# Clustering of a Health Dataset Using Diagnosis Co-Occurrences
## 1 Introduction  
To create a coherent territorial healthcare offer, the general patient population needs to be assessed by evaluation and quantification of their health profiles. This task requires an epidemiologic analysis of the population, based on their demographic characteristics, their health problems, and their healthcare usage [1]. This evaluation could help inform public health policy, particularly in Emergency Departments (EDs), which represent a key element of the healthcare system with a role of safety net for the surrounding population. EDs are systems under tension, and admission volumes are steadily rising, with an increase from 10 to 20 million visits annually in France, corresponding to an average growth of 3.5% per year [2]. This situation has led to overcrowding and saturation of EDs, with negative repercussions on quality of care [3, 4, 5], and on working conditions for healthcare professionals. In this context, only a detailed study of healthcare needs, including analysis of patient flow and patient expectations, will enable the development of adequate solutions for healthcare delivery. The assessment of a patient population can be done through a classification based on their sociodemographic characteristics, their healthcare usage, and a clinical evaluation oftheir health state [1; 6]. Particularly, in EDs, multiple classification systems exist to describe patients according to the severity of their condition and their treatment requirements [7; 8]. However, they are ad hoc systems that are based on expert knowledge and not on actual data analysis. Furthermore, they are essentially targeted at allocating adequate nursing staff and not designed for detailed analysis of the population. To capture the nature of patients' health problems, the diagnosis seems to be the most appropriate candidate. It offers an adequate clinical typology of patients' visits, and a similarity structure based on either concept hierarchies [9] or co-occurrence associations [10; 11]. An adequate clustering strategy using this variable would yield an unsupervised classification based on patients' recorded data with the goal of obtaining compact and well-separated cluster classes, i.e., where clustered patients are very similar to the patients of their own cluster and very dissimilar to those of other clusters [12]. Although some approaches to ED classification based on diagnoses already exist [13; 14], no approach has been developed, to the best of our knowledge, using co-occurrences of diagnoses in ED patients, with multimorbidity pattern analysis. The analysis of multimorbidity patterns constitutes an effective and appropriate tool to model and assess the complexity of patients in terms of the diversity and statistical co-occurrences of their health conditions [15]. The literature on multimorbidity patterns was reviewed in 2014 by [PERSON] et al. and in 2019 by [PERSON] et al., and several methods and population contexts were identified [16; 17]. The methods were factor analysis, to discover underlying common factors of diseases [18; 19]; clustering analysis, to regroup either diseases or people into clusters [20; 21; 22]; or network analysis, to study the links between pairs of diseases [23]. These approaches are mainly focused on disease analysis of complex and chronic patients, which represent the greatest burden on the healthcare economy. Many opportunities still exist to extend the application of theses methodologies to broader contexts, across wider populations and with more robust strategies. Therefore, the goal of this study was to implement a new methodology to analyze multimorbidity patterns in an ED population. This paper proposes an original hierarchical clustering approach, based on multimorbidity analysis, for the classification of ED patients' visits. The proposed approach creates clusters by merging patient profiles according to their diagnosis co-occurrences.