# Clustering of a Health Dataset Using Diagnosis Co-Occurrences
## 4 Discussion
Other approaches, identified by [PERSON] [16], used diagnoses from the International Classification of Primary Care (ICPC), the ICD-9 and ICD-10 classification and others from an ad hoc list, limiting the number of baseline diagnoses between 10 to 50 for most of them (13 out of 14), by focusing on a specific set of diseases or by collapsing diagnoses into groups. Eight out of the 14 studies focused on elderly patients aged over 60 years, three used stratification by age and sex, and 10 studies selected the diagnosis based on their chronicity. These tendencies are further confirmed in the literature review by [PERSON] et al. [17], where 46 of the 51 studies identified used 32 or fewer baseline diagnoses, and 32 studies focussed on populations older than 50 years. Therefore, with 151 blocks of diagnoses and a population spanning allages, the present study proposes one of the most general multimorbidity approaches, with readable and coherent results through the 16 clusters found. The choice of similarity measure is the most crucial element of the clustering algorithm, as it will dictate how the entities are clustered together. In the context of categorical variables, and furthermore with the specificities of the diagnosis variable presented here, the design of the measure requires specific attention [29]. Particularly, with each diagnostic label represented as a binary variable, multimorbidity pattern analysis relies on statistical co-occurrences in patients of pairs of diagnoses. These co-occurrences are either measured during one visit or at another time, during multiple visits, as it is the case in the present study and in most other studies [16; 17]. This timeframe raises the problem of the design choices regarding the duration between co-occurrences. The design should consider whether the co-occurrences are meaningful, given the time interval between them, the population observed, and the study period. The present study empirically limited this duration to 6 months out of a 2-year study period, as this seemed to be a meaningful design for ED visits. Integrating the temporal aspect of co-occurrences directly into the proximity measure could also be considered, but would make the clustering design and interpretation of the results more complex. The choice of study period duration will also have an impact the quality of the results. Indeed, while being more time specific, a shorter period provides less occurrences and co-occurrences and therefore statistical sampling than a longer one. The sensitivity analysis on a nine-week period shows that the algorithm is quite robust regarding the study-period for the construction of a performant solution. However, with more than a third of all the blocks being filtered due to a number of occurrences less than 10, it also shows that the length of the study period is crucial to have enough statistical sampling of the occurrences and co-occurrences. Thus, shorter periods would begin to obscure the multimorbidity patterns that can be found in the ED population. The diagnoses co-occurrences can be expressed with contingency tables, with positive matches, negative matches, and positive-negative matches between diagnoses. From these tables, three proximity measures are often used in the literature [16; 17]: the Jaccard coefficient, that relies on positive matches to measure the tetrachoric correlation matrix, and Yule Q that relies on all types of matches. However, negative and negative-positive matches are very poorly informative on the diseases' relationships compared to positive matches, because they can be mainly attributed to the multimorbidity context, i.e., the number of diagnoses per patient. This is constrained by their number of visits, which do not represent an exhaustive view of the patient's health problems. Therefore, especially in the low multimorbidity context of general populations, the RR measure presented in this study and the Jaccard measure are appropriate measures based on positive matches.