# Comorbidity Pattern Analysis for Predicting Amyotrophic Lateral Sclerosis
## 1 Introduction  
Amyotrophic Lateral Sclerosis (ALS) is a multi-syndrome and fatal neurodegenerative disorder that results in progressive loss of bulbar and limb function [1]. The prevalence of ALS is uniformly distributed across most countries [2]. According to the ALS Association, the incidence rate of ALS is approximately between 1.8 and 2 per 100,000 person-years. Death from ALS occurs from respiratory failure, generally within 2-3 years from the onset of the bulbar symptom and 3-5 years after the limb onset [3]. For the majority of patients with ALS, it usually takes 9 to 15 months from symptom onset to definitive diagnosis by two or three specialists [1]. The diagnostic processes for ALS are very complicated compared to other diseases. Several steps are required to ensure that all medical evaluation items are completely performed. These processes include neurological examination and a series of diagnostic tests such as electromyography (EMG), magnetic resonance imaging (MRI), blood and urine tests, etc. However, there is yet no definitive diagnostic testing standard for ALS. Different medical evaluations are always performed after disease progression in different combinations of suggestive clinical signs of pathologies. Currently, the etiologyof sporadic ALS is unclear, and there is no cure for ALS. Treatment is mainly aimed at delaying the progression of the disease and not at eliminating the symptoms [4; 5]. Hence, if at-risk subjects of ALS can be identified during the early stages, they can be advised to focus on strengthening their immune system and on improving the environmental conditions in which they live. Early prognosis may slow the progressive deterioration of ALS symptoms. Since there is a near two-year lead-time interval prior to definitive diagnosis of ALS, the symptoms and comorbidities could provide important clues for ALS prediction. Hence, we consider Electronic Medical Records (EMRs) as useful for discriminating ALS and non-ALS patients in the early stages, and the developed classifier could serve as an alternative diagnostic approach or an early warning signal for doctors and ALS patients.  
This study was aimed at identifying high-risk Amyotrophic Lateral Sclerosis (ALS) subjects in the early stage using a novel detection mechanism solely based on EMRs. The novel prediction index used in this study is a modified version of the Jaccard index (JI). The traditional JI is a statistical value for comparing the similarity and diversity between two different sample sets. It measures the similarity between two limited sample groups. The value is directly proportional to the similarity between the two groups [6]. Studies have demonstrated that it is more effective to consider the weighted coefficients on similarity analysis for specific problems [7].  
To enhance the traditional JI indicator and the evidence of different populations with an identical disease possessing high comorbidity similarities, we proposed a novel weighted JI (WJI) that can effectively reflect the comorbidity distribution of EMRs, instead of using the binary status of comorbidity; further, compared with traditional approaches, we formulated indices to provide accurate prediction results. The details and experimental results are described in the following sections.