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

Universidade do Minho Escola de Engenharia Ana Rita Sousa Moura Detecting important electrocardiogram characteristics for the diagnosis of Fabry disease via statistics and machine learning techniques March of 2022 UMinho | 2022 Ana Moura Detecting important electrocardiogram characteristics for the diagnosis of Fabry disease via statistics and machine learnings techniques Ana Rita Sousa Moura Detecting important electrocardiogram characteristics for the diagnosis of Fabry disease via statistics and machine learning techniques Master’s dissertation Integrated Master’s in Biomedical Engineering Medical electronics Work elaborated under the supervision of Prof. Dr. Estela Bicho (Supervisor) Dr. Flora Ferreira (Co-supervisor) Universidade do Minho Escola de Engenharia March of 2022 DIREITOS DE AUTOR E CONDIÇÕES DE UTILIZAÇÃO DO TRABALHO POR TERCEIROS Este é um trabalho académico que pode ser utilizado por terceiros desde que respeitadas as regras e boas práticas internacionalmente aceites, no que concerne aos direitos de autor e direitos conexos. Assim, o presente trabalho pode ser utilizado nos termos previstos na licença abaixo indicada. Caso o utilizador necessite de permissão para poder fazer um uso do trabalho em condições não previstas no licenciamento indicado, deverá contactar o autor, através do RepositóriUM da Universidade do Minho. Licença concedida aos utilizadores deste trabalho Atribuição-NãoComercial-SemDerivações CC BY-NC-ND https://creativecommons.org/licenses/by-nc-nd/4.0/ ii 0.1 Agradecimentos Tenho que agradecer a algumas pessoas, pelo apoio que me proporcionaram, de diversas formas, durante a minha dissertação e todo o meu percurso académico. Em primeiro lugar, agradeço à professora Estela Bicho por me ter aceite neste projeto e pela sua disponibilidade e à Doutora Flora Ferreira pela ajuda e orientação durante toda a dissertação, pela confiança, pela disponibilidade e pelos conhecimentos que me transmitiu. Agradeço também ao Doutor Miguel Gago e à Doutora Olga Azevedo, por terem lançado o desafio, fornecido os dados e ajudado nas questões clínicas que surgiram neste trabalho, sem eles esta dissertação não seria possível. Aos meus pais e ao meu irmão pelos esforços que fizeram para me possibilitarem esta oportunidade, por me apoiarem e quererem sempre o melhor para a minha vida. Sem eles não tinha conseguido chegar aqui. Obrigada por tudo Mãe. Um grande obrigada a todos os meus amigos e familiares, que durante estes anos da minha vida, estando perto ou longe, me acompanharam e incentivaram, em especial à Bárbara, à Helena, à Mariana, ao Nuno e à prima Carolina. Ao meu afilhado por alegrar os meus dias e à minha madrinha. Não podia deixar de agradecer ao meu namorado, Tiago, que durante a minha dissertação e durante o curso, que percorremos juntos, esteve sempre presente para me ajudar, motivar e acima de tudo aturar. Esta conquista também é um pouco tua. iii STATEMENT OF INTEGRITY I hereby declare having conducted this academic work with integrity. I confirm that I have not used plagiarism or any form of undue use of information or falsification of results along the process leading to its elaboration. I further declare that I have fully acknowledged the Code of Ethical Conduct of the University of Minho. iv 0.2 Resumo Título: Deteção de características do electrocardiograma importantes para o diagnóstico da doença de Fabry utilizando estatística e técnicas de machine learning. A doença de Fabry (DF) é uma doença genética rara de depósito lisossômico que afeta a qualidade de vida e pode mesmo levar à morte prematura. O diagnóstico ainda tardio reduz a eficiência da terapia de reposição enzimática. Assim, é extremamente importante identificar biomarcadores que possam auxiliar no diagnóstico precoce da DF. Apesar dos progressos nos últimos anos, a DF continua a ser mal compreendida. Desta forma, esta dissertação teve como objetivo identificar características de electrocardiograma (ECG) importantes para o diagnóstico da DF, mais especificamente, para diferenciar os pacientes de DF com e sem lesões da matéria branca, e estes de pacientes com miocardiopatia hipertrófica sarcomérica. Para este fim, foram desenvolvidos e aplicados modelos estatísticos e de machine learning (ML). Quinze características de ECG foram avaliadas usando diversos métodos de inferência estatística, sobretudo para identificar diferenças significativas entre os grupos tendo em conta o sexo e a idade. Dois métodos de seleção de atributos foram aplicados, um baseado nos valores do fator de inflação da variância (VIF), e uma eliminação recursiva de atributos usando logistic regression,support vector machine (SVM) linear e random forest como classificadores. Depois, avaliou-se a performance de cinco algoritmos de ML -logistic regression, SVM com função de base radial (RBF), random forest ek-nearest neighbor (KNN) - a distinguir os diferentes grupos, para identificar o melhor modelo para cada problema de classificação. A idade revelou ser significativamente diferente entre os grupos e estar relacionada com as variáveis de ECG. Após subdividir em três faixas etárias, algumas características revelaram-se importantes para distinguir os grupos, não sendo afetadas pela idade. Com base nas características de ECG selecionadas, os resultados mostraram boa taxa de acerto, com os melhores resultados a variar de 80% a 85%, obtidos usando SVM RBF, random forest e KNN. Estas descobertas demonstram o potencial das técnicas de ML baseadas em características de ECG como ferramenta complementar ao diagnóstico da DF, com e sem lesões da matéria branca, o que pode ser útil para reduzir a demora no diagnóstico. Palavras-chave: Classificação, Doença de Fabry, Eletrocardiograma, Estatística, Machine Learning. v 0.3 Abstact Title: Detecting important electrocardiogram characteristics for the diagnosis of Fabry disease via statistics and machine learning techniques. Fabry disease (FD) is a rare genetic lysosomal storage disorder that affects life quality and may even lead to premature death. The mean delay between the onset of symptoms and the diagnosis is still very high, reducing enzyme replacement therapy’s efficiency. Therefore, it is extremely important to identify biomarkers that could assist in the early diagnosis of FD. Despite all the progress in recent years, FD remains misunderstood. Thus, this dissertation aimed to identify important electrocardiogram (ECG) characteristics for diagnosing FD, and more specifically, to differentiate FD with white matter lesions (WMLs) from FD without WMLs patients and these from patients with sarcomeric hypertrophic cardiomyopathy. To this end, statistics and machine learning (ML) models have been developed and applied. Fifteen ECG variables were evaluated using several statistical inference methods mainly to identify significant differences between groups, considering sex and age. Two feature selection methods were applied, one based on variance inflation factor (VIF) values, and a recursive feature elimination using logistic regression, linear support vector machine (SVM), and random forest classifiers. Then, the performance of five ML algorithms - logistic regression, linear SVM, radial basis function (RBF) SVM, random forest, and K-nearest neighbor (KNN) - at distinguishing the different groups were evaluated to identify the best model for each classification problem. Age was found to be significantly different between groups and to be related to the ECG variables values. After subdivision into three categories by age, some ECG characteristics were identified as important to distinguish the groups and unaffected by age. Based on selected ECG characteristics, the results showed good classification accuracies, with the best scores ranging from 80% to 85%, obtained using RBF SVM, random forest, or KNN. These findings demonstrate the potential of ML techniques based on ECG characteristics as a complementary tool for diagnosing FD with or without WMLs that could be useful to reduce the diagnosis delay. Keywords: Classification, Electrocardiogram, Fabry Disease, Machine Learning, Statistics. vi Contents 0.1 Agradecimentos ................................... iii 0.2 Resumo ....................................... v 0.3 Abstact........................................ vi List of Figures xi List of Tables xii Acronyms xvi I : Introduction and State of the Art 1 1 Introduction 2 1.1 Motivation ...................................... 2 1.2 Goals......................................... 3 1.3 DissertationStructure................................. 3 2 Fabry disease and hypertrophic cardiomyopathy disease 5 2.1 FabryDisease .................................... 5 2.1.1 Description.................................. 6 2.1.2 Phenotype and Clinical Manifestations . . . . . . . . . . . . . . . . . . . . 6 2.1.3 Diagnosis .................................. 8 2.1.4 Treatment .................................. 8 2.2 Hypertrophic Cardiomyopathy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 vii 31 Statistically non-significant logistic regression results of HCM and FD with WMLs groups withagesabove59..................................114 32 Hyperparameters values/status per machine learning model and classification problem for patients aged between 40 and 59 (inclusive) . . . . . . . . . . . . . . . . . . . . 115 33 Accuracy values per machine learning model and classification problem for patients aged between 40 and 59 (inclusive) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 34 Hyperparameters values/status per machine learning model and number of features for HCM and FD without WMLs patients aged 40 to 59 (inclusive) . . . . . . . . . . . . . 117 35 Hyperparameters values/status per machine learning model and number of features for HCM and FD with WMLs patients aged 40 to 59 (inclusive) . . . . . . . . . . . . . . . 118 36 Hyperparameters values/status per machine learning model and number of features for FD with WMLs and FD without WMLs patients aged 40 to 59 (inclusive) . . . . . . . . 119 37 Hyperparameters values/status per machine learning model and classification problem forpatientsagedabove59 ..............................120 38 Accuracy values per machine learning model and classification problem for patients aged above59.......................................120 39 Hyperparameters values/status per machine learning model and number of features for HCM and FD with WMLs patients aged above 59 . . . . . . . . . . . . . . . . . . . . 121 xiv Acronyms ANOVA Analysis of variance. AUC Area under curve. ECG Electrocardiogram. ERT Enzyme replacement therapy. FD Fabry disease. GLA Galactosidase alpha. HCM Hypertrophic cardiomyopathy. HR Heart rate. HRV Heart rate variability. KNN K-nearest neighbor. LOOCV Leave-one-out cross-validation. LR Logistic regression. LVH Left ventricular hypertrophy. ML Machine learning. xv MRI Magnetic resonance imaging. OR Odds ratio. RBF Radial basis function. RF Random forest. RFE Recursive feature elimination. SVM Support vector machine. VIF Variance inflation factor. WMLs White matter lesions. xvi Part I : Introduction and State of the Art 1 Chapter 1 Introduction This Chapter presents the motivation of this dissertation as well as its goals. Finally, a description of how the dissertation is structured is presented. 1.1 Motivation Fabry disease (FD) is a rare genetic disease that affects life quality and may lead to premature death. There are treatments for this disease, like Enzyme replacement therapy (ERT) [1] [2]. Although this treatment has shown good results, it may not be able to stabilize disease manifestations if it is already in an advanced stage, so it is essential to begin ERT as early as possible [1]. The mean delay between the symptom onset and diagnosis is around 14.7 and 15.1 years in male and female patients, respectively [3]. Therefore, it is extremely important to find biomarkers that could assist in an early diagnosis of Fabry disease. Despite all the progress in recent years, FD remains misunderstood. There is evidence that specific cardiovascular, neurological, and cerebrovascular manifestations may be characteristics of this disease [4]. Hence, it is important to identify significant electrocardiogram (ECG) characteristics for diagnosing FD, and differentiate FD with white matter lesions (WMLs) from FD without WMLs patients. In this dissertation, 24-hour ECG data (Holter) is used since Electrocardiogram (ECG) is a medical 2 exam that is usually performed to diagnose and follow patients with cardiac diseases, like FD [5]. The cohort of patients may have or not have white matter lesions. Patients with Hypertrophic Cardiomyopathy are also included in the study because this disease has similarities in cardiac manifestations to those found in FD, mainly left ventricular hypertrophy. Statistics and machine learning models are developed and applied to extract and select important information from clinical data to understand better and achieve a more accurate disease prediction [6]. 