Multiple great economic challenges as most of the

Multiple Sclerosis is an auto-immune disorder of the central nervous system (brain and spinal cord), which is preceded by the degeneration of the myelin sheath. The protective sheath that covers the nerve fibers in an individual is attacked by own immune system thereby causing disruption in communication between the brain and the rest of the body. Hence, lack of muscle coordination, muscle weakness, slurry speech, decreased memory, decreased spontaneity, paresthesia, bladder dysfunction and visual impairment citep{goldenberg2012multiple}. Although the cause of Multiple Sclerosis is unknown, it is widely believed to occur as a result of the synergistic effect of non-genetic and genetic factors. Some triggers such as viruses, bacteria, stress, smoking and other environmental factors in combination with genetic susceptibility have been implicated in the cause and progression of MS citep{koriem2016multiple}.   \Young people between 20 to 50 years of age are more likely to suffer from MS. This present great economic challenges as most of the people affected loose ability to keep working after about 10 years of the attack thereby resulting in total economic dependency. According to Atlas of MS 2013 
ocite{multiple2013atlas}, the estimated number of people with MS has increased from 2.1 million in 2008 to 2.3 million in 2013 and the incidence of MS in females approximately double that of males. The prevalence of MS varies across regions of the world but the large population of Nothern European Countries, Canada, New Zealand, and some other countries in the temperate regions are believed to suffer more from the disease than others citep{milo2010multiple}. Although, this has not been fully established since the disease is caused by both hereditary and non-hereditary factors but lack of vitamin D has been implicated these areas citep{koriem2017corrigendum}.\ Multiple sclerosis has been categorized into types based on the disease course; Relapsing – Remitting MS, Secondary Progressive MS, Primary Progressive MS, and Progressive-Relapsing MS citep{goldenberg2012multiple,hauser2005multiple,loma2011multiple}. Relapsing-Remitting MS (RRMS) is the most common form of the disease characterized by periods of sudden worsening of symptoms(relapse or exacerbation) and immediate improvement or total absence of symptoms. The progression of RRMS with or without periods of relapsing or remitting is known as Secondary Progressive MS(SPMS) whereas, in Primary Progressive MS (PPMS), the symptoms of the disease worsen from onset without periods of relapsing or remission. The Progressive-relapsing MS (PRMS) is the least common form of the disease with the progression of the disease from the onset and intermittent worsening of the disease over the years. Patients who only experience a single episode with clinical symptoms are reported to have clinically Isolated Syndrome (CIS).\ However, it is quite difficult to diagnose MS and available methods are not specific for detecting the disease alone but other diseases that could present the same symptoms. Therefore, a number of tests are employed to rule out other types of diseases and confirm MS especially after two or more episodes of MS-related symptoms. Both clinical and para-clinical tests are used to diagnose MS. Blood tests, Lumbar puncture, magnetic resonance imaging (MRI) and Evoked potential tests are jointly used. MRI scans are basically used to detect lesions or scarring of the myelin sheath in the brain or spinal chords while Evoked potential tests capture how long it takes messages from the eyes, hands, and legs to reach the brain and vice versa through an electrode because scaring of the myelin sheath obstruct the rapid passage of signals. Although the use of evoked potential tests have been a subject for debates, it is believed to be more useful for monitoring the course of multiple sclerosis than the subjective Expanded disability status scale (EDSS) introduced by citet{kurtzke1983rating}\The Expanded Disability Status Scale (EDSS) is a 20-point scale (ranging from $0 = ext{normal} $ to $  10 = ext{death due to MS}$, marked by $0.5 $ increments) and is currently the most widely used measurement scale by neurologist to quantify disability due to MS citep{kurtzke1983rating, mckay2016factors}. MS patients who are able to walk without aid are categorized within the range 1 to 4.5 while patients that fall within the scale of $5$ to $9.5$ are defined by the inability to walk properly (see section
