# Clustering of a Health Dataset Using Diagnosis Co-Occurrences
## 4 Discussion  
The multimorbidity clustering algorithm presented in this study provides an original and innovative method to detect comorbidity patterns and describe their structure on a global population scale with a 2-step clustering approach. It enables a coherent and clinically meaningful evaluation of an ED population with diagnosis clusters that embed highly coherent diagnoses within one cluster, and sufficiently differentiate between clusters. From the four statistical techniques of multimorbidity patterns analysis identified by [PERSON] et al. [17], the approach proposed in this study is based on a cluster analysis of diseases with hard clusters, which implies a discrete association between diseases and clusters. In the literature, methods based on this statistical technique used the HAC algorithm with a Jaccard coefficient or Yule's Q as a similarity measure. Using new quality metrics, the present method is compared to the HAC approach with the Jaccard coefficient and Yule's Q coefficient, and with an MCA approach, usually used for clustering people but adjustable for clustering diagnoses. As such, compared to the state-of-the-art HAC methods, the present approach proposes three innovations: a new similarity measure based on the relative risk of co-occurrence, an adaptation of the HAC algorithm to this type of statistical context, which is neither categorical nor numerical, and the introduction of quality metrics based on the new similarity measure. Furthermore, the approach is used in a novel context with the analysis of a global ED population and its specific multimorbidity patterns. The clustering strategy can be compared to other approaches found in the literature based on its three stages of design, necessary to any multimorbidity clustering study, namely the stage of choosing the representation and selecting both diagnosis and population; the stage of choosing an embedded space and a similarity measure to compare entities; and the final stage of choosing the clustering algorithm and the appropriate quality indicators. The comparison of multimorbidity analysis methods, which is still rare [36], will help explain why the other approaches tested, named here HAC Jaccard and MCA HAC and similar to those found in the literature [20; 21], failed to provide adequate results in the present context. The choice of representation and the selection of the diagnoses and population depend primarily on the end goal of the clustering study, and secondarily on the aim of limiting sampling biases in the co-occurrence count of the diagnoses. Since the present study was further used to analyze the evolution of ED visits over the 2-year study period, and since it requires an assessment of the general population, we included all diagnoses that had an occurrence of at least 10 episodes of visits, and all visits with at least one of these diagnoses. We also did not apply any stratification, and we chose a high block level representation of the ICD10 classification, as it provides adequate semantic precision for a general population assessment, limiting the number of clusters and the complexity of the diagnosis relationships. Hybrid approaches using both ICD10 concept similarity and semantic and co-occurrence similarity could be conceptualized, but would represent additional challenges to find a coherent measure that would strike a balance between the two heterogeneous similarities [9; 10; 11]. The exclusion of specific diagnoses, like R codes (_symptoms, signs, and abnormal clinical and laboratory findings, not elsewhere classified_) and \(Z\) codes (_factors influencing health status and contact with health services_) [21], could have enhanced the quality of the clustering, as they are linked to many heterogeneous health problems, but would have ignored 28.9% of all ED visits.