1.2 Goals The main goal of this dissertation is to detect important electrocardiogram characteristics for the diagnosis of Fabry disease, using for that statistics and machine learning methods. More precisely, the objectives of this dissertation are: • Detect important ECG characteristics to differentiate FD patients with white matter lesions (WMLs) from FD patients without WMLs, and these two groups from patients with sarcomeric hypertrophic cardiomyopathy (HCM); • Investigate which physical characteristics, like age and sex, are correlated with ECG characteristics and, therefore, could impact the classification results; • Implement and evaluate the performance of different Machine Learning models on the differentiation between the groups of patients. 1.3 Dissertation Structure This dissertation is divided into three Parts and, in turn, these Parts are divided into Chapters, then Sections and Subsections. 3 The first Part (Part I) is denoted “Introduction and State of Art”, which, as indicated by the name, includes an introduction where the motivation, goals and structure (current subsection) of this dissertation are presented. It also includes a Chapter relative to Fabry and Hypertrophic Cardiomyophaty diseases, in which, for each disease, a description, its phenotype and clinical manifestations, how it is diagnosed, and possible treatments, are presented. The value of electrocardiogram (ECG) characteristics as data for classification is also explored in this part, mainly through studies that have already used ECG characteristics to diagnose and distinguish diseases. Machine learning diagnosis value is also explained and several studies that use ECG-based machine learning models for classification problems are also presented. In Part II the materials and methods are delineated. The study data is first presented, followed by the description of the adopted methodology to performed statistical analysis and a summarized explanation of the different implemented statistical methods. Last in this part, the adopted machine learning methodology and a brief explanation of the different methods and concepts incorporated in this methodology, are presented. The last Part of this dissertation (Part III) incorporates the statistical results and machine learning results Chapters. Thus, the results obtained from the application of the statistical and machine learning methods, respectively, are presented and discussed in these Chapters. In this Part there is also a Chapter dedicated to the conclusion of the dissertation as well as it limitations and future work. The Appendices can be found in the last pages of this dissertation. These include an appendix that is relative to the statistical analysis and another one that is relative to some results obtained using machine learning techniques. The content of the appendices is intermediate results, that is, results that were necessary to reach the final results and conclusions. 4 Chapter 2 Fabry disease and hypertrophic cardiomyopathy disease Since the main goal of this study is to detect important electrocardiogram characteristics to support and assist in an early diagnosis of Fabry disease, it is essential to present a description of this disease, its phenotype and clinical manifestations, how to diagnose it, and possible treatments. Thus, this is the focus of the first section of this chapter. Fabry is not the only disease addressed in this chapter, Hypertrophic Cardiomyopathy is also described in the second section. This disease is included in this study due to the similarities in the cardiac manifestations of these two diseases, mainly left ventricular hypertrophy (LVH), which is normally (40-60% of cases) caused by Sarcomeric Hypertrophic Cardiomyopathy, however, in about 5-10% of cases, unexplained LVH can be caused by other non-genetic or rarer genetic disorders, such as Fabry [7]. 2.1 Fabry Disease This section includes a description of Fabry disease, its phenotype and clinical manifestations (with a description of White Matter Lesions), how it is diagnosed and the possible treatments. 5 2.1.1 Description Fabry disease (FD), first recognized as a systemic vascular disease, is an X-chromosome-linked lysosomal storage disorder caused by mutations in the galactosidase alpha (GLA) gene, that result in a deficient or even absent activity of the enzyme alpha-galactosidase A (α-GAL A). This deficient activity leads to lysosomal accumulation of globotriaosylceramide (Gb3) and other related glycosphingolipids, since α-GAL A is responsible for catalyzing the hydrolysis of glycosphingolipids and participates in their degradation in the lysosome. Gb3 can accumulate in cells and organs, for example, body fluids, vascular endothelial cells, perithelial, smooth-muscle cells of blood vessels, cardiomyocytes, cardiac conduction tissue, and valvular fibroblasts. Fabry disease affects a small percentage of the population, and so, it is considered a rare disease [1] [4] [8] [9]. 2.1.2 Phenotype and Clinical Manifestations The mutations in the GLA can cause a practically null enzymatic activity or can lead to residual enzymatic activity (REA). The first case is related to severe and early onset classical phenotypes that develop in childhood or adolescence, like acroparesthesias (burning, tingling, or prickling sensations or numbness in the extremities), neuropathic pain, hypohydrosis (decreased sweating), heat, cold and exercise intolerance, cornea verticillata (whorl-like pattern of golden brown or gray deposits in the inferior interpalpebal portion of the cornea), angiokeratomas (vascular lesions in the skin and mucous membranes), gastrointestinal symptoms and proteinuria (high proteins concentration in the urine); in adulthood, patients also experience sensorineural deafness and cardiac, renal and cerebrovascular manifestations. The second case is associated with attenuated and late-onset phenotypes such as those indicated for adulthood and the phenotype may be influenced by the participation of an organ, such as the kidneys or the heart [4] [10]. Some of the cardiac manifestations in FD are left ventricular hypertrophy (LVH) (unexplained by abnormal cardiac loading conditions), which is the most common, palpitations and arrhythmias, exertional dyspnoea (person feels short of breath during exercise), small-vessel coronary disease (condition in which 6 the walls of the small arteries in the heart are not working properly), and even heart failure. Therefore, this disease leads to premature death, being cardiac complications one of the most common causes [1] [4] [9]. It has been proved that symptoms occur earlier in males than in females, including cardiac symptoms like left ventricular hypertrophy and that the disease manifests in a moderate way in women [1]. A study including Fabry patients with p.F113L mutation reported white matter lesions (WMLs) as a common manifestation that increases with age and becomes a universal finding above 70 years old (in both sexes). However, due to the higher prevalence of WMLs in young patients without other comorbidities, WMLs seem to be caused by FD, probably mainly by Gb3 deposits in microglial cells and astrocytes, and not by age or other conditions. A similar conclusion was found in a large cohort of p.N215S patients, differing only in the appearing age, which is early before 30 years old in the p.F113L mutation and before 40 years in this cohort [4]. White Matter Lesions The exchange of information and communication between different areas of the gray matter is carried out by a network of nerve fibers denominated white matter (WM). The White matter is located below gray matter in the brain covering almost half of it and is superficial to gray matter in the spinal cord. The neural networks are formed by nerve fibers called axons that are the extensions of nerve cells (neurons). The axons are surrounded by a type of sheath, the myelin, that allows electrical impulses to transmit quickly and efficiently along the nerve cells. Since myelin is composed of protein and fatty substances it is responsible for the white color in the white matter [11] [12] [13]. White matter lesions (WMLs) are a consequence of cerebral small vessel disease (CSVD) on the brain parenchyma, along with lacunar infarcts, cerebral microbleeds and enlarged perivascular spaces. The term CSVD incorporates all the pathological processes of the cerebral small vessels and it is the most common cause of vascular cognitive impairment and dementia. White matter lesions are also called eukoaraiosis or white matter hyperintensities being the last one more of a descriptive expression used on magnetic resonance imaging (MRI) since these lesions are best seen as hyperintensities on T2 weighted and FLAIR (Fluid-attenuated inversion recovery) sequences of MRI. Non-vascular conditions may also lead to WMLs, for example, any change in chemical composition, damage, or ischemia of myelinated fibers. Dementia, 7 the depolarization and repolarization of heart muscle (cardio) allowing the identification and location of pathology. This electrical activity (electro) is small and is detected by contact electrodes placed on different parts of patient’s chest and limb [23] [24]. The ECG may be composed of 12 leads which provides views of the heart in both frontal and horizontal planes, thus obtaining records in different orientations and perspectives. There are two types of leads: the limb leads that view the heart in frontal plane and the precordial leads or chest leads that view the heart in horizontal plane. The first one is composed by the leads I, II and III, called the standard leads and the ones that form the Eithoven’s triangle, and also by three augmented limb leads, aVR, aVL and aVF. The second one, the precordial leads are V1, V2, V3, V4, V5 and V6 [25] [26]. The vertical axis of an ECG record is voltage and the horizontal is time, therefore, measurements in horizontal axis indicate the overall heart rate, regularity, and the time intervals during electrical activation. In vertical axis, measurements indicate the voltage that is measured in the surface and that represent the “summation” of the electrical activation of all the cardiac cells [27]. Interpretation of ECG may detect many cardiac abnormalities, some only by a single ECG record and others by serial recording over time [27]. Records of heart’s activity during 24 to 48 hours, or even more, are archived by a portable device called Holter monitor [28]. Electrocardiogram characteristics, such as intervals, amplitudes, and rates, can be obtained by interpreting the ECG. There are already several electrocardiographic findings observed in Fabry disease patients. A short PR interval, signs of LVH, T wave inversion, bradycardia, and atrial fibrillation are examples of these electrocardiographic findings [8] [10]. Shortening of QRS width and increased QTc duration are also identified in some studies [29] [30]. As previously described, patients with HCM also exhibit electrocardiographic abnormalities, for example, signs of ventricular hypertrophy with increased precordial voltages, and non-specific ST segment and T-wave abnormalities, deep inferior and/or lateral Q-waves (suggestive of a hypertrophied septal depolarization), P-wave abnormalities (suggestive of left atrial enlargement), and T-wave inversions [18] [20] [21]. This proves that Fabry disease and HCM patients do, in fact, show electrocardiographic abnormalities. Also, there is a huge need to identify other causes of LVH besides sarcomeric HCM and electrocardiography 14 is one of the first steps when evaluating these patients. Therefore, electrocardiogram could be an important tool to distinguish and diagnose these diseases. Some studies already tried to identify ECG characteristics to distinguish between FD and HCM, which is the case of Junqua et al. [5] and Namdar et al [31]. Junqua et al. [5] aimed to assess the diagnostic value of electrocardiographic scores for LVH in Fabry disease patients and also the diagnostic value for Fabry disease of a model combining electrocardiographic and echocardiographic criteria. Junqua et al. evaluated several ECG characteristics of 61 Fabry disease patients and 59 patients with sarcomeric HCM. These characteristics were heart rate (bpm), corrected PQ (ms), QRS duration (ms), corrected QT (ms), RBBB, LBBB, Left anterior hemiblock, Left posterior hemiblock, pre-excitation, pathologic Q wave, atrial fibrillation, and LVH indexes (Cornell voltage index (mm), Gubner index (mm), Sokolow—Lyon voltage index (mm), Romhilt—Estes score, Sokolow—Lyon product (mm.ms), and Cornell product (mm.ms)). A univariate analysis was performed, using Student’s t-test for continuous variables and Fisher test or chi-squared test for qualitative variables. Among the characteristics, QRS duration was significantly higher and RBBB more frequent in the Fabry group. The LVH indexes, Gubner index and Sokolow—Lyon product, were also higher in this group (Fabry patients). As for the remaining ECG characteristics, Junqua et al. did not find significant differences between FD and HCM patients. A multivariable analysis, with the electrocardiogram and echocardiogram variables that presented a p-value ≤0.01 in the univariate analysis, was performed. Among the ECG variables, only RBBB and Sokolow—Lyon product were independently associated with Fabry disease. It is important to mention that Junqua et al. found that age was significantly different between FD and HCM groups, being Fabry patients older than HCM patients [5]. The aim of the study of Namdar et al. [31] was to investigate the value of common ECG parameters in the diagnosis of patients with Fabry disease (FD), amyloidosis, hypertensive heart