN 1.03 (1.01 - 1.06) 0.0130 1.04 (1.01 - 1.07) 0.0077 1.03 (1.01 - 1.06) 0.0119 Age - - 1.11 (0.98 - 1.26) 0.0867 - - Sex - - - - 0.52 (0.14 - 1.91) 0.3235 68 7.3 Resul s om pa ien s o e 59 yea s old The a iables summa y and he compa ison o means/medians be ween he wo g oups, o pa ien s wi h age > 59 , a e p esen ed in Table 14. The no mali y and homogenei y o a iances es esul s can be consul ed in Table 30 o Appendix A. G oup di e ences we e ound in he sex a iable, HR Min, HR Mean and HR Max Hol e a iables (p < 0.0421) which we e highe in he FD pa ien s wi h WMLs. In con as , QT Min and QT Mean Hol e a iables (p < 0.0182) we e lowe in hese pa ien s. The logis ic eg ession analysis esul s o p edic g oup membe ship a e displayed in Table 15 o esul s ha we e signi ican ly associa ed and in Table 31 o Appendix A o esul s ha we e no associa ed. In Table 15 we can see ha 4 Hol e a iables we e signi ican ly associa ed wi h g oup classi ica ion, HR Min, HR Mean, QT Min and QT Mean (p < 0.0444). When he model was adjus ed o age, his a iable was no signi ican ly associa ed wi h g oup membe ship and all 4 Hol e a iables emained associa ed (p < 0.0402). Howe e , when adjus ed o sex, only wo Hol e a iables emained signi ican ly associa ed, which we e HR Mean and QT Min (p < 0.0422), and he sex a iable was no associa ed. The e o e, he highe he hea a e a iables (HR Min and HR Mean alues) a e, he highe a e he odds o ha ing FD wi h WMLs ins ead o HCM (OR = 1.10, 95% CI = 1.00 - 1.20 o HR Min and OR = 1.09, 95% CI = 1.02 - 1.17 o HR Mean). The inc ease o ei he o he wo QT analysis a iables (QT Min and QT Mean), in con as , leads o inc eased odds o ha ing HCM a he han FD wi h WMLs (OR = 0.98, 95% CI = 0.96 - 0.99 o QT Min and OR = 0.98, 95% CI = 0.96 - 1.00 o QT Mean). 69 Table 14: Va iables summa y and compa ison o means/medians o HCM and FD wi h WMLs pa ien s aged abo e 59 Va iable HCM (n=19) FD w/ WMLs (n=30) P-Value Sex (Female numbe (%)) 6 (31.58) 19 (63.33) p = 0.0421 a Age 67.00 (62.00 - 77.00) 69.00 (63.25 - 75.00) p = 0.9590 b HR Min 45.84 ±8.98 50.57 ±6.00 p = 0.0319 c HR Mean 65.84 ±11.69 73.37 ±7.81 p = 0.0095 c HR Max 102.00 (94.50 - 111.50) 116.07 ±11.17 p = 0.0065 b ASDNN 5 48.60 (38.15 - 58.10) 48.80 (40.05 - 68.43) p = 0.5866 b SDANN 5 109.39 ±25.41 114.76 ±28.66 p = 0.5082 c SDNN 121.70 (100.75 - 154.65) 134.05 ±34.09 p = 0.8535 b RMSSD 46.20 (28.75 - 57.20) 44.05 (32.45 - 86.75) p = 0.7272 b QT Min 340.63 ±38.60 301.00 (285.75 - 339.75) p = 0.0059 b QT Mean 442.53 ±40.63 417.00 ±32.08 p = 0.0182 c QT Max 533.00 (485.00 - 576.00) 503.50 (474.00 - 533.50) p = 0.1788 b QTc Min 372.05 ±44.34 363.23 ±43.10 p = 0.4934 c QTc Mean 453.32 ±33.14 455.10 ±32.70 p = 0.8539 c QTc Max 569.00 (527.00 - 626.50) 559.50 (545.00 - 624.00) p = 0.9427 b QTc > 450 41.00 (10.00 - 81.50) 62.50 (17.25 - 80.00) p = 0.6965 b Longes R-R 1.70 (1.65 - 2.00) 1.60 (1.43 - 1.80) p = 0.0573 b I da a ha e a no mal dis ibu ion hey a e ep esen ed as mean ±s anda d de ia ion. In case o a non-no mal dis ibu ion hey a e ep esen ed as median (qua ile1 −qua ile3). In e e y compa ison o means es αis conside ed 0.05. aFishe ’s Exac Tes bMann Whi ney U Tes cS uden ’s T-Tes 70 Table 15: S a is ically signi ican logis ic eg ession esul s o HCM and FD wi h WMLs g oups wi h ages abo e 59 Va iables Uni a ia e logis ic e- g ession Mul i a iable logis ic eg ession - Adjus ed o age Mul i a iable logis ic eg ession - Adjus ed o sex OR (95% C.I) p- alue OR (95% C.I) p- alue OR (95% C.I) p- alue HR Min 1.10 (1.00 - 1.20) 0.0444 1.10 (1.00 - 1.21) 0.0402 1.08 (0.98- 1.18) 0.1068 Age - - 0.98 (0.91 - 1.06) 0.5904 - - Sex - - - - 2.94 (0.82 - 10.56) 0.0985 HR Mean 1.09 (1.02 - 1.17) 0.0163 1.09 (1.02 - 1.17) 0.0145 1.08 (1.01 - 1.16) 0.0288 Age - - 0.97 (0.90 - 1.06) 0.5309 - - Sex - - - - 3.30 (0.91 - 12.02) 0.0703 QT Min 0.98 (0.96 - 0.99) 0.0090 0.97 (0.96 - 0.99) 