ef{edss}). The EDSS classification is made from scoring impairment on the scale of $0$ to $5$ or $6$ in eight functional systems (FSS), which are pyramidal(weakness), cerebellar(tremor), brain-stem (speech problems), sensory(numbness), bowel and bladder function, visual function, mental function and others. Apart from the fact that EDSS is subjective, it is largely dependent on walking abilities and the fact that increment of one at a lower scale does not translate to the same effect at a higher scale. But, it is the most popularly used score for monitoring MS progression, especially in clinical trials. However, to further assess the cognitive abilities and abilities to carry out daily activities, new outcome measures such as MS functional composites (MSFC) and patients reported outcome measures (PROM) have been proposed. See citet{van2017outcome} for details.\Various forms of evoked potential tests are widely in use. They are; visual evoked potentials (VEPs), and somatosensory evoked potentials (SEPs),  motor evoked potential  (MEP). MEP test which was employed in this study is carried out by single or repeated pulse stimulation of the brain which causes the spinal cord and the peripheral muscles to produce neuro-electrical signals. These signals are recorded by intramuscular needle electrodes from hands or legs. The amplitude, latency, threshold and time taken by the signal to reach the peripheral muscles are important in the prognosis of MS disease. A decrease in amplitude of the signal over time can be indicative of an injury or lesion on the signal path (see section
ef{evoke} for details). Also, due to the fact that the transcranial stimulation on the head is varied from spot to spot around a segment of the brain and these spots might vary from neurologist to neurologist thereby inducing a lot of variation. \Therefore, the objectives of this study are to develop a generic method to analyze raw signals (time series data) instead of the average of amplitude and latency that has been used in literature. The raw signals are represented in another domain using wavelets method and thresholding is applied before a functional lasso regression model is fitted to select a number of features both clinical and non-clinical (MEP) which predict the outcome measure of MS diseases, the EDSS of each patient. Section two of this reports described the methodology employed to achieve study objectives, the results obtained are given in section three and section four contains further discussion and conclusion from the study.%missing data\%? why more variation,Using the whole data could capture more variation and would increase the power of MEP to predict and monitor MS disease progression.% However,it is quite difficult to diagnose MS and available  The diagnosis of multiple sclerosis (MS) is based on the detection of multiple inflammatory, demyelinating white matter lesions, which are disseminated in time and space.  In many patients, clinical assessment is insufficient and para-clinical studies must be performed. These tests, such as MRI, cerebrospinal fluid (CSF) studies, visual evoked potentials (VEPs), and somatosensory evoked potentials (SEPs), may be used in conjunction with motor evoked potential (MEP) studies to establish the diagnosis of MS.  section{METHODOLOGY}subsection{Data Description} label{evoke}The data used in this study contains evoked potential measurements of 447 patients at their first visit to the clinic. A repeated transcranial stimulation of a preselected region of the brain is carried out and an electrode is attached to either the left or right limbs to record the amplitude of the signal as it travels from the brain to the limbs. The region of the brain to be used is divided into two; left and right part and stimulation of these parts of the brain are done repeatedly to find a spot that induces activation of evoked potential in the neuronal tract of the patients. From the series of these stimulations on each patient, the MEP signal with the highest peak to valley is selected as the most representative signal to be used in the prediction of MS.\The interest of this study lies in analyzing a single evoked potential for individual patients from the different repeated measurements recorded over time, a visual method was used to select the signal with the highest peak to valley amplitude over time(Milliseconds). Peak selection is done visually by plotting a graph of repeated signals of an individual and the signal with the highest peak to valley is selected. However, since a lot of patients are involved, an ad-hoc method was implemented for computational ease by selecting the signal with the maximum absolute amplitude (millivolt). Other clinical measures such as age, gender, EDSS score, amplitude, latency, FSS score were also recorded. The EDSS score which is the clinical outcome measure is categorized into two levels. Patients within the range of 1 to 4.5 are classified as fully ambulatory while patients within the range of 5 to 9.5 are categorized as impaired according to the EDSS scale by citet{kurtzke1983rating}.