disease (HHD), aortic stenosis (AS), and nonobstructive hypertrophic cardiomyopathy (HC). These ECG parameters include resting heart rate (beats/min), P-wave duration (ms), P wave corrected for heart rate (ms), PQ interval (ms), corrected PQ interval (ms), PQ interval < 120 ms, PQ interval minus P-wave duration in lead II (ms), QRS duration (ms), Sokolow–Lyon index (mV, left ventricular hypertrophy and right ventricular hypertrophy), maximum peak to end of T wave (ms), corrected QT mean interval (ms), and corrected QT dispersion (ms). It should be noted that, in this study, groups were matched for age and left ventricular muscle 15 mass index so that it would not influence ECG parameters. Namdar et al. compared the continuous variables with analysis of variance for repeated measurements and post hoc analysis with Fisher’s probable least-significant differences test and/or Student’s t-test. As for categorical variables, these were compared using Fisher’s exact test. The study included 94 patients, being 17 diagnosed with FD, 20 with HHD, 17 with amyloidosis, 20 with AS, and 20 with HC. In the FD group, PQ interval, corrected PQ interval, and PQ interval minus P-wave duration in lead II variables were significantly shorter. These two last characteristics led to the highest diagnostic performance for the diagnosis of FD, with cut-off values of 114 ms and 40 ms, specificity of 90% and 99%, AUC of 0.90 and 0.94, respectively, and sensitivity of 82% on both. However, Namdar et al. realised that the combination of normal correct QT interval (i.e., < 440 ms) and short PQ interval minus P-wave duration in lead II (i.e., < 40 ms) gave a better diagnostic performance for the diagnosis of FD, with specificity of 99% and sensitivity of 100%. Should be noted that none of the HC patients fulfilled these two criteria [31]. As previously mentioned, WMLs are a manifestation in FD patients, and similar to the studies that aimed to distinguish FD from HCM patients, there is also studies that aimed to distinguish FD patients with WMLs from FD patients without WMLs, based on electrocardiogram characteristics, which is the case of Braga (2021) [32]. Braga (2021) [32] evaluated ECG characteristics of 114 FD patients, in which 61 have WMLs and 53 do not have WMLs. These ECG characteristics include heart rate variables (HR Min, HR Mean, HR Max), HRV variables (ASDNN 5, SDANN 5, SDNN, RMSSD), QT analysis variables (QT Min, QT Mean, QT Max, QTc Min, QTc Mean, QTc Max, QTc ≥450). and a supraventricular ectopy variable (Longest R-R). Braga (2021) identified that 6 ECG characteristics, HR Max, QT Min, QT Mean, QT Max, QTc Mean, and QTc ≥450, were significantly different between the two groups. Age was also significantly different between the groups, with FD with WMLs being older than FD without WMLs patients. These comparison of continuous variable was done with t-test and Mann Whitney U Test, for normally and non-normally distributed variables, respectively. Then, Braga (2021) performed a univariate logistic regression analysis to evaluate the association between each ECG variable and the presence of WMLs and realised that HR Max, QT Min, QT Mean, QTc Mean, and QTc ≥450 variables presented a significant association with the presence of WMLs. However, when adjusted by age, none of the ECG variables presented a significant association with the presence of WMLs. Due to the significant difference in the age of the two groups, Braga (2021) divided the patients into age 16 classes, and repeated the univariate and multivariable analysis in the age class of [40,60[ (the only class with similar number of patients in each group) that did not present significant differences on patients’ age or sex. Two variables, of HRV, were significantly associated with the presence of WMLs, SDANN 5 and SDNN variables. When adjusted to age or sex, these two variables remained associated with the presence of WMLs [32]. Another relevant study, Galluzzi et al. [33], also uses ECG data, more specifically, HRV data of patients with and without WMLs. However, in this study, patients have mild cognitive impairment (MCI) instead of FD. Thus, the aim of this study was to evaluate the independent association of HRV with WMLs in patients with mild cognitive impairment (MCI). Galluzzi et al. used 24-hour ECG recordings of 82 MCI patients, in which 32 present WMLs, to calculate HRV variables. In time domain, standard deviation of the RR intervals, standard deviation of the 5-minute mean values of RRs for each 5-minute interval, average of standard deviations of RR for each 5-minute interval, and the RMSSD were calculated. As for frequency domain, low frequency (LF) 0.04 – 0.15 Hz, HF 0.15 – 0.40 Hz, and low high-frequency ratio were calculated. The differences between MCI with and without WMLs groups were assessed using t-test and Mann-Whitney for normally distributed and non-normally distributed continuous variables, respectively, and chi-square for categorical variables. Galluzzi et al. also evaluated the association between each HRV index and WMLs (ARWMC, age-related white matter changes, scale total score, from magnetic resonance imaging) through linear regression models, and the potential of HRV indices to predict the extent of WMLs with a stepwise multiple regression model. In this study, age was significantly different between the two groups, patients with WMLs being older than those without WMLs. Differences were also found in RMSSD and LF that were reduced in MCI patients with WMLs. Galluzzi et al. found that RMSSD, LF, and HF were inversely associated with the extent of WMLs in the unadjusted models, however, in the adjusted models, RMSSD was the only variable that remained inversely associated. As for the stepwise results, these showed that RMSSD and age were significant predictors of WMLs [33]. In conclusion, all the presented studies demonstrate that ECG characteristics are already used as data to diagnose and to distinguish diseases and/or manifestations, which is the case of Fabry disease and White Matter Lesions, and initially promising results have been achieved. 17 3.2 ECG-based machine learning algorithms for classification Machine learning (ML) is a branch of computational algorithms that are intended to reproduce human intelligence by being able to detect meaningful patterns in data even if the datasets are complex and large [34]. A correct diagnosis of a disease or condition is a complex process since a lot of symptoms are nonspecific and variable among patients, some diagnostic tests are not regularly done and are expensive, and it requires a huge human effort, as well as time. Also, physicians are usually susceptible to cognitive bias during the diagnosis stage, being more biased to diseases or conditions that they have already diagnosed in the past and, therefore, are more familiar with. Due to the prevalence of rare diseases, there is a higher probability that physicians have cognitive bias during the diagnosis stage of these diseases [35] [36] [37]. Machine learning is useful for medical diagnosis since with unbiased and balanced datasets, ML algorithms are able to attenuate the cognitive bias problem and, thus, produce higher accuracy. Machine learning has been applied to a variety of medical diagnosis problems, for example, breast cancer, diabetes, cancer tissues, and thyroid [35] [37]. Similar to what is proposed in this study, several studies have also applied classification supervised ML algorithms to ECG data, which is the case of Hijari et al. [6], Vigier et al. [38], Munla et al. [39], and Braga (2021) [32]. What is proposed by each of these studies, as well as the main methods and results, are now going to be briefly explained. Hijari et al.[6] attempted to identify patients at risk of Long QT Syndrome (LQTS) symptoms, by training ML algorithms with input variables extracted from raw ECG data. The purpose was for a classifier to be able to output “symptoms expected” or “no symptoms expected” based on some measurements from an ECG. Hijari et al. considered that QT and RR intervals were the most relevant markers for their study and used 24-hour ECG records of 434 patients with the most common LQTS genotypes. Then, they implemented several classification algorithms, such as k-nearest neighbors, linear SVM, RBF SVM, random forest, and AdaBoost, using scikit-learn (Python library) [40]. Finally, they determined the classifiers’ accuracy by leaving 30% of the samples for testing and 70% for training, and doing the process of selection of training data, training and testing 50 times for each classifier, then calculating the average result. In conclusion, 18 the classifier that performed better, in the test phase, in the Hijari et al. study, was the RBF SVM classifier with about 70% accuracy, and the random forest classifier achieved the second-best accuracy [6]. Vigier et al. [38] aimed to create and evaluate a machine learning model able to discriminate between cancer patients and healthy controls based on 5-min ECG recordings. They selected 12 heart rate variability (HRV) features, which were then reduced to the top 5 (SDNN, RMSSD, pNN50%, HRV triangular index, and SD1) with recursive feature elimination (RFE). These features were then used as input to three different machine learning algorithms: linear discrimination analysis (LDA), random forest, and naive bayes. An ensemble model based on the stacking method, which comprised the predictions of the three base classifiers, was also implemented. The study included 77 cancer patients (breast, prostate, lung, colorectal, and pancreatic cancers) and 57 healthy controls, 40% of the dataset was used for testing and the remaining 60% for training, with a tenfold cross validation. Vigier et al. concluded that among the three base ML algorithms, random forest was the one that performed best during the training evaluation, with an accuracy of 85%. The ensemble model performed better than all base classifiers, with an accuracy of 0.929 in the training phase and 0.865 in the test phase [38]. A study, performed by Munla et al. [39], investigated stress level detection of a driver during a real word driving experiment, based on heart rate variability (HRV) analysis. Munla et al. performed different HRV analyses, in time, frequency, non-linear, and time-frequency. The features extracted from these analyses were used, separately, as input data to three ML algorithms, k-nearest neighbor (KNN), radial basis function (RBF) and support vector machine with linear and RBF kernels, in order to classify data into two physiological states of the driver, highly stressed or normal. The SVM with RBF kernel was the model that presented the best results, with a correct prediction rate of 83.33% both with time and non-linear parameters, and 66.66% with frequency, poincare (a non-linear analysis) and STFT (a time-frequency analysis method) parameters [39]. One of the objectives of a study performed by Braga (2021) was to evaluate the effectiveness of machine learning methods to discriminate Fabry disease (FD) patients with white matter lesions (WMLs) from Fabry disease patients without white matter lesions based on ECG data. For this, Braga (2021) used 48 Fabry disease patients, where 23 have WMLs and 25 do not have WMLs. After performing two feature selection methods, one being a filter method that selected the 10 most significant features not correlated (using Mann Whitney U Test and a |ρ|<0.80) and the other recursive feature elimination (RFE), Braga 19 (2021) ended up with 4 electrocardiogram features, which were heart rate mean and maximum, QT maximum, and SDANN 5. Using these 4 features and SDANN 5 feature alone, five classification algorithms, logistic regression (LR), SVM linear Kernel, SVM RBF kernel, random forest (RF), and k-nearest neighbors (KNN), were applied, in order to identify the optimal combination of features and the classification model with the best performance. In the case of the 4-feature combination, the model that gave the highest validation accuracy, 79.72%±1.40%, was RF, followed by KNN with a validation accuracy equal to 77.75%±1.57%. However, using only the SDANN 5 feature, the model that gave the highest validation accuracy was SVM linear kernel with 74.53%±0.67%, followed by LR with 74.52%±0.72%. To note that to evaluate the models’ performance a 5-fold cross validation was used [32]. All these studies are examples of the medical diagnosis power of machine learning, in this case, more specifically, when it is applied to ECG data, since they show several machine learning algorithms that lead to high classification performances (most above 70%). 20 Part II : Materials and Methods 21 Chapter 4 Study data This chapter introduces the sample of individuals included in this study and some of their demographic characteristics. The evaluated variables and their normal reference range of values according to age and/or sex are also presented in this chapter. 4.1 Study Sample The study sample included Fabry disease (FD) patients and Sarcomeric Hypertrophic cardiomyopathy (HCM) patients from the Cardiology and Neurology Departments of Hospital Senhora da Oliveira in Guimarães city, Portugal. This study retrospectively enrolled 114 patients with FD (GLA gene mutation c.337T>C (p.F113L)), in which 61 (53.51%) have WMLs and 53 (46.49%) do not, and also 39 patients with Sarcomeric HCM. The patients’ ages range between 19-91 years inclusive (Table 1). While the percentages of females in the FD with WMLs group and the FD without WMLs are 62,3% and 60,4% respectively, in the HCM group it is only 33,3%. 