0.0067 0.98 (0.96 - 1.00) 0.0422 Age - - 0.96 (0.89 - 1.05) 0.3806 - - Sex - - - - 2.18 (0.56 - 8.49) 0.2589 QT Mean 0.98 (0.96 - 1.00) 0.0258 0.98 (0.96 - 1.00) 0.0205 0.98 (0.96 - 1.00) 0.0470 Age - - 0.97 (0.89 - 1.05) 0.3959 - - Sex - - - - 3.28 (0.91 - 11.80) 0.0684 7.4 Discussion Conside ing all pa ien s (aged abo e 18 yea s) signi ican di e ences in age and sex be ween g oups we e ound. FD pa ien s wi h WMLs a e olde han FD pa ien s wi hou WMLs and HCM pa ien s a e also olde han FD wi hou WMLs pa ien s (Table 6). The age di e ence ound in FD wi h and wi hou WMLs g oups ha e also been iden i ied in he s udy o B aga (2021) [32]. Galluzzi e al. [33] also iden i ied ha MCI pa ien s wi h WMLs we e olde han he ones wi hou WMLs. In ac , WMLs a e qui e common in he elde ly gene al popula ion [43] [79]. Se e al ECG cha ac e is ics gi e a signi ican associa ion wi h he dependen a iable (g oup class) in 71 selec ion me hod based in he VIF alues is he same, since his was applied o all he pa ien s aged be ween 40 and 59 yea s old. As o he hype pa ame e s alues/s a us ob ained in he hype pa ame e uning, hese a e di e en , o cou se, and can be consul ed in Table 32 o Appendix B. The accu acy alues ob ained by hese models a p edic ing i a pa ien has FD a e displayed in Table 33, also in Appendix B. Applying he RFE me hod wi h logis ic eg ession as classi ie led o he esul s in Figu e 7a, whe e he maximum accu acy alue is 0.6923 o 5 ea u es, being hese ea u es he HR Mean, RMSSD, QTc Min, QTc Max, and QTc > 450. Using linea SVM as classi ie , he maximum accu acy alue is also 0.6923, howe e , wi h his model, his maximum was ob ained wi h 6 ea u es, as shown in Figu e 7b, which we e HR Mean, HR Max, RMSSD, QTc Min, QTc Max, and QTc > 450. I is no iceable ha hese a e he same 5 ea u es selec ed by logis ic eg ession plus HR Max ea u e. The esul s o when andom o es algo i hm is he classi ie a e in Figu e 7c, in which he bes accu acy is ob ained using all ea u es (9 ea u es) and is equal o 0.7692. 78 (a) RFECV o logis ic eg ession model. (b) RFECV o linea SVM model. (c) RFECV o andom o es model. Figu e 7: RFECV esul s o he di e en machine lea ning models o he HCM s FD wi h WMLs pa ien s aged 40 o 59 (inclusi e). Conside ing ha he 3 models ha we e w apped by RFE ga e h ee di e en combina ions o ea u es, hese combina ions we e all applied o he classi ica ion s age, ha is, applied o he 5 machine lea ning algo i hms, jus like wha was done p e iously. The pe o mance me ics ob ained in each case a e shown in Table 18. By analysing his able we see ha he bes model, in gene al, is using 6 ea u es and KNN model, whe e an accu acy o 0.8461 and an AUC o 0.8370 a e ob ained. This accu acy alue means ha he model co ec ly p edic ed 33 pa ien s in a o al o 39 (numbe o HCM and FD wi h WMLs pa ien s aged be ween 40 and 59). Also, he 6- ea u e combina ion seems o be he bes combina ion o use o p edic i a pa ien has FD (compa ing wi h HCM pa ien s), since i is he combina ion wi h he bes classi ica ion pe o mance me ics. The hype pa ame e s alues/s a us o each o hese machine lea ning models can be consul ed in Table 35 o Appendix B. 79 Table 18: Models’s classi ica ion pe o mance me ics pe numbe o ea u es o HCM and FD wi h WMLs pa ien s aged 40 o 59 (inclusi e) Numbe o ea u es (Fea u es) ML Model Me ics Accu acy Sensi i i y Speci ici y AUC 5 ea u es (HR Mean, RMSSD, QTc Min, QTc Max, and QTc > 450) LR 0.7179 0.9130 0.4375 0.7473 Linea SVM 0.7179 0.8696 0.5000 0.6630 RBF SVM 0.8462 0.9130 0.7500 0.7446 RF 0.7179 0.8261 0.5625 0.7826 KNN 0.7692 0.8696 0.6250 0.7962 6 ea u es (HR Mean, HR Max, RMSSD, QTc Min, QTc Max, and QTc > 450) LR 0.7179 0.8696 0.5000 0.7554 Linea SVM 0.7179 0.8696 0.5000 0.7446 RBF SVM 0.8205 0.8696 0.7500 0.8370 RF 0.7949 0.8261 0.7500 0.8397 KNN 0.8462 0.8696 0.8125 0.8370 9 ea u es (All) LR 0.6923 0.9130 0.3750 0.6902 Linea SVM 