22 Table 1: Demographic characteristics of the study sample HCM (n=39) FD with WMLs (n=61) FD without WMLs (n=53) Sex (Female number) 13 38 32 Age ([Minimum, Maximum] years) [21, 87] [20, 91] [19, 71] Since Holter variable measures vary across age and sex [41] and age is the strongest known risk factor for the onset of WMLs [42] [43], the patients were subgrouped into three age classes: age 19-39 years, age 40-59 years, and age > 59 years (Table 2). The number of FD patients with WMLs and HCM patients in age class 19–39 years is very low, with 8 and 4 patients, respectively. Thus, this age class was not included in this study. Furthermore, as there are only 3 FD patients without WMLs older than 59 years, this subgroup of patients was also excluded. Table 2: Patients count per group and age class Age Class HCM FD with WMLs FD without WMLs Patients (Females) Patients (Females) Patients (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-Hour Holter As mentioned in Section 3.1, an Electrocardiogram (ECG) is an exam that records the potential changes at skin surface that result from the depolarization and repolarization of the heart muscle, thus, allowing the identification and location of pathologies. Therefore, a single ECG or a recording over time (24 to 48 hours) achieved by a Holter monitor, are powerful exams since they can detect many cardiac abnormalities [23] [27]. 23 variances. Welch test has the advantage of keeping type I error rate despite heteroscedastic variances [51] [52] [53]. • Null hypothesis (H0): All group means in the population are equal. • Alternative hypothesis (H1): At least one group mean in the population differs from the others. To apply the Welch-ANOVA test, a function from the pingouin library [47], the welch_anova() function, was used. And, as explained, this test was applied to the variables that have a normal distribution (evaluated previously by Shapiro test) but do not have homogeneity of variances (evaluated by Levene’s test) . Kruskal-Wallis Test The Kruskal-Wallis test is the nonparametric equivalent of the one-way ANOVA and so it is used to determine whether more than two independent samples have a different distribution [51]. • Null hypothesis (H0): Population median of all groups are equal. • Alternative hypothesis (H1): Population median of all groups are not equal. The rejection of the null hypothesis (significant test) and therefore the acceptance of the alternative hypothesis, means that at least one of the samples is different from the other samples. Like in one-way ANOVA, Kruskal-Wallis also does not identify where the difference occurs neither how many occur. We do not reject the null hypothesis when the test is non-significant and, so, we conclude that all sample distributions are equal. Since this test is the nonparametric equivalent of the one-way ANOVA test, it was only performed on the variables which were not normally distributed (evaluated previously by Shapiro-Wilk test). One more time, the test statistic and p-value were obtained, but this time with the kruskal() function from the scipy.stats module [45]. 30 Unpaired t-test The unpaired t-test is also known as independent t-test and it is a statistical hypothesis test used to test whether the means of two groups are equal, when there is two independent (unrelated) groups and one numerical or ordinal variable of interest. This test makes some assumptions, such as that the variable of interest is normally distributed in each group and that there is homogeneity of variances (the variances of the two groups are equal) [49] [51]. • Null hypothesis (H0): The population means in the two groups are equal. • Alternative hypothesis (H1): The population means in the two groups are not equal. So, when we reject the null hypothesis (significant test, with p < 0.05) that indicates that there is sufficient evidence that the population means in the two groups are different, and so, the distributions are not equal. However, if we do not reject the null hypothesis, (non-significant test, with p > 0.05) then it indicates that the population means in the two groups are equal. The Python function used for this test was ttest_ind() from the statsmodels library [46], stats.weightstats module. Due to test assumptions, this function was only applied to the variables that presented a normal distribution (verified by Shapiro-Wilk test) and homogeneity of variances (verified by Levene’s test). Mann Whitney U Test The Mann-Whitney is the non-parametric equivalent to the unpaired t-test. This test was named for Henry Mann and Donald Whitney, although it is sometimes called the Wilcoxon-Mann-Whitney test, from Frank Wilcoxon, who also developed a variation of the test or Wilcoxon’s rank sum test. This test is a statistical significance test used to determine whether two independent samples were drawn from a population with the same distribution [49] [51]. • Null hypothesis (H0): Sample distributions are equal. • Alternative hypothesis (H1): Sample distributions are not equal. So, if we do not reject the null hypothesis (p > 0.05) it means that both samples were drawn from a population with the same distribution. On the other hand, we conclude that sample distributions are not 31 equal when we reject the null hypothesis and that happens when the test is significant (p < 0.05). This test was applied through the mannwhitneyu() function from the stats module of the scipy library [45]. Since this test is the non-parametric equivalent to the unpaired t-test, it was only applied to those variables which were not normally distributed (evaluated previously by the Shapiro-Wilk test). Post Hoc Tests Post hoc tests, also referred to as a posteriori or unplanned tests, or even multiple comparison tests, are statistical tests that are applied after a significant F test. As explained, the previous tests, i.e, one-way ANOVA, Welch ANOVA and Kruskal-Wallis only indicate that there is a significant means difference between the groups, they do not indicate in which groups pair or pairs that difference occurs. To overcome this, post hoc tests allow comparisons between a pair of group means in order to specify which of the pairs of means are statistically significantly different from each other. This is almost similar to taking every pair of groups and performing a t-test on each pair, however, pairwise comparisons have an advantage, they control the familywise error by correcting the level of significance for each test, so that the overall Type I error rate across all comparisons remains at 0.05 [50] [54] [55]. The Tukey test uses pairwise post hoc testing to determine which of three or more sample means are significantly different after obtaining a significant ANOVA F-test. Thus, this test is an ANOVA post hoc test, which is usually known as Tukey’s HSD (Honestly Significant Difference), however, the Tukey HSD is only used when the samples sizes for the groups are equal. This test was modified by Kramer, so that it could be used in cases where the samples sizes of the groups are not equal and it is called the Tukey-Kramer method [56] [57] [58]. Then, this test was only applied on the variables that gave a significant one-way ANOVA, through the pairwise_tukey() function from the pingouin library [47]. This function applies the pairwise Tukey HSD post hoc test, however, if the samples sizes are not equal, it automatically uses the Tukey-Kramer method. The Games-Howell test is an extension of the Tukey-Kramer test and is appropriate in cases with unequal variances as well as unequal sample sizes. The test controls the type I error for the whole comparison and also maintains the default significance level even when the size of the sample is different. However, this test may be too liberal for small sample sizes and therefore should only be used in sample sizes greater than five [56] [59]. Since this test is indicated for cases with unequal variances, Games32 Howell is the post hoc test of Welch ANOVA, and, therefore, is applied only in the variables that had a significant result in Welch ANOVA test. The Python function used for this test was pairwise_gameshowell() from the pingouin library [47]. There is also Dunn’s test which is a post hoc pairwise test for multiple comparisons of mean rank sums. This test is the appropriate procedure after a significant Kruskal-Wallis test [60]. For Dunn’s test, the Python function used was posthoc_dunn() from the scikit-posthocs package [40]. 5.2.4 Differences between independent samples: qualitative data Chi-Squared Test Chi-squared test, also known as Pearson’s Chi-squared test, named for Karl Pearson, is a statistical hypothesis test to determine whether there is a relationship between two categorical variables (factors), more specifically, whether the proportions of individuals who possess a certain characteristic are the same in the independent groups. This data can be represented in a r x c contingency table, with r rows and c columns, in which for each cell we calculate the expected frequencies, then, determine whether the division of the groups, called the observed frequencies, matches the expected frequencies. The result is a test statistic that has a Chi-Squared distribution, denominated for the Greek lowercase letter chi (χ) [49] [50] [51]. • Null hypothesis (H0): There is no association between the categories of one factor and the categories of the other factor in the population. • Alternative hypothesis (H1): The two factors are associated in the population. So, if the test is significant (p < 0.05) we should reject the null hypothesis and accept the alternative one, that the two factors are associated in the population. On the other hand, if the test is non-significant (p > 0.05), we should not reject the null hypothesis, so, there is no association between the categories of one factor and the categories of the other factor in the population, that is, they are independent. 33 The Python function used for Chi-Squared test was chi2_contingency() from the scipy library [45], stats module. This function was applied to determine whether there was a relationship between Sex (Female or Male) and group, after the acquisition of the 3x2 contingency table with these proportions. Fisher’s Exact test Fisher’s exact test is normally used when there are two independent groups and we are interested in whether the proportions of individuals who have a characteristic are the same in both groups. This test should be applied in small samples (where the expected frequencies are small) since it was designed to overcome a problem with these samples which is that the sampling distribution of the chi-square statistic differ substantially from a chi-square distribution. In fact, Fisher’s exact test is mostly a way of computing the exact probability of the chi-square statistic, instead of a test [49] [50]. This test can also be used as post hoc test by applying a 2x2 Fisher’s exact test to each of the pairwise comparisons, but then correct for multiple comparisons using for example the Bonferroni correction (used to control the familywise error rate) [58]. • Null hypothesis (H0): the proportions of individuals with the characteristic are equal in the two groups in the population. • Alternative hypothesis (H1): these population proportions are not equal. Identically to other hypothesis tests, when the Fisher’s exact test is non-significant (p > 0.05), we must not reject the null hypothesis, and in this case that means that the proportions of individuals with the characteristic are equal in the two groups in the population. On the other hand, if the test is significant (p < 0.05) we should reject the null hypothesis and accept the alternative one, which indicates that these population proportions are not equal. This test was applied to evaluate whether the proportions of female and male individuals (sex variable) are the same in two groups. That way, the Python function fisher_exact() from the scipy librabry [45], stats module was used, after obtaining the 2x2 contingency table. When used as post hoc test, the function multipletests() from statsmodel librabry, stats.multitest module, was also applied. This function takes the pvalues obtained in the Fisher’s exact test as argument and, the “method” argument equal to “bonferroni”. 34 5.3 Logistic Regression Analysis Logistic regression is used when the outcome/dependent variable (Y) is categorical and there is one or more predictor/explanatory/independent variables (X) that are continuous or categorical. When the outcome variable has only two possible categorical outcomes, this regression is known as binary logistic regression. When we analyze the relationship between one independent variable and one dependent variable, we often call it univariate analysis. When we analyze the relationship between two or more independent variables and one outcome variable (dependent) we call it a multivariable analysis. In the case of relationships of several predictors with two or more outcome/dependent variables at the same time, it is called a multivariate analysis [49] [50] [61] [62]. The function used to express the relationship between the predictor variables and the binary outcome variable is the logistic, this is why it is called logistic regression. The logistic regression equation enables the determination of which explanatory variables influence the outcome and, using an individual´s values of the explanatory variables, evaluate the probability that the individual will have a particular outcome. A multivariable logistic regression model (two or more explanatory variables) is expressed as [49] [50] [61]: logit(p) = a+b1x1+b2x2+... +bkxk(5.1) Where, logit(p) = ln p 1−p(5.2) In these equations: • xiis the ith explanatory variable (i=1,2,3,...,k); •pis a binomial proportion; •ais the estimated constant term; •b1,b2, . . . , bkare the estimated logistic regression coefficients. 