0.6923 0.8696 0.4375 0.6739 RBF SVM 0.7949 0.8696 0.6875 0.7663 RF 0.7692 0.8261 0.6875 0.7663 KNN 0.7179 0.9130 0.4375 0.7201 ML: machine lea ning; LR: logis ic eg ession; SVM: suppo ec o machine; RBF: adial basis unc ion; RF: andom o es ; KNN: K-Nea es Neighbou The hi d p edic ion is o p edic i a pa ien has WMLs using FD pa ien s, wi h and wi hou WMLs. Fo his p edic ion, since i was, once again, wi h pa ien s aged be ween 40 and 59 (inclusi e), we a e dealing wi h 9 ea u es (a e he VIF s ep) which a e HR Mean, HR Max, SDANN 5, RMSSD, QT Min, QTc Min, QTc Max, QTc > 450, and Longes R-R. Once again, he hype pa ame e s alues/s a us o each machine lea ning model and he accu acy alues ob ained by hese models a p edic ing he p esence o WMLs, can be consul ed in he Appendix B, Tables 32 and 33, espec i ely. These models we e hen w apped by RFE me hod o a second ea u e selec ion. Wi h logis ic eg es- 80 sion model, he bes accu acy, 0.6667, was ob ained wi h only one a iable, as can be obse ed in Figu e 8a, being his a iable he SDANN 5 a iable. Wi h linea SVM as classi ie , he RFE me hod iden i ied ha he bes accu acy was 0.6875 and i was ob ained wi h 2 ea u es, as p esen ed in Figu e 8b, which we e SDANN 5 and QTc Min ea u es. Howe e , wi h andom o es model, he bes accu acy, wi h a alue equal o 0.8125, occu ed wi h all he 9 a iables, as shown in Figu e 8c. (a) RFECV o logis ic eg ession model. (b) RFECV o linea SVM model. (c) RFECV o andom o es model. Figu e 8: RFECV esul s o he di e en machine lea ning models o he FD wi h WMLs s FD wi hou WMLs pa ien s aged 40 o 59 (inclusi e). These di e en combina ions o ea u es we e hen used o ain he 5 machine lea ning algo i hms, as p e iously explained, and he esul s ob ained o each o hese combina ions o he FD pa ien s, wi h and wi hou WMLs, a e p esen ed in Table 19. We quickly ealize ha he bes model is wi h all ea u es (9 ea u es) and wi h andom o es as classi ie , whe e he accu acy is equal o 0.8125. This alue means ha in 48 p edic ions (numbe o FD pa ien s wi h and wi hou WMLs aged be ween 40 and 59), he model co ec ly p edic ed 39. As o bo h 1 ea u e and 2 ea u es si ua ions, he RBF SVM classi ie show 81 a be e pe o mance, wi h accu acy o 0.729 and 0.750, espec i ely. Looking a he accu acy o all classi ie s, in he 9 ea u es case, we see ha , excep o andom o es , all he classi ie s ha e a weake pe o mance compa ed wi h he pe o mance ob ained wi h bo h 1 ea u e and 2 ea u es cases. This sugges s ha , al hough he highes accu acy is in he 9- ea u e combina ion, i we a e in e es ed in selec ing he bes ea u e combina ion among classi ie s, his may no be he bes combina ion o p edic i a FD pa ien has WMLs. The e o e, he 2- ea u e combina ion, which includes SDANN 5 and QTc Min a iables, is he bes combina ion, since i p esen s highe accu acy, sensi i i y and AUC han he 1 ea u e combina ion. The alues/s a us o he hype pa ame e s, o each model, can be consul ed in Table 36 o Appendix B. 82 Table 19: Models’s classi ica ion pe o mance me ics pe numbe o ea u es o FD wi h WMLs and FD wi hou WMLs pa ien s aged 40 o 59 (inclusi e) Numbe o ea u es (Fea u es) ML Model Me ics Accu acy Sensi i i y Speci ici y AUC 1 ea u e (SDANN 5) LR 0.6667 0.6087 0.7200 0.6939 Linea SVM 0.6875 0.4783 0.8800 0.6783 RBF SVM 0.7292 0.4783 0.9600 0.6087 RF 0.7292 0.4783 0.9600 0.5757 KNN 0.7292 0.4783 0.9600 0.5670 2 ea u es (SDANN 5 and QTc Min) LR 0.6667 0.5652 0.7600 0.6765 Linea SVM 0.7083 0.5217 0.8800 0.6870 RBF SVM 0.7500 0.5217 0.9600 0.6504 RF 0.7083 0.4348 0.9600 0.5878 KNN 0.7292 0.4348 1.0000 0.5948 9 ea u es (All) LR 0.6250 0.6087 0.6400 0.6000 Linea SVM 0.6875 0.5652 0.8000 0.5696 RBF SVM 0.6875 0.6087 0.7600 0.6122 RF 0.8125 0.7391 0.8800 0.8348 KNN 0.6667 0.4348 0.8800 0.6861 ML: machine lea ning; LR: logis ic eg ession; SVM: suppo ec o machine; RBF: adial basis unc ion; RF: andom o es ; KNN: K-Nea es Neighbou 8.2 Resul s om pa ien s o e 59 yea s old Fo he pa ien s aged abo e 59 yea s old, he i s ea u e selec ion p ocedu e, based on VIF alues, iden i ied 5 ea u es wi h mul icollinea i y. The e o e, hese 5 ea u es we e excluded and 10 emained, which we e HR Min, HR Max, ASDNN 5, SDANN 5, QT Min, QT Mean, QTc Min, QTc Max, QTc > 450, and Longes R-R ea u es. The VIF alues ob ained in each i e a ion o he p ocess a e displayed in Table 20 83 and, in his able, he held ea u es a e in bold ype and he highes alue pe i e a ion is in ed colo . Table 20: VIF alues o pa ien s aged abo e 59 Fea u es I e a ion 1º 2º 3º 4º 5º 6º HR Min 4.55 4.49 3.74 3.65 3.47 3.13 HR Mean 18.94 9.33 9.28 9.08 - - HR Max 3.19 3.18 3.06 3.06 2.95 2.86 ASDNN 5 6.07 5.90 5.37 5.36 5.23 2.00 SDANN 5 9.90 9.48 2.11 1.98 1.95 1.64 SDNN 30.90 30.11 - - - - RMSSD 30.12 28.23 6.16 6.14 6.06 - QT Min 5.40 4.35 4.27 4.27 3.77 3.76 QT Mean 25.07 6.97 6.84 6.46 3.00 2.95 QT Max 11.24 11.17 11.16 - - - QTc Min 4.40 3.97 3.85 3.82 3.52 3.52 QTc Mean 31.69 - - - - - QTc Max 9.01 8.32 8.32 1.79 1.73 1.72 QTc > 450 9.19 5.32 5.26 5.26 2.05 2.03 Longes R-R 1.73 1.69 1.65 1.64 1.62 1.37 In Table 37 and Table 38 o Appendix B, a e he hype pa ame e s alues/s a us o each machine lea ning model ob ained in he i s hype pa ame e uning and he espec i e accu acy alues ob ained a p edic ing i a pa ien has FD, espec i ely. The highes accu acy alue ob ained wi h logis ic eg ession as classi ie , which esul s a e in Figu e 9a, was 0.7551, and i occu ed wi h 5 ea u es: HR Min, SDANN 5, QT Min, QT Mean, and QTc > 450. In he case o linea SVM algo i hm, he RFE me hod iden i ied ha he highes accu acy is ob ained wi h all he 10 ea u es, and his accu acy alue is 0.7755, as shown in Figu e 9b. A 9- ea u e combina ion, including HR Min, HR Max, ASDNN 5, SDANN 5, QT Min, QT Mean, QTc Min, QTc > 450, and Longes 84 R-R ea u es, is he combina ion ha led o he highes accu acy, wi h a 0.7959 alue, o andom o es algo i hm. The RFE esul s o his model can be obse ed in Figu e 9c. (a) RFECV o logis ic eg ession model. (b) RFECV o linea SVM model. (c) RFECV o andom o es model. Figu e 9: RFECV esul s o he di e en machine lea ning models o he HCM s FD wi h WMLs pa ien s aged abo e 59. The hype pa ame e s alues/s a us o each ea u e combina ion and machine lea ning algo i hm conjuga ion, ob ained in he hype pa ame e uning s ep, ha was pe o med a e he RFE, a e displayed in Table 39 o Appendix B. The espec i e ob ained classi ica ion pe o mance me ics a e p esen ed in Table 21. Random o es is he algo i hm ha shows be e pe o mance o bo h 9 ea u es and 10 ea u es. Fo 5 ea u es he algo i hm wi h he highes accu acy is he RBF SVM. Howe e , he ea u e combina ion and algo i hm conjuga ion ha has he highes accu acy, 0.8163, is he one wi h 9 ea u es (all a iables excep QTc Max) and andom o es algo i hm as classi ie . Since he model p edic ed 49 si ua ions (numbe o HCM and FD wi h WMLs pa ien s aged abo e 9 yea s), he accu acy alue ob ained means ha , in he 49 85 p edic ions, 40 we e co ec ly p edic ed. Also, his 9- ea u e combina ion seems o be he bes combina ion o his classi ica ion p oblem. Table 21: Models’s classi ica ion pe o mance me ics pe numbe o ea u es o HCM and FD wi h WMLs pa ien s aged abo e 59 Numbe o ea u es (Fea u es) ML Model Me ics Accu acy Sensi i i y Speci ici y AUC 5 ea u es (HR Min, SDANN 5, QT Min, QT Mean, and QTc > 450) LR 0.7755 0.9000 0.5789 0.7333 Linea SVM 0.7755 0.9000 0.5789 0.7702 RBF SVM 0.7959 0.9333 0.5789 0.7351 RF 0.7755 0.8333 0.6842 0.7193 KNN 0.7143 0.9333 0.3684 0.6965 9 ea u es (HR Min, HR Max, ASDNN 5, SDANN 5, QT Min, QT Mean, QTc Min, QTc > 450, and Longes R-R) LR 0.7347 0.8333 0.5789 0.6825 Linea SVM 0.7755 0.8667 0.6316 0.7404 RBF SVM 0.7959 0.9000 0.6316 0.7509 RF 0.8163 0.9000 0.6842 0.8368 KNN 0.7143 1.0000 0.2632 0.6377 10 ea u es (All) LR 0.7143 0.8000 