35 In a logistic regression model, the odds ratio (OR) is a measure of association between an explanatory variable and the outcome. The OR represents the odds that an outcome will occur given a particular explanatory variable, compared to the odds of the outcome occurring in the absence of that predictor variable. The OR is obtained by the exponential of a coefficient. For example, exp(b1) is the estimated odds of an outcome for (x1+ 1) relative to the estimated odds of an outcome for x1, while adjusting for all other x’s in the equation. Therefore, using the exp(b1) example, it means that when there is a one unit change in the x1and the other explanatory variables are held constant, the odds of Y = 1 change by exp(b1) units. When the odds ratio value is above one this indicates an increased odds of having the outcome linked to Y= 1, on the other hand, if the odds ratio value is below one, then it indicates a decreased odds of having the outcome linked to Y= 1, as the particular explanatory variable increases by one unit [49] [61]. It is possible to obtain a Wald test statistic for each explanatory variable [49]: • Null hypothesis (H0): The relevant logistic regression coefficient is zero. • Alternative hypothesis (H1): The relevant logistic regression coefficient is different from zero. It is also possible to evaluate all explanatory variables and their effect on the outcome, for example with chi-square for covariates [49]: • Null hypothesis (H0): All the logistic regression coefficients in the model are zero. • Alternative hypothesis (H1): At least one logistic regression coefficient is different from zero. For each Holter variable, a univariate logistic regression analysis, assuming the Holter variable as the exploratory variable and the presence of one of the diseases as the outcome, was performed, using the Logit() function from the statsmodels library [46], discrete.discrete_model module. As the association of a Holter variable with the presence of a disease could be affected by Sex and Age differences [63] [64], for each Holter variable, two multivariable logistic regression analyses were also performed: 1) Age and Holter variable as explanatory variables; and 2) Sex and Holter variable as explanatory variables. These logistic regression models have also been applied through the Logit() function. 36 Chapter 6 The implemented Machine Learning methods This chapter incorporates a description of the different steps that were applied to our data in order to achieve the final classification machine learning models. The main steps are presented in the flowchart of Figure 1. As can be seen, the methodology is divided into two different phases: feature selection and classification. Figure 1: Methodology machine learning-based flowchart. 37 First, data were submitted to a filter supervised feature selection method. The goal was to determine if there was any multicollinearity between the independent variables in this study. This was done by determining the variance inflation factor (VIF) values and the highly correlated variables (which have a great VIF value) were excluded from the set through a stepwise procedure. Then, for each of the 3 machine learning algorithms (logistic regression (LR), support vector machines with linear kernel (linear SVM), and random forest (RF)), the hyperparameters values/status that adjusted better to the data (higher accuracy), were discovered. This is called hyperparameter tuning and was done with a grid search strategy using the standardized data to train the models and leave-one-out crossvalidation (LOOCV) to evaluate the performance of the models. After the hyperparameters tuning each of the improved models was used in a second feature selection method. This time a wrapper feature selection method was performed, the recursive feature elimination (RFE), to discover which number and combination of features lead to better classification performances. The just described procedures are part of the feature selection phase. Now that features are selected, the classification phase takes place. Each of the feature combinations was used to train 5 different machine learning models: logistic regression (LR), SVM with linear kernel (linear SVM), SVM with radial basis function (RBF) kernel (RBF SVM), random forest (RF), and k-nearest neighbors (KNN). Since the data that is used in these models is not the original data, the hyperparameters tuning procedure, described previously, is also applied in the classification phase. This way, the final classification models are achieved. The described methodology is applied to three distinct binary classification problems. In one problem the classes indicate whether an FD patient has WMLs (class 1) or not (class 0), the other whether a patient has FD with WMLs (class 1) or has HCM (class 0), and the last, whether a patient has FD without WMLs (class 1) or has HCM (class 0). 38 6.1 Cross-validation When we are building a machine learning model, we are interested in evaluating its performance, mainly, in discovering how well the model performs on unseen data. Overfitting is the most common problem in applied machine learning and it leads to models with poor performance. Overfitting happens when a model is too adjusted to the training data, that is, when the model actually learns too much of the detail and noise of the training data. This results in a model with poor performance because the model interprets the learned noise as concepts and, with new data, these concepts do not exist, so, the model’s performance on the new data is negatively affected. This is a huge problem because this is the performance that we are most interested in, not the training performance [65] [66]. To overcome this problem we can use cross-validation to estimate the model’s performance on unseen data. In cross-validation, the training dataset is split into train set and validation set, in different ways (different observations in each set, each time) using some strategy and then, multiple iterations of each model on these different splits are built [65] [66]. There are several cross-validation strategies that differ only in the way that the initial train set is divided into the train set and validation set. In this study leave-one-out cross-validation (LOOCV) is the used strategy since several studies defend its use to evaluate the performance of a classification model when the sample size is small, which is our case. In LOOCV, the validation set includes only an observation (in our case, a patient), and the remaining observations, n-1 (being n the sample size), are part of the train set, thus, this strategy performs n iterations of each model [65] [66] [67] [68]. The scikit-learn [40] library has a LeaveOneOut class that was used in this study to apply the leaveone-out cross-validation. As previously mentioned, this cross-validation strategy is incorporated in the hyperparameter tuning process, which will now be explained. 39 specific, this output variable is categorical, in fact, is dichotomous, since it is either having or not having a condition/disease. So, as explained, this is a classification problem, and, therefore, the models applied to our data are logistic regression, support vector machine, random forest, and also K-nearest neighbors. 6.4.1 Logistic Regression Logistic regression was already described in Section 5.3 where it was used to express the relationship between the predictor variables and the binary outcome variable. This time we are using logistic regression as a predictive model. However, the logistic regression function is the same in both situations, the only difference is that when using logistic regression as a predictive model, we want to calculate the probability of the default class (the first class), and, therefore, we use Equation 6.2, which is equivalent to Equation 5.2 (introduced in Section 5.3) [65] [66]. p(x) = ea+b1x1+b2x2+...+bkxk 1 + ea+b1x1+b2x2+...+bkxk (6.2) The logistic regression coefficients (b1,b2, ..., bk) are estimated from the training data using maximumlikelihood estimation (common learning algorithm). After estimating these coefficients, they are used in the equation, as well as the input vector x (x1,x2, ..., xk), to calculate the probability (p(x)) [65] [66]. Then, the probability prediction is transformed into a binary value/ class (0 or 1) [65] [66]: prediction =     0,if p(x)<0.5 1,if p(x)≥0.5 (6.3) It is important to notice that, when there are highly correlated inputs, the likelihood estimation process can fail to converge and the logistic regression model can overfit. Therefore, it is important to remove highly correlated inputs before applying the logistic regression [65] [66]. In this study, the logistic regression model was created using the LogisticRegression scikit-learn’s class [40]. 46 6.4.2 Support Vector Machines The support vector machine (SVM) model is a supervised machine learning algorithm that finds a hyperplane, in a multidimensional space, that is able to separate the training data by labels/class. For example, if we have two known labels and two input variables (features), then, this forms a two-dimensional space. In this case, the selected hyperplane, to separate the points in the space by their class, is a line. The perpendicular distance between the line and the closest points is known as the margin. The maximalmargin hyperplane is the name given to the optimal hyperplane, the one that separates the classes with the largest margin. The closest points are, in fact, the only relevant points to define the hyperplane and to construct the classifier. These points are called the support vectors. Figure 2 illustrates a possible two-dimensional space situation with the respective hyperplane, support vectors, and margin [65] [73]. After discovering the hyperplane, the equation that defines it can be used to make predictions, by inserting the input values into the equation. The label of the new input variable is indicated by whether the point is above or below the hyperplane (easier to understand when the hyperplane is a line) [65] [73]. Figure 2: Example of support machine classification results [73]. However, the maximal-margin classifier is a hypothetical classifier, since real data may not be perfectly 47 separated by a hyperplane. So, in real situations, the margin is not maximized, and some points of the training data are allowed to violate the separating line. The amount of violation of the margin that is allowed is defined by the parameter C, being that larger C values indicate that more violations of the hyperplane are allowed. Thus, C parameter also influences the number of support vectors used by the model [65] [73]. In practice, the SVM algorithm is implemented using a kernel. This kernel can be linear, polynomial or radial. In this study, linear and radial kernels were used. The linear kernel uses the dot-product and defines the similarity between new data and the support vectors. The radial kernel can create complex regions and, for this kernel, a gamma parameter should be specified to the algorithm [65] [73]. We obtained SVM classifier using the SVC class from scikit-learn library [40] and set the kernel parameter to “linear” or “rbf” according to the desired model. 6.4.3 Random Forest Random Forest is an ensemble method based on bagging (bootstrap aggregating) where independent classification or regression un-pruned decision trees are aggregated (using majority vote for classification or averaging for regression) to produce a more accurate classification [65] [74] [75]. Therefore, first, let’s understand what are decision trees and how they work. Decision trees, or CART (classification and regression trees), as indicated by the name, are inspired in the ordinary tree structure, which is composed of a root and nodes (the positions where the branches divide), branches, and leaves. Similarly, a decision tree is formed from nodes that are represented by circles and the branches that are represented by the segments that connect the nodes. The decision tree starts in the root node, moves downward and ends in the leaf node and normally is drawn from left to right. Each internal node (a node that is not a leaf node) can have two or more branches. A node represents a certain characteristic and the branches represent a range of values. The described decision tree structure can be observed in Figure 3 [65] [74] [75]. 