0.5789 0.6579 Linea SVM 0.7755 0.8667 0.6316 0.7193 RBF SVM 0.7755 0.8667 0.6316 0.7351 RF 0.7959 0.9667 0.5263 0.7825 KNN 0.6939 0.8333 0.4737 0.6561 ML: machine lea ning; LR: logis ic eg ession; SVM: suppo ec o machine; RBF: adial basis unc ion; RF: andom o es ; KNN: K-Nea es Neighbou 8.3 Discussion Tu ns ou ha se e al ECG cha ac e is ics a e highly co ela ed wi h each o he , ha is, mul icollinea i y occu s. Fo pa ien s aged be ween 40 and 59 yea s (inclusi e), mul icollinea i y occu ed in six a iables 86 (VIF > 5). These a iables do no belong o a speci ic ype, in ac , one is om HR (HR Min), wo a e om HRV (ASDNN 5 and SDNN), and h ee a e om QT analysis (QT Mean, QT Max and QTc Mean). As o he pa ien s aged abo e 59 yea s old, mul icollinea i y occu ed in i e a iables, one om HR (HR Mean), wo om HRV (SDNN and RMSSD), and wo om QT analysis (QT Max and QTc Mean). SVM wi h RBF ke nel was he model ha showed he bes classi ica ion pe o mance in he case o he pa ien s aged be ween 40 and 59 o g oups HCM and FD wi hou WMLs (accu acy o 0.8049). Also, his is he algo i hm ha leads o be e classi ica ion pe o mances in almos e e y ea u e combina ion. In he s udies Hija i e al. [6] and Munla e al. [39], RBF SVM was also he model ha led o be e classi ica ion pe o mances, a classi ying i symp oms we e o we e no expec ed based on some ECG measu emen s, and classi ying s ess le el in o highly s essed o no mal based on HRV analysis, espec i ely. This model’s pe o mance was ob ained when using a 4- ea u e combina ion (HR Mean, SDANN 5, RMSSD, and QTc > 450). F om hese ea u es, he only ha was expec ed, aking in o conside a ion he s a is ical esul s, was HR Mean, since, his a iable was signi ican ly associa ed wi h he dependen a iable in he logis ic eg ession analysis esul s o hese pa ien s. The emaining a iables, ha is, SDANN 5, RMSSD, and QTc > 450, we e no signi ican ly associa ed wi h he dependen a iable. The ones ha we e signi ican ly associa ed we e all excluded du ing he il e ea u e selec ion me hod, based on VIF alues, and, he e o e, we e no e en used as inpu da a o he machine lea ning models. Howe e , i is wo h emembe ing ha he excluded a iables by he i e a i e p ocess based on VIF alues can be p edic ed by o he independen a iables in he emaining subg oup o a iables. As o he classi ica ion o HCM and FD wi h WMLs pa ien s aged be ween 40 and 59 yea s, he bes model was KNN wi h a 6- ea u e combina ion (HR Mean, HR Max, RMSSD, QTc Min, QTc Max, and QTc > 450) (accu acy o 0.8462). This is p obably he mos disc epan esul . Howe e , RBF SVM was he second bes model wi h his ea u e combina ion, and he bes wi h he o he combina ions, p o ing, once again, i s alue o classi ica ion p oblems based on ECG cha ac e is ics. E alua ing he ea u e combina ions, some o he a iables (HR Mean, QTc Max and QTc > 450) we e expec ed, since hey we e signi ican ly associa ed wi h he dependen a iable (HCM o FD) in he logis ic eg ession esul s. 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A ailable: h ps://www.hindawi.com/jou nals/ jd /2018/3407306/. 103 Table 27: S a is ically non-signi ican logis ic eg ession esul s o HCM and FD wi hou WMLs g oups wi h ages be ween 40 and 59 (including) Va iables Uni a ia e logis ic e- g ession Mul i a iable logis ic eg ession - Adjus ed o age Mul i a iable logis ic eg ession - Adjus ed o sex OR (95% C.I) p- alue OR (95% C.I) p- alue OR (95% C.I) p- alue HR Max 1.03 (1.00 - 1.07) 0.0838 1.01 (0.97 - 1.06) 0.5162 1.03 (0.99 - 1.07) 0.1201 Age - - 0.90 (0.78 - 1.04) 0.1478 - - Sex - - - - 3.23 (0.83 - 12.59) 0.0908 SDANN 5 0.98 (0.96 - 1.00) 0.0821 0.97 (0.95- 1.00) 0.0279 0.98 (0.96 - 1.01) 0.1376 Age - - 0.83 (0.72 - 0.97) 0.0155 - - Sex - - - - 3.10 (0.79 - 12.07) 0.1035 RMSSD 0.97 (0.93 - 1.00) 0.0699 0.97 (0.93 - 1.00) 0.0876 0.96 (0.92 - 1.00) 0.0411 Age - - 0.90 (0.79 - 1.02) 0.1036 - - Sex - - - - 6.24 (1.24 - 31.48) 0.0265 QT Min 0.97 (0.95 - 1.00) 0.0541 0.98 (0.95 - 1.01) 0.1964 0.98 (0.95 - 1.01) 0.1180 Age - - 0.90 (0.79 - 1.03) 0.1192 - - Sex - - - - 2.76 (0.69 - 10.97) 0.1495 QTc Min 1.01 (0.99 - 1.03) 0.4962 1.00 (0.98 - 1.02) 0.8699 1.01 (0.99 - 1.03) 0.3714 Age - - 0.88 (0.77 - 1.00) 0.0436 - - Sex - - - - 3.88 (1.00 - 15.08) 0.0503 QTc Mean 0.98 (0.96 - 1.01) 0.1705 0.98 (0.95 - 1.01) 0.2002 0.98 (0.95 - 1.01) 0.1159 Age - - 0.88 (0.77 - 0.99) 0.0412 - - Sex - - - - 4.23 (1.04 - 17.11) 0.0432 QTc Max 0.99 (0.98 - 1.00) 0.0633 0.99 (0.98 - 1.00) 0.1299 0.99 (0.98 - 1.00) 0.0254 Age - - 0.89 (0.78 - 1.01) 0.0683 - - Sex - - - - 6.66 (1.34 - 33.08) 0.0204 QTc > 450 0.98 (0.96 - 1.00) 0.0873 0.98 (0.96 - 1.00) 0.1169 0.98 (0.96 - 1.00) 0.0783 Age - - 0.87 (0.77 - 1.00) 0.0453 - - Sex - - - - 3.96 (0.98 - 16.01) 0.0538 Longes R-R 0.29 (0.09 - 0.98) 0.0470 0.39 (0.11 - 1.42) 0.1542 0.18 (0.04 - 0.78) 0.0218 Age - - 0.91 (0.80 - 1.04) 0.1545 - - Sex - - - - 7.11 (1.41 - 36.01) 0.0177 110 Table 28: S a is ically non-signi ican logis ic eg ession esul s o HCM and FD wi h WMLs g oups wi h ages be ween 40 and 59 (including) Va iables Uni a ia e logis ic e- g ession Mul i a iable logis ic eg ession - Adjus ed o age Mul i a iable logis ic eg ession - Adjus ed o sex OR (95% C.I) p- alue OR (95% C.I) p- alue OR (95% C.I) p- alue HR Min 1.08 (0.98 - 1.20) 0.1211 1.09 (0.98 - 1.21) 0.1112 1.09 (0.98 - 1.21) 0.1117 Age - - 0.90 (0.79 - 1.04) 0.1447 - - Sex - - - - 2.33 (0.60 - 9.09) 0.2230 HR Max 1.03 (0.99 - 1.08) 0.1443 1.03 (0.98 - 1.08) 0.2661 1.04 (0.99 - 1.08) 0.1266 Age - - 0.93 (0.81 - 1.07) 0.3016 - - Sex - - - - 2.34 (0.60 - 9.09) 0.2192 ASDNN 5 0.98 (0.95 - 1.01) 0.1700 0.98 (0.95 - 1.01) 0.1918 0.98 (0.95 - 1.01) 0.1626 Age - - 0.91 (0.80 - 1.04) 0.1770 - - Sex - - - - 2.26 (0.59 - 8.70) 0.2356 SDANN 5 1.01 (0.99 - 1.03) 0.4467 1.00 (0.98- 1.02) 0.7280 1.01 (0.99 - 1.03) 0.3240 Age - - 0.92 (0.80 - 1.05) 0.2096 - - Sex - - - - 2.48 (0.64 - 9.64) 0.1888 SDNN 0.99 (0.98 - 1.01) 0.5143 0.99 (0.98 - 1.01) 0.4550 1.00 (0.98 - 1.01) 0.5863 Age - - 0.91 (0.79 - 1.04) 0.1478 - - Sex - - - - 2.10 (0.56 - 7.81) 0.2685 RMSSD 0.98 (0.96 - 1.00) 0.1247 0.98 (0.96 - 1.01) 0.1595 0.98 (0.96 - 1.00) 0.1073 Age - - 0.93 (0.81 - 1.06) 0.2857 - - Sex - - - - 2.76 (0.66 - 11.60) 0.1652 QT Min 0.98 (0.95 - 1.02) 0.3316 0.99 (0.96 - 1.02) 0.4028 0.99 (0.95 - 1.02) 0.3627 Age - - 0.91 (0.80 - 1.04) 0.1846 - - Sex - - - - 2.11 (0.56 - 7.90) 0.2681 QTc Min 1.02 (1.00 - 1.05) 0.0953 1.02 (0.99 - 1.05) 0.1258 1.03 (1.00 - 1.06) 0.0707 Age - - 0.92 (0.80 - 1.05) 0.2137 - - Sex - - - - 2.72 (0.67 - 11.10) 0.1626 Longes R-R 0.54 (0.22 - 1.33) 0.1813 0.64 (0.25 - 1.65) 0.3586 0.47 (0.18 - 1.19) 0.1120 Age - - 0.93 (0.81 - 1.07) 0.3072 - - Sex - - - - 2.85 (0.69 - 11.67) 0.1462 111 Table 29: S a is ically non-signi ican logis ic eg ession esul s o FD wi h WMLs and FD wi hou WMLs g oups wi h ages be ween 40 and 59 (including) Va iables Uni a ia e logis ic e- g ession Mul i a iable logis ic eg ession - Adjus ed o age Mul i a iable logis ic eg ession - Adjus ed o sex OR (95% C.I) p- alue OR (95% C.I) p- alue OR (95% C.I) p- alue HR Min 0.91 (0.82 - 1.01) 0.0868 0.91 (0.82 - 1.01) 0.0719 0.92 (0.82 - 1.02) 0.1061 Age - - 1.07 (0.96 - 1.19) 0.2447 - - Sex - - - - 0.71 (0.21 - 2.42) 0.5897 HR Mean 0.96 (0.89 - 1.03) 0.2188 0.96 (0.90 - 1.04) 0.3075 0.96 (0.89 - 1.03) 0.2901 Age - - 1.04 (0.93 - 1.17) 0.4516 - - Sex - - - - 0.73 (0.21 - 2.50) 0.6175 HR Max 0.98 (0.94 - 1.03) 0.4288 0.99 (0.95 - 1.04) 0.7129 0.99 (0.95 - 1.03) 0.5771 Age - - 1.05 (0.93 - 1.18) 0.4501 - - Sex - - - - 0.69 (0.20 - 2.39) 0.5542 ASDNN 5 1.03 (0.99 - 1.08) 0.1618 1.04 (0.99 - 1.09) 0.1060 1.03 (0.98 - 1.08) 0.1998 Age - - 1.08 (0.97 - 1.21) 0.1736 - - Sex - - - - 0.71 (0.21 - 2.42) 0.5876 RMSSD 1.03 (0.99 - 1.08) 0.1730 1.03 (0.99 - 1.08) 0.1479 1.03 (0.99 - 1.08) 