48 Figure 3: Decision tree structure [76]. Predictions can be made by visiting the tree and performing the tests included in the root and internal nodes, and, when a leaf node is reached, the predicted label corresponds to the reported class [65] [74] [75]. To build a decision tree, a greedy approach (the very best split point is chosen in each time) is used to divide the input space, called recursive binary splitting. In this procedure all the values are lined up and then, using a cost function, different split points are tried and tested. The split that presents the lowest cost is the chosen one. For classifications problems, the cost function used is the Gini, which indicates how pure the leaf nodes are. Gini cost (G) is calculated as shown in Equation 6.4, where ˆpkis the faction of training instances with class K in the rectangle of interest [65] [74] [75]. G= n X k=1 ˆpk(1 −ˆpk)(6.4) Thus, a node that has all the training instances of the same class (perfect class purity), has a G = 0. On the other hand, G reaches its maximum value (G = 0.5) when there is a 50-50 split of classes (ˆpk=1 2) [65] [74] [75]. The recursive binary splitting requires a stopping procedure to know when it should stop splitting. This stopping procedure can be limiting the minimum level of impurity to split a node or the minimum number of samples per node. In the second procedure, if the count of training instances is less than the minimum, then, the split is not accepted and the respective node is taken as a final leaf node [65] [74] [75]. However, rigorous stopping criteria can lead to underfitting trees. To solve this problem, pruning 49 criteria is used instead. So, better performances can be achieved by training an unrestricted tree and then pruning it using for that, for example, the weakest link pruning procedure on which a learning parameter (alpha) is used to weigh whether nodes can be removed based on the size of the sub-tree [65] [74] [75]. Although decision trees present desirable properties and success, their discrete nature involves high variance in predictions. As previously explained, random forest is an ensemble method, and these type of methods allow the construction of models that produce better predictions by aggregating the predictions of a set of individual classifiers. Random forest is based on bagging which is a procedure that reduces the variance for algorithms that have high variance, like decision trees [65] [74] [75]. As previously explained, decision trees are greedy. When dealing with multiple decision trees, these trees can have structural similarities and, so, highly correlated predictions. The ensemble methods are more accurate if the predictions from the sub-trees are weakly correlated, ideally, uncorrelated. Thus, in random forest, the sub-trees learn in a way that their predictions have less correlation. In decision trees (or CART) the learning algorithm, when selecting a split point, is allowed to look to all variables and all their values to select the most optimal split-point. However, in random forest, the learning algorithm search is limited to a random sample of features. The number of features that can be searched at each split point must be specified as a parameter to the algorithm [65] [74] [75]. In Python, random forest model was implemented through the RandomForestClassifier class, from the scikit-learn library [40]. 6.4.4 K-Nearest Neighbors In the K-nearest neighbors (KNN) algorithm, no learning is in fact necessary, all the procedure of KNN is made when a prediction is required. The only model in KNN is storing the entire training dataset. So, KNN stores the training dataset and makes a prediction for a new data point by searching, in the entire dataset, for the K most similar instances, called the neighbors. A distance measure is used to find out which K instances, in the training dataset, are most similar to the new input. Euclidean distance is the most common distance measure for real-valued input variables and it is the measure used in this study. However, there are other distance measures like Hamming distance and Manhattan distance [65]. 50 The Euclidean distance is calculated as the square root of the sum of the squared differences between a point a and point b across all input attributes i, as presented in Equation 6.5 [65]. EuclideanDistance(a, b) = v u u t n X i=1 (ai−bi)2(6.5) For classification problems, the class of the new input point can be predicted by determining, from among the K most similar instances, the class with higher frequency. Thus, for a new input instance, we determine the K most similar instances and, then, for this set, we calculate the normalized frequency of samples that belong to each class, as exemplified in Equation 6.6 [65]. p(class = 0) = count(class = 0) count(class = 0) + count(class = 1) (6.6) This algorithm is more indicated for lower dimensional data, so it can benefit from feature selection to reduce the dimensions of the input feature space [65]. The KNN version for classification problems was achieved with the KNeighborsClassifier() class from the scikit-learn library [40]. 6.5 Performance Metrics To evaluate a model’s performance some performance metrics are measured in the validation phase, such as accuracy, sensitivity, specificity, and area under curve (AUC). To better comprehend these metrics, first, we should understand what is a confusion matrix. So, a confusion matrix is not a metric but is a way to evaluate a classification model since its representation can be used to delineate several metrics. This representation is obtained by comparing the predicted labels, that were given by the classifier, with the true labels, that are already known. A typical confusion matrix for a binary classification problem is presented in Figure 4, where p designates the positive class and n designates the negative class and where the columns represent the predicted labels and the rows the true labels. To note that the confusion matrix can also be represented with the predicted labels in the rows and 51 the true labels in the columns. As can be seen, the comparison between predicted and true labels leads to four different terms: true negative, false negative, false positive, and, true positive [66]. • True Positive (TP): Total counts of when the true label is positive and the predicted label is positive. • True Negative (TN): Total counts of when the true label is negative and the predicted label is negative. • False Positive (FP): Total counts of when the true label is negative and the predicted label is positive. • False Negative (FN): Total counts of when the true label is positive and the predicted label is negative. Figure 4: Confusion Matrix structure [66]. Thus, from the confusion matrix, it is possible to obtain the desired metrics. First, the accuracy, this metric is one of the most popular to evaluate a classifier performance and it is defined as the proportion of correct predictions of the model, since, as illustrated in Equation 6.7, it is the number of correct predictions (true) over the total amount of predictions (equal to the sample size) [66]. Accuracy =T P +TN TP +TN +F P +F N (6.7) Sensitivity, also known as recall, is a measure to identify the percentage of relevant data points. Sensitivity is calculated as presented in Equation 6.8 and it is defined as the number of cases of the positive class that were correctly predicted [66]. 52 Sensitivity =T P TP +FN (6.8) Specificity, in turn, is defined as the number of cases of the negative class that were correctly predicted and is measured as presented in Equation 6.9 [77]. Specificity =TN FP +TN (6.9) The receiver operating characteristic (ROC) curve is also an important visual tool to interpret classification models that is obtained by plotting the true positive rate (TPR), which is equal to sensitivity, versus the false positive rate (FPR), which is equal to 1 - specificity. So, each prediction result, obtained from the confusion matrix, takes one point in the ROC space, which is between (0,0) and (1,1). An illustration of a ROC curve is presented in Figure 5. In this figure, we can see a diagonal line, which corresponds to the ROC curve of a classifier that does a random guess. An ideal model would result in a ROC curve at the (0,1) point, however, this is not realistic, so, as close is the ROC curve to this point, which is situated in the top left corner of the graph, the better is the classifier [66] [77]. Figure 5: Example of ROC curve and AUC [78]. In order to compare models, a metric is calculated from the ROC curve, which is called area under curve (AUC). The ROC curve illustrated in Figure 5 has the respective area under curve, which is the graycolored area. This metric can be calculated by integrating the areas under the steps of the ROC curve. So, if ROC curve is obtained by connecting the points {(x1,y1), (x2,y2), ..., (xm,ym)}, where x1= 0 and 53 xm= 1, then, AUC is estimated as presented in Equation 6.10. Since this metric represents the area under the ROC curve, its value will always be between 0 and 1. An ideal classifier would result in a unit AUC value, and, due to the diagonal ROC curve, a realistic classifier has an AUC value above 0.5 (area under the diagonal). Thus, with the AUC it is possible to compare models, and generally, the best model is the one that presents the higher AUC value [66] [77]. AUC =1 2 m−1 X i=1 (xi+1 −xi)·(yi+yi+1)(6.10) In this study, these metrics (accuracy, sensitivity, specificity, and AUC) were calculated during the hyperparameter tuning process to enable the selection of the best hyperparameter value/status, however, the decision relied on the accuracy, and, in case of ties, on the AUC. These performance metrics were obtained, in Python and using scikit-learn [40], in different ways. The accuracy was obtained by accessing the mean of the validation results produced by the accuracy_score() function. The AUC was obtained applying the auc() function to the FPR and TPR values given by the roc_curve() function. As for the sensitivity and specificity, first, the TP, TN, FP, and FN values were obtained for each cross-validation iteration by comparing the true and predicted labels, and then, these two metrics were determined using the formulas previously presented in Equation 6.8 and 6.9, respectively. 54 Part III : Results, Discussion, Conclusion, and Future Work 55 Table 8: Statistically significant logistic regression results of HCM and FD with WMLs groups Variables Univariate logistic regression Multivariable logistic regression - Adjusted to age Multivariable logistic regression - Adjusted to sex OR (95% C.I) p-value OR (95% C.I) p-value OR (95% C.I) p-value 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: Statistically significant logistic regression Results of FD without WMLs and FD with WMLs groups Variables Univariate logistic regression Multivariable logistic regression - Adjusted to age Multivariable logistic regression - Adjusted to sex OR (95% C.I) p-value OR (95% C.I) p-value OR (95% C.I) p-value 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 Results from patients aged 40 to 59 years (inclusive) The descriptive results of each Holter variable per group (HCM, FD with WMLs and FD Without WMLs) and comparative results, for this age class, are presented in Table 10. Once again, data with a normal distribution is presented as mean ±standard deviation and data with a non-normal distribution is presented as median (quartile 1 - quartile 3). The normality and the homogeneity of variance test results can be consulted in Table 26 of Appendix A. We can see that, in contrast to the results obtained from the patients over 18 years old, for this subgroup of patients, sex and age variables were not significantly different between groups (p > 0.0601). However, group differences were found in some of the Holter variables, such as, HR Min, HR Mean, SDANN 5, SDNN, QT Mean, QT Max and, QTc > 450 (p < 0.0414). In the patients aged 40 to 59 years (inclusive), HCM patients presented higher QT Mean and QT Max compared with FD patients, both with and without WMLs (p < 0.0048) and also a higher QTc > 450 compared to FD with WMLs patients (p = 0.0131). The FD without WMLs patients presented a lower SDNN compared with HCM and FD with WMLs patients (p < 0.0171). The SDANN 5 variable means in the FD with WMLs and FD without WMLs groups were different (p = 0.0117), with a lower value in the FD patients without WMLs. Two differences between the HCM and FD without WMLs groups were found, in the HR Min and HR Max variables (p < 0.0059), which were both higher in the FD without WMLs patients. 64 Table 10: Variables summary and comparison of means/medians between HCM, FD with WMLs and FD without WMLs patients aged 40 to 59 (inclusive) Variable HCM (n=16) FD w/ WMLs (n=23) FD w/o WMLs (n=25) P-Value -All groups HCM vs FD w/ WMLs HCM vs FD w/o WMLs FD w/ WMLs vs FD w/o WMLs Sex (Female number (%)) 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 fp = 0.0094 fp = 0.0171 f 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 fp = 0.0007 fp = 0.5520 f QT Max 525.50 (491.75 - 633.25) 462.13 ±40.12 455.00 (424.00 - 489.00) p = 0.0016 dp = 0.0011 fp = 0.0017 fp = 0.8424 f 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 fp = 0.0633 fp = 0.4607 f Longest R-R 1.80 (1.40 - 2.33) 1.50 (1.35 - 1.75) 1.50 (1.30 - 1.60) p = 0.1504 d- - - If data have a normal distribution, they are represented as mean ±standard deviation. In case of a non-normal distribution they are represented as median (quartile1 −quartile3). In every comparison of means test αwas considered 0.05. aChi-Squared Test bOne-Way ANOVA Test. cWelch - ANOVA Test. dKruskal-Wallis H Test. eTukey HSD Test as Post hoc. fDunn’s Test as Post hoc. 65 Similar to what was presented for patients aged above 18 years old, in Tables 11, 12 and, 13 are the binary logistic results that were significantly associated with group classification (HCM vs FD without WMLs, HCM vs FD with WMLs, and FD without WMLs vs FD with WMLs) of the patients aged 40 to 59 years. The results that were not significantly associated are presented in Tables 27, 28 and 29 of Appendix A. Table 11 is relative to the following two outcomes: having HCM (Y = 0) or having FD without WMLs (Y = 1) logistic regression results. We can see that 6 out of 15 Holter variables were significantly associated with group membership, which were, HR Min, HR Mean, ASDNN 5, SDNN, QT Mean and QT Max (p < 0.0425). When the model was adjusted to age, this variable was statistically significant only in the model with SDNN as Holter variable, and, in turn, this variable remained significantly associated with group membership (p = 0.0134). Only two other Holter variables remained significantly associated with group membership when adjusted to age, HR Min and QT Mean variables (p < 0.0297). When adjusted to sex, this variable was not significant in all models and the 6 Holter variables remained significantly associated with group membership (p < 0.0389). From these results we can see that a higher HR Min and HR Mean lead to higher odds of having FD without WMLs rather than HCM (OR ≥1.10, 1.02 ≤95% CI ≤1.30), on the other hand, an increase in ASDNN 5, SDNN, QT Mean and QT Max lead to decreased odds of having FD without WMLs (OR ≤0.99, 0.92 ≤95% CI ≤1.00). Six variables, HR Mean, QT Mean, QT Max, QTc Mean, QTc Max and QTc > 450, were significantly associated with group membership (p < 0.0331) when the two possible outcomes were: having HCM (Y = 0) or having FD with WMLs (Y = 1), as can be seen in Table 12. In the models adjusted to age and to sex, both variables were not significant in all models and only one Holter variable was no longer significant, which was HR Mean variable when adjusted to age (p = 0.0602). Only the increase of the HR Mean variable leads to increased odds of having FD with WMLs rather than HCM (OR = 1.11, 95% CI= 1.01 - 1.21), when the remaining 5 Holter variables of QT analysis (QT Mean, QT Max, QTc Mean, QTc Max and QTc > 450) increase the odds of having FD with WMLs decrease (OR ≤0.99, 0.93 ≤95% CI ≤1.00). The results for when the dependent variable has the outcomes: having FD without WMLs (Y = 0) or having FD with WMLs (Y = 1), are presented in Table 13. In this case, only 2 out of 15 Holter variables were significantly associated with group membership, SDANN 5 and SDNN (p < 0.0130), and these variables remained significant when the model was adjusted both to age and sex (which were not significant in all 66 models). A higher heart rate variability (SDNN and SDANN 5 values) lead to higher odds of having WMLs within FD patients (OR = 1.03, 95% CI = 1.01 - 1.06 for SDNN and OR = 1.04, 95% CI = 1.01 – 1.07 for SDANN5). Table 11: Statistically significant logistic regression results of HCM and FD without WMLs patients aged 40 to 59 (inclusive) Variables Univariate logistic regression Multivariable logistic regression - Adjusted to age Multivariable logistic regression - Adjusted to sex OR (95% C.I) p-value OR (95% C.I) p-value OR (95% C.I) p-value 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: Statistically significant logistic regression results of HCM and FD with WMLs patients aged 40 to 59 (inclusive) Variables Univariate logistic regression Multivariable logistic regression - Adjusted to age Multivariable logistic regression - Adjusted to sex OR (95% C.I) p-value OR (95% C.I) p-value OR (95% C.I) p-value 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: Statistically significant logistic regression results of FD without WMLs and FD with WMLs patients aged 40 to 59 (inclusive) Variables Univariate logistic regression Multivariable logistic regression - Adjusted to age Multivariable logistic regression - Adjusted to sex OR (95% C.I) p-value OR (95% C.I) p-value OR (95% C.I) p-value SDANN 5 1.04 (1.01 - 1.07) 0.0080 1.05 (1.011.08) 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 Results from patients over 59 years old The variables summary and the comparison of means/medians between the two groups, for patients with age > 59 , are presented in Table 14. The normality and homogeneity of variances test results can be consulted in Table 30 of Appendix A. Group differences were found in the sex variable, HR Min, HR Mean and HR Max Holter variables (p < 0.0421) which were higher in the FD patients with WMLs. In contrast, QT Min and QT Mean Holter variables (p < 0.0182) were lower in these patients. The logistic regression analysis results to predict group membership are displayed in Table 15 for results that were significantly associated and in Table 31 of Appendix A for results that were not associated. In Table 15 we can see that 4 Holter variables were significantly associated with group classification, HR Min, HR Mean, QT Min and QT Mean (p < 0.0444). When the model was adjusted to age, this variable was not significantly associated with group membership and all 4 Holter variables remained associated (p < 0.0402). However, when adjusted to sex, only two Holter variables remained significantly associated, which were HR Mean and QT Min (p < 0.0422), and the sex variable was not associated. Therefore, the higher the heart rate variables (HR Min and HR Mean values) are, the higher are the odds of having FD with WMLs instead of HCM (OR = 1.10, 95% CI = 1.00 - 1.20 for HR Min and OR = 1.09, 95% CI = 1.02 - 1.17 for HR Mean). The increase of either of the two QT analysis variables (QT Min and QT Mean), in contrast, leads to increased odds of having HCM rather than FD with WMLs (OR = 0.98, 95% CI = 0.96 - 0.99 for QT Min and OR = 0.98, 95% CI = 0.96 - 1.00 for QT Mean). 69 Table 14: Variables summary and comparison of means/medians for HCM and FD with WMLs patients aged above 59 Variable HCM (n=19) FD w/ WMLs (n=30) P-Value Sex (Female number (%)) 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 Longest R-R 1.70 (1.65 - 2.00) 1.60 (1.43 - 1.80) p = 0.0573 b If data have a normal distribution they are represented as mean ±standard deviation. In case of a non-normal distribution they are represented as median (quartile1 −quartile3). In every comparison of means test αis considered 0.05. aFisher’s Exact Test bMann Whitney U Test cStudent’s T-Test 70 Table 15: Statistically significant logistic regression results of HCM and FD with WMLs groups with ages above 59 Variables Univariate logistic regression Multivariable logistic regression - Adjusted to age Multivariable logistic regression - Adjusted to sex OR (95% C.I) p-value OR (95% C.I) p-value OR (95% C.I) p-value HR Min 1.10 (1.00 - 1.20) 0.0444 1.10 (1.00 - 1.21) 0.0402 1.08 (0.981.18) 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 Considering all patients (aged above 18 years) significant differences in age and sex between groups were found. FD patients with WMLs are older than FD patients without WMLs and HCM patients are also older than FD without WMLs patients (Table 6). The age difference found in FD with and without WMLs groups have also been identified in the study of Braga (2021) [32]. Galluzzi et al. [33] also identified that MCI patients with WMLs were older than the ones without WMLs. In fact, WMLs are quite common in the elderly general population [43] [79]. Several ECG characteristics give a significant association with the dependent variable (group class) in 71 selection method based in the VIF values is the same, since this was applied to all the patients aged between 40 and 59 years old. As for the hyperparameters values/status obtained in the hyperparameter tuning, these are different, of course, and can be consulted in Table 32 of Appendix B. The accuracy values obtained by these models at predicting if a patient has FD are displayed in Table 33, also in Appendix B. Applying the RFE method with logistic regression as classifier led to the results in Figure 7a, where the maximum accuracy value is 0.6923 for 5 features, being these features the HR Mean, RMSSD, QTc Min, QTc Max, and QTc > 450. Using linear SVM as classifier, the maximum accuracy value is also 0.6923, however, with this model, this maximum was obtained with 6 features, as shown in Figure 7b, which were HR Mean, HR Max, RMSSD, QTc Min, QTc Max, and QTc > 450. It is noticeable that these are the same 5 features selected by logistic regression plus HR Max feature. The results for when random forest algorithm is the classifier are in Figure 7c, in which the best accuracy is obtained using all features (9 features) and is equal to 0.7692. 78 (a) RFECV for logistic regression model. (b) RFECV for linear SVM model. (c) RFECV for random forest model. Figure 7: RFECV results for the different machine learning models of the HCM vs FD with WMLs patients aged 40 to 59 (inclusive). Considering that the 3 models that were wrapped by RFE gave three different combinations of features, these combinations were all applied to the classification stage, that is, applied to the 5 machine learning algorithms, just like what was done previously. The performance metrics obtained in each case are shown in Table 18. By analysing this table we see that the best model, in general, is using 6 features and KNN model, where an accuracy of 0.8461 and an AUC of 0.8370 are obtained. This accuracy value means that the model correctly predicted 33 patients in a total of 39 (number of HCM and FD with WMLs patients aged between 40 and 59). Also, the 6-feature combination seems to be the best combination to use to predict if a patient has FD (comparing with HCM patients), since it is the combination with the best classification performance metrics. The hyperparameters values/status of each of these machine learning models can be consulted in Table 35 of Appendix B. 79 Table 18: Models’s classification performance metrics per number of features for HCM and FD with WMLs patients aged 40 to 59 (inclusive) Number of features (Features) ML Model Metrics Accuracy Sensitivity Specificity AUC 5 features (HR Mean, RMSSD, QTc Min, QTc Max, and QTc > 450) LR 0.7179 0.9130 0.4375 0.7473 Linear 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 features (HR Mean, HR Max, RMSSD, QTc Min, QTc Max, and QTc > 450) LR 0.7179 0.8696 0.5000 0.7554 Linear 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 features (All) LR 0.6923 0.9130 0.3750 0.6902 Linear 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 learning; LR: logistic regression; SVM: support vector machine; RBF: radial basis function; RF: random forest; KNN: K-Nearest Neighbour The third prediction is to predict if a patient has WMLs using FD patients, with and without WMLs. For this prediction, since it was, once again, with patients aged between 40 and 59 (inclusive), we are dealing with 9 features (after the VIF step) which are HR Mean, HR Max, SDANN 5, RMSSD, QT Min, QTc Min, QTc Max, QTc > 450, and Longest R-R. Once again, the hyperparameters values/status of each machine learning model and the accuracy values obtained by these models at predicting the presence of WMLs, can be consulted in the Appendix B, Tables 32 and 33, respectively. These models were then wrapped by RFE method for a second feature selection. With logistic regres80 sion model, the best accuracy, 0.6667, was obtained with only one variable, as can be observed in Figure 8a, being this variable the SDANN 5 variable. With linear SVM as classifier, the RFE method identified that the best accuracy was 0.6875 and it was obtained with 2 features, as presented in Figure 8b, which were SDANN 5 and QTc Min features. However, with random forest model, the best accuracy, with a value equal to 0.8125, occurred with all the 9 variables, as shown in Figure 8c. (a) RFECV for logistic regression model. (b) RFECV for linear SVM model. (c) RFECV for random forest model. Figure 8: RFECV results for the different machine learning models of the FD with WMLs vs FD without WMLs patients aged 40 to 59 (inclusive). These different combinations of features were then used to train the 5 machine learning algorithms, as previously explained, and the results obtained for each of these combinations for the FD patients, with and without WMLs, are presented in Table 19. We quickly realize that the best model is with all features (9 features) and with random forest as classifier, where the accuracy is equal to 0.8125. This value means that in 48 predictions (number of FD patients with and without WMLs aged between 40 and 59), the model correctly predicted 39. As for both 1 feature and 2 features situations, the RBF SVM classifier show 81 a better performance, with accuracy of 0.729 and 0.750, respectively. Looking at the accuracy of all classifiers, in the 9 features case, we see that, except for random forest, all the classifiers have a weaker performance compared with the performance obtained with both 1 feature and 2 features cases. This suggests that, although the highest accuracy is in the 9-feature combination, if we are interested in selecting the best feature combination among classifiers, this may not be the best combination to predict if a FD patient has WMLs. Therefore, the 