0.1840 Age - - 1.07 (0.96 - 1.20) 0.2334 - - Sex - - - - 0.63 (0.19 - 2.11) 0.4571 QT Min 1.02 (0.99 - 1.04) 0.1564 1.02 (0.99 - 1.04) 0.2257 1.02 (0.99 - 1.04) 0.2173 Age - - 1.04 (0.93 - 1.16) 0.4904 - - Sex - - - - 0.79 (0.23 - 2.79) 0.7186 QT Mean 1.00 (0.98 - 1.03) 0.6414 1.00 (0.98 - 1.02) 0.8787 1.00 (0.98 - 1.02) 0.7580 Age - - 1.06 (0.94 - 1.18) 0.3520 - - Sex - - - - 0.64 (0.19 - 2.11) 0.4591 QT Max 0.99 (0.99 - 1.00) 0.3038 0.99 (0.98 - 1.00) 0.1745 0.99 (0.98 - 1.00) 0.2801 Age - - 1.08 (0.97 - 1.22) 0.1680 - - Sex - - - - 0.58 (0.18 - 1.94) 0.3785 QTc Min 1.01 (0.99 - 1.03) 0.4166 1.01 (0.99 - 1.03) 0.3701 1.01 (0.99 - 1.03) 0.3818 Age - - 1.06 (0.95 - 1.19) 0.2755 - - Sex - - - - 0.59 (0.18 - 1.93) 0.3797 QTc Mean 0.99 (0.97 - 1.02) 0.5175 0.99 (0.96 - 1.02) 0.4054 0.99 (0.96 - 1.02) 0.5227 Age - - 1.07 (0.96 - 1.19) 0.2472 - - Sex - - - - 0.61 (0.19 - 2.00) 0.4167 QTc Max 0.99 (0.98 - 1.00) 0.2440 0.99 (0.98 - 1.00) 0.1650 0.99 (0.98 - 1.01) 0.3228 Age - - 1.08 (0.96 - 1.21) 0.2025 - - Sex - - - - 0.72 (0.21 - 2.48) 0.6048 QTc > 450 0.99 (0.97 - 1.01) 0.4543 0.99 (0.96 - 1.01) 0.2947 0.99 (0.97 - 1.01) 0.3523 Age - - 1.08 (0.96 - 1.21) 0.2059 - - Sex - - - - 0.54 (0.16 - 1.83) 0.3213 Longes R-R 1.76 (0.56 - 5.46) 0.3311 1.64 (0.52 - 5.19) 0.3977 1.87 (0.59 - 5.97) 0.2881 Age - - 1.05 (0.94 - 1.17) 0.3669 - - Sex - - - - 0.56 (0.17 - 1.87) 0.3500 112 Table 30: No mali y o HCM and FD wi h WMLs g oups and homogenei y o a iance esul s, o pa ien s aged abo e 59 Va iables No mali y - p alues Homogenei y o a iances - p aluesHCM FD wi h WMLs Age p = 0.0355 p = 0.0185 - HR Min p = 0.2937 p = 0.3408 p = 0.3538 HR Mean p = 0.4186 p = 0.6448 p = 0.1068 HR Max p = 0.0247 p = 0.4152 - ASDNN 5 p = 0.0001 p = 0.0107 - SDANN 5 p = 0.5551 p = 0.3493 p = 0.5958 SDNN p = 0.0003 p = 0.2821 - RMSSD p < 0.0001 p = 0.0001 - QT Min p = 0.3854 p = 0.0342 - QT Mean p = 0.3932 p = 0.8572 p = 0.1415 QT Max p = 0.0002 p = 0.0007 - QTc Min p = 0.9707 p = 0.1330 p = 0.5846 QTc Mean p = 0.7889 p = 0.8998 p = 0.8367 QTc Max p = 0.0041 p = 0.0089 - QTc > 450 p = 0.0219 p = 0.0060 - Longes R-R p < 0.0001 p < 0.0001 - 113 Table 31: S a is ically non-signi ican logis ic eg ession esul s o HCM and FD wi h WMLs g oups wi h ages abo e 59 Va iables Uni a ia e logis ic e- g ession Mul i a iable logis ic eg ession - Adjus ed o age Mul i a iable logis ic eg ession - Adjus ed o sex OR (95% C.I) p- alue OR (95% C.I) p- alue OR (95% C.I) p- alue HR Max 1.03 (0.99 - 1.06) 0.1342 1.03 (0.99 - 1.06) 0.1333 1.03 (0.99 - 1.06) 0.1281 Age - - 0.99 (0.92 - 1.07) 0.7602 - - Sex - - - - 3.94 (1.12 - 13.81) 0.0323 ASDNN 5 1.00 (0.98 - 1.02) 0.9291 1.00 (0.98 - 1.02) 0.9158 1.00 (0.98 - 1.02) 0.9507 Age - - 0.99 (0.92 - 1.06) 0.7775 - - Sex - - - - 3.74 (1.10 - 12.67) 0.0340 SDANN 5 1.01 (0.99 - 1.03) 0.4996 1.01 (0.99 - 1.03) 0.5088 1.02 (0.99 - 1.04) 0.1653 Age - - 0.99 (0.92 - 1.07) 0.8122 - - Sex - - - - 5.18 (1.34 - 20.04) 0.0172 SDNN 1.00 (0.98 - 1.01) 0.5939 1.00 (0.98 - 1.01) 0.5699 1.00 (0.98 - 1.01) 0.6474 Age - - 0.99 (0.92 - 1.06) 0.7352 - - Sex - - - - 3.71 (1.09 - 12.61) 0.0354 RMSSD 1.00 (0.99 - 1.01) 0.7086 1.00 (0.99 - 1.01) 0.7080 1.00 (0.99 - 1.00) 0.4582 Age - - 0.99 (0.92 - 1.07) 0.7820 - - Sex - - - - 4.06 (1.16 - 14.25) 0.0285 QT Max 1.00 (0.99 - 1.00) 0.1248 1.00 (0.99 - 1.00) 0.1227 1.00 (0.99 - 1.00) 0.1391 Age - - 0.99 (0.91 - 1.06) 0.7215 - - Sex - - - - 3.93 (1.11 - 13.98) 0.0344 QTc Min 1.00 (0.98 - 1.01) 0.4852 1.00 (0.98 - 1.01) 0.4951 1.00 (0.98 - 1.01) 0.5487 Age - - 0.99 (0.92 - 1.07) 0.8165 - - Sex - - - - 3.70 (1.09 - 12.57) 0.0363 QTc Mean 1.00 (0.98 - 1.02) 0.8502 1.00 (0.98 - 1.02) 0.8713 1.00 (0.98 - 1.02) 0.7139 Age - - 0.99 (0.92 - 1.07) 0.7956 - - Sex - - - - 3.82 (1.12 - 13.08) 0.0325 QTc Max 1.00 (0.99 - 1.00) 0.5775 1.00 (0.99 - 1.00) 0.5660 1.00 (0.99 - 1.00) 0.4064 Age - - 0.99 (0.92 - 1.06) 0.7564 - - Sex - - - - 4.07 (1.16 - 14.24) 0.0283 QTc > 450 1.00 (0.99 - 1.02) 0.5860 1.00 (0.99 - 1.02) 0.6058 1.01 (0.99 - 1.03) 0.3378 Age - - 0.99 (0.92 - 1.07) 0.8306 - - Sex - - - - 4.26 (1.19 - 15.23) 0.0256 Longes R-R 0.87 (0.51 - 1.49) 0.6124 0.88 (0.51 - 1.50) 0.6311 0.78 (0.44 - 1.40) 0.4109 Age - - 0.99 (0.92 - 1.07) 0.8225 - - Sex - - - - 4.08 (1.16 - 14.34) 0.0283 114 Appendix B Machine Lea ning Appendix Table 32: Hype pa ame e s alues/s a us pe machine lea ning model and classi ica ion p oblem o pa ien s aged be ween 40 and 59 (inclusi e) ML Model Model Pa ame e s Classi ica ion P oblem HCM s FD w/o WMLs HCM s FD w/ WMLs FD w/ WMLs s FD w/o WMLs LR C 0.5 0.05 0.7 Linea SVM C 0.1 0.05 3 RF boo s ap False T ue (de aul ) False n_es ima o s 2 24 1 max_dep h None (de aul ) 6 5 max_lea _nodes None (de aul ) None (de aul ) 9 min_samples_lea 1 (de aul ) 1 (de aul ) 1 (de aul ) min_samples_spli 2 (de aul ) 2 (de aul ) 2 (de aul ) ML: machine lea ning; LR: logis ic eg ession; SVM: suppo ec o machine; RF: andom o es 115 Table 33: Accu acy alues pe machine lea ning model and classi ica ion p oblem o pa ien s aged be ween 40 and 59 (inclusi e) ML Model Classi ica ion P oblem HCM s FD w/o WMLs HCM s FD w/ WMLs FD w/ WMLs s FD w/o WMLs LR 0.7561 0.6923 0.6250 Linea SVM 0.7317 0.6923 0.6875 RF 0.7561 0.7692 0.8125 ML: machine lea ning; LR: logis ic eg ession; SVM: suppo ec o ma- chine; RF: andom o es 116 Table 34: Hype pa ame e s alues/s a us pe machine lea ning model and numbe o ea u es o HCM and FD wi hou WMLs pa ien s aged 40 o 59 (inclusi e) ML Model Model Pa ame e s Numbe o ea u es (Fea u es) 4 Fea u es (HR Mean, SDANN 5, RMSSD, and QTc > 450) 6 Fea u es (HR Mean, SDANN 5, RMSSD, QTMin, QTc Max, and QTc > 450) 9 Fea u es (All) LR C 2 0.8 0.5 Linea SVM C 0.3 0.07 0.1 RBF SVM C 70 3 3 gamma 0.002 0.03 0.04 RF boo s ap T ue (de aul ) T ue(de aul ) False n_es ima o s 40 31 2 max_dep h 3 5 None (de aul ) max_lea _nodes None (de aul ) None (de aul ) None (de aul ) min_samples_lea 1(de aul ) 1 (de aul ) 1 (de aul ) min_samples_spli 3 2 (de aul ) 2 (de aul ) KNN n_neighbo s 8 3 8 weigh s uni o m uni o m uni o m ML: machine lea ning; LR: logis ic eg ession; SVM: suppo ec o machine; RBF: adial basis unc ion; RF: andom o es ; KNN: K-Nea es Neighbou 117 Table 35: Hype pa ame e s alues/s a us pe machine lea ning model and numbe o ea u es o HCM and FD wi h WMLs pa ien s aged 40 o 59 (inclusi e) ML Model Model Pa ame e s Numbe o ea u es (Fea u es) 5 Fea u es (HR Mean, RMSSD, QTc Min, QTcMax and QTc > 450) 6 Fea u es (HR Mean, HR Max, RMSSD, QTcMin, QTc Max and QTc > 450) 9 Fea u es (All) LR C 0.06 0.4 0.05 Linea SVM C 0.9 0.08 0.05 RBF SVM C 500 30 100 gamma 0.009 0.02 0.02 RF boo s ap False False T ue (de aul ) n_es ima o s 900 40 24 max_dep h 5 8 6 max_lea _nodes None (de aul ) None (de aul ) None (de aul ) min_samples_lea 1(de aul ) 1 (de aul ) 1 (de aul ) min_samples_spli 2 (de aul ) 0.3 2 (de aul ) KNN n_neighbo s 6 4 6 weigh s uni o m uni o m uni o m ML: machine lea ning; LR: logis ic eg ession; SVM: suppo ec o machine; RBF: adial basis unc ion; RF: andom o es ; KNN: K-Nea es Neighbou 118 Table 36: Hype pa ame e s alues/s a us pe machine lea ning model and numbe o ea u es o FD wi h WMLs and FD wi hou WMLs pa ien s aged 40 o 59 (inclusi e) ML Model Model Pa ame e s Numbe o ea u es (Fea u es) 1 Fea u e (SDANN 5) 2 Fea u es (SDANN 5 and QTc Min) 9 Fea u es (All) LR C 6 20 0.7 Linea SVM C 0.2 10 3 RBF SVM C 9 900 30 gamma 0.3 0.007 0.007 RF boo s ap T ue (de aul ) False False n_es ima o s 50 46 1 max_dep h 2 1 5 max_lea _nodes None (de aul ) None (de aul ) 9 min_samples_lea 5 10 1 (de aul ) min_samples_spli 2 (de aul ) 2 (de aul ) 2 (de aul ) KNN n_neighbo s 16 8 2 weigh s uni o m uni o m uni o m ML: machine lea ning; LR: logis ic eg ession; SVM: suppo ec o machine; RBF: adial basis unc ion; RF: andom o es ; KNN: K-Nea es Neighbou 119