2-feature combination, which includes SDANN 5 and QTc Min variables, is the best combination, since it presents higher accuracy, sensitivity and AUC than the 1 feature combination. The values/status of the hyperparameters, of each model, can be consulted in Table 36 of Appendix B. 82 Table 19: Models’s classification performance metrics per number of features for FD with WMLs and FD without WMLs patients aged 40 to 59 (inclusive) Number of features (Features) ML Model Metrics Accuracy Sensitivity Specificity AUC 1 feature (SDANN 5) LR 0.6667 0.6087 0.7200 0.6939 Linear 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 features (SDANN 5 and QTc Min) LR 0.6667 0.5652 0.7600 0.6765 Linear 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 features (All) LR 0.6250 0.6087 0.6400 0.6000 Linear 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 learning; LR: logistic regression; SVM: support vector machine; RBF: radial basis function; RF: random forest; KNN: K-Nearest Neighbour 8.2 Results from patients over 59 years old For the patients aged above 59 years old, the first feature selection procedure, based on VIF values, identified 5 features with multicollinearity. Therefore, these 5 features were excluded and 10 remained, which were HR Min, HR Max, ASDNN 5, SDANN 5, QT Min, QT Mean, QTc Min, QTc Max, QTc > 450, and Longest R-R features. The VIF values obtained in each iteration of the process are displayed in Table 20 83 and, in this table, the held features are in bold type and the highest value per iteration is in red color. Table 20: VIF values for patients aged above 59 Features Iteration 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 Longest R-R 1.73 1.69 1.65 1.64 1.62 1.37 In Table 37 and Table 38 of Appendix B, are the hyperparameters values/status of each machine learning model obtained in the first hyperparameter tuning and the respective accuracy values obtained at predicting if a patient has FD, respectively. The highest accuracy value obtained with logistic regression as classifier, which results are in Figure 9a, was 0.7551, and it occurred with 5 features: HR Min, SDANN 5, QT Min, QT Mean, and QTc > 450. In the case of linear SVM algorithm, the RFE method identified that the highest accuracy is obtained with all the 10 features, and this accuracy value is 0.7755, as shown in Figure 9b. A 9-feature combination, including HR Min, HR Max, ASDNN 5, SDANN 5, QT Min, QT Mean, QTc Min, QTc > 450, and Longest 84 R-R features, is the combination that led to the highest accuracy, with a 0.7959 value, for random forest algorithm. The RFE results of this model can be observed in Figure 9c. (a) RFECV for logistic regression model. (b) RFECV for linear SVM model. (c) RFECV for random forest model. Figure 9: RFECV results for the different machine learning models of the HCM vs FD with WMLs patients aged above 59. The hyperparameters values/status for each feature combination and machine learning algorithm conjugation, obtained in the hyperparameter tuning step, that was performed after the RFE, are displayed in Table 39 of Appendix B. The respective obtained classification performance metrics are presented in Table 21. Random forest is the algorithm that shows better performance for both 9 features and 10 features. For 5 features the algorithm with the highest accuracy is the RBF SVM. However, the feature combination and algorithm conjugation that has the highest accuracy, 0.8163, is the one with 9 features (all variables except QTc Max) and random forest algorithm as classifier. Since the model predicted 49 situations (number of HCM and FD with WMLs patients aged above 9 years), the accuracy value obtained means that, in the 49 85 predictions, 40 were correctly predicted. Also, this 9-feature combination seems to be the best combination for this classification problem. Table 21: Models’s classification performance metrics per number of features for HCM and FD with WMLs patients aged above 59 Number of features (Features) ML Model Metrics Accuracy Sensitivity Specificity AUC 5 features (HR Min, SDANN 5, QT Min, QT Mean, and QTc > 450) LR 0.7755 0.9000 0.5789 0.7333 Linear 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 features (HR Min, HR Max, ASDNN 5, SDANN 5, QT Min, QT Mean, QTc Min, QTc > 450, and Longest R-R) LR 0.7347 0.8333 0.5789 0.6825 Linear 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 features (All) LR 0.7143 0.8000 0.5789 0.6579 Linear 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 learning; LR: logistic regression; SVM: support vector machine; RBF: radial basis function; RF: random forest; KNN: K-Nearest Neighbour 8.3 Discussion Turns out that several ECG characteristics are highly correlated with each other, that is, multicollinearity occurs. For patients aged between 40 and 59 years (inclusive), multicollinearity occurred in six variables 86 (VIF > 5). These variables do not belong to a specific type, in fact, one is from HR (HR Min), two are from HRV (ASDNN 5 and SDNN), and three are from QT analysis (QT Mean, QT Max and QTc Mean). As for the patients aged above 59 years old, multicollinearity occurred in five variables, one from HR (HR Mean), two from HRV (SDNN and RMSSD), and two from QT analysis (QT Max and QTc Mean). SVM with RBF kernel was the model that showed the best classification performance in the case of the patients aged between 40 and 59 of groups HCM and FD without WMLs (accuracy of 0.8049). Also, this is the algorithm that leads to better classification performances in almost every feature combination. In the studies Hijari et al. [6] and Munla et al. [39], RBF SVM was also the model that led to better classification performances, at classifying if symptoms were or were not expected based on some ECG measurements, and classifying stress level into highly stressed or normal based on HRV analysis, respectively. This model’s performance was obtained when using a 4-feature combination (HR Mean, SDANN 5, RMSSD, and QTc > 450). From these features, the only that was expected, taking into consideration the statistical results, was HR Mean, since, this variable was significantly associated with the dependent variable in the logistic regression analysis results of these patients. The remaining variables, that is, SDANN 5, RMSSD, and QTc > 450, were not significantly associated with the dependent variable. The ones that were significantly associated were all excluded during the filter feature selection method, based on VIF values, and, therefore, were not even used as input data to the machine learning models. However, it is worth remembering that the excluded variables by the iterative process based on VIF values can be predicted by other independent variables in the remaining subgroup of variables. As for the classification of HCM and FD with WMLs patients aged between 40 and 59 years, the best model was KNN with a 6-feature combination (HR Mean, HR Max, RMSSD, QTc Min, QTc Max, and QTc > 450) (accuracy of 0.8462). This is probably the most discrepant result. However, RBF SVM was the second best model with this feature combination, and the best with the other combinations, proving, once again, its value to classification problems based on ECG characteristics. Evaluating the feature combinations, some of the variables (HR Mean, QTc Max and QTc > 450) were expected, since they were significantly associated with the dependent variable (HCM or FD) in the logistic regression results. 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Available: https://www.hindawi.com/journals/ jdr/2018/3407306/. 103 Table 27: Statistically non-significant logistic regression results of HCM and FD without WMLs groups with ages between 40 and 59 (including) Variables Univariate logistic regression Multivariable logistic regression - Adjusted to age Multivariable logistic regression - Adjusted to sex OR (95% C.I) p-value OR (95% C.I) p-value OR (95% C.I) p-value 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 (0.951.00) 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 Longest 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: Statistically non-significant logistic regression results of HCM and FD with WMLs groups with ages between 40 and 59 (including) Variables Univariate logistic regression Multivariable logistic regression - Adjusted to age Multivariable logistic regression - Adjusted to sex OR (95% C.I) p-value OR (95% C.I) p-value OR (95% C.I) p-value 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 (0.981.02) 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 Longest 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: Statistically non-significant logistic regression results of FD with WMLs and FD without WMLs groups with ages between 40 and 59 (including) Variables Univariate logistic regression Multivariable logistic regression - Adjusted to age Multivariable logistic regression - Adjusted to sex OR (95% C.I) p-value OR (95% C.I) p-value OR (95% C.I) p-value 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 Longest 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: Normality of HCM and FD with WMLs groups and homogeneity of variance results, for patients aged above 59 Variables Normality - pvalues Homogeneity of variances - pvaluesHCM FD with 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 - Longest R-R p < 0.0001 p < 0.0001 - 113 Table 31: Statistically non-significant logistic regression results of HCM and FD with WMLs groups with ages above 59 Variables Univariate logistic regression Multivariable logistic regression - Adjusted to age Multivariable logistic regression - Adjusted to sex OR (95% C.I) p-value OR (95% C.I) p-value OR (95% C.I) p-value 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 Longest 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 Learning Appendix Table 32: Hyperparameters values/status per machine learning model and classification problem for patients aged between 40 and 59 (inclusive) ML Model Model Parameters Classification Problem HCM vs FD w/o WMLs HCM vs FD w/ WMLs FD w/ WMLs vs FD w/o WMLs LR C 0.5 0.05 0.7 Linear SVM C 0.1 0.05 3 RF bootstrap False True (default) False n_estimators 2 24 1 max_depth None (default) 6 5 max_leaf_nodes None (default) None (default) 9 min_samples_leaf 1 (default) 1 (default) 1 (default) min_samples_split 2 (default) 2 (default) 2 (default) ML: machine learning; LR: logistic regression; SVM: support vector machine; RF: random forest 115 Table 33: Accuracy values per machine learning model and classification problem for patients aged between 40 and 59 (inclusive) ML Model Classification Problem HCM vs FD w/o WMLs HCM vs FD w/ WMLs FD w/ WMLs vs FD w/o WMLs LR 0.7561 0.6923 0.6250 Linear SVM 0.7317 0.6923 0.6875 RF 0.7561 0.7692 0.8125 ML: machine learning; LR: logistic regression; SVM: support vector machine; RF: random forest 116 Table 34: Hyperparameters values/status per machine learning model and number of features for HCM and FD without WMLs patients aged 40 to 59 (inclusive) ML Model Model Parameters Number of features (Features) 4 Features (HR Mean, SDANN 5, RMSSD, and QTc > 450) 6 Features (HR Mean, SDANN 5, RMSSD, QTMin, QTc Max, and QTc > 450) 9 Features (All) LR C 2 0.8 0.5 Linear SVM C 0.3 0.07 0.1 RBF SVM C 70 3 3 gamma 0.002 0.03 0.04 RF bootstrap True (default) True(default) False n_estimators 40 31 2 max_depth 3 5 None (default) max_leaf_nodes None (default) None (default) None (default) min_samples_leaf 1(default) 1 (default) 1 (default) min_samples_split 3 2 (default) 2 (default) KNN n_neighbors 8 3 8 weights uniform uniform uniform ML: machine learning; LR: logistic regression; SVM: support vector machine; RBF: radial basis function; RF: random forest; KNN: K-Nearest Neighbour 117 Table 35: Hyperparameters values/status per machine learning model and number of features for HCM and FD with WMLs patients aged 40 to 59 (inclusive) ML Model Model Parameters Number of features (Features) 5 Features (HR Mean, RMSSD, QTc Min, QTcMax and QTc > 450) 6 Features (HR Mean, HR Max, RMSSD, QTcMin, QTc Max and QTc > 450) 9 Features (All) LR C 0.06 0.4 0.05 Linear SVM C 0.9 0.08 0.05 RBF SVM C 500 30 100 gamma 0.009 0.02 0.02 RF bootstrap False False True (default) n_estimators 900 40 24 max_depth 5 8 6 max_leaf_nodes None (default) None (default) None (default) min_samples_leaf 1(default) 1 (default) 1 (default) min_samples_split 2 (default) 0.3 2 (default) KNN n_neighbors 6 4 6 weights uniform uniform uniform ML: machine learning; LR: logistic regression; SVM: support vector machine; RBF: radial basis function; RF: random forest; KNN: K-Nearest Neighbour 118 Table 36: Hyperparameters values/status per machine learning model and number of features for FD with WMLs and FD without WMLs patients aged 40 to 59 (inclusive) ML Model Model Parameters Number of features (Features) 1 Feature (SDANN 5) 2 Features (SDANN 5 and QTc Min) 9 Features (All) LR C 6 20 0.7 Linear SVM C 0.2 10 3 RBF SVM C 9 900 30 gamma 0.3 0.007 0.007 RF bootstrap True (default) False False n_estimators 50 46 1 max_depth 2 1 5 max_leaf_nodes None (default) None (default) 9 min_samples_leaf 5 10 1 (default) min_samples_split 2 (default) 2 (default) 2 (default) KNN n_neighbors 16 8 2 weights uniform uniform uniform ML: machine learning; LR: logistic regression; SVM: support vector machine; RBF: radial basis function; RF: random forest; KNN: K-Nearest Neighbour 119