The optimal number of clusters was determined using a combination of an elbow plot, silhouette score, and Calinski-Harabasz index. The corresponding plots are shown in Fig. 2.

presents the elbow plot, silhouette score, and Calinski-Harabasz index. The number of clusters ranges from 2 to 20

As seen in the elbow plot in Fig. 2, there was no clear “elbow” indicating the optimal number of clusters. Additionally, WCSS decreased as the number of clusters increased. The decision was additionally supplemented by the silhouette score and the Calinski-Harabasz index. In the elbow plot, the presumed elbow region appeared to be between 4 and 7 clusters. Both the Calinski–Harabasz and Silhouette indices suggested a 2-cluster solution but also yielded acceptable values for 3 and 4 clusters. Considering statistical criteria, model simplicity, and clinical interpretability, 4 clusters were identified as the optimal choice.

In general, the average age of the multimorbid population was 65 years and included a slightly larger proportion of women (54.5%). On average, individuals in this population have 3.26 chronic conditions which can be seen in Table 2. As seen in Table 3, the three most prevalent chronic conditions were hypertension (70%), high cholesterol (45%), and osteoarthritis (23%).

Cluster size: This cluster included 24,017 individuals, corresponding to 2.03% of the total multimorbid population, which was the second lowest in size compared to the other clusters.

Utilization of healthcare services: This cluster had the highest levels of medication usage (9.3), hospitalizations (4.2), bed days (29.5), and outpatient visits (16.1). General practitioner (21.7) and psychologist (0.039) consultations were the second highest, while specialist doctor visits ranked third among the clusters.

Chronic conditions in the cluster: This cluster had the highest average number of chronic conditions (4.5). The three most common conditions were hypertension (70.7%), high cholesterol (37.7%), and depression (33.1%), while the least prevalent were skin cancer (0.99%), multiple sclerosis (1.1%), and Parkinson’s disease (1.8%). Compared to the expected numbers in the multimorbid population, a higher observed occurrence was found for 30 out of the 33 chronic conditions. The greatest deviations were found for schizophrenia (O/E:7.41; corresponding to a 641% increase), personality disorder (6.30; 530%), and addictive disorder (6.27; 527%). Furthermore, it was worth noticing that kidney disease had a higher observed occurrence (3.67; 267%) compared to the other clusters. The remaining can be seen in Table 3.

Combinations of chronic conditions in the cluster: Among combinations of conditions in the chronic condition portfolios, hypertension, high cholesterol, and depression were the most prevalent (Table 4). When risk factors were excluded (Table 5 in appendix), depression remained a key component in most of the combinations of two and three, but it was less common in combinations of four. The combination of atrial fibrillation, heart failure, and ischemic heart disease was also frequent observed in the combinations of four chronic conditions.

Sociodemographic characteristics: The average age in this cluster was the third highest (64.8 years), and it had the highest proportion of men (52.9%). This cluster also had the highest rate of individuals living alone (53.2%) and the highest proportion of residents from Capital Region of Denmark (32.2%) among the clusters. It was also observed that proportion of residents in the North Denmark Region and Central Denmark Region was the lowest in this cluster. The percentage of retired individuals was the second highest (57.4%). Additionally, this cluster had the lowest level of higher educational attainment, with only 11.6% having a higher education degree. Incomes were the lowest in this cluster, with 78.3% falling within the first and second quartiles.

Conclusion: This cluster included individuals with hypertension, high cholesterol, addictive disorders, and especially mental conditions (depression, schizophrenia, and personality disorders). It had the highest average number of chronic conditions and the highest healthcare utilization. A large proportion of individuals in this cluster were single (53.2%). Additionally, this cluster ranked lowest in social position regarding education and income.

Cluster size: The cluster consisted of the fewest individuals, N = 5,035, representing only 0.43% of the total population with multimorbidity.

Utilization of healthcare services: Psychologist consultations were the highest in this cluster (8.8), while bed days (1.67) and specialist doctor visits (4.33) were the second highest among the clusters. Additionally, medication usage (5.6), hospitalizations (0.05), general practitioner (3.2), and outpatient visits ranked (0.47) as the third highest.

Chronic conditions in the cluster: This cluster had the lowest average number of chronic conditions (2.98). Depression (53.7%), hypertension (46.1%), and high cholesterol (25.1%) were the most prevalent chronic conditions, while Parkinson Disease (0.36%), Schizophrenia (0.54%), and dementia (0.62%) were the least common. Furthermore, 11 of the 33 chronic conditions showed an observed/expected ratio above 1. The largest increases were observed for anxiety (O/E: 4.88; corresponding to a 388% increase), depression (2.61;161%), and personality disorder (2.37; 137%).

Combinations of chronic conditions in the cluster: In combination of two conditions, depression was prominent. In combination of three and four, depression, high cholesterol, and hypertension appeared in most combinations (Table 4). When risk factors were excluded ( Table 5 in appendix), depression played an even greater role, appearing in nearly every combination of chronic conditions. COPD and allergies also became more prominent. Additionally, osteoarthritis was more frequently observed in combinations of three and four.

Sociodemographic characteristics: This cluster had the lowest average age (51.5 years) among the four clusters. It had the highest proportion of women (75.6%). The majority were either single (43%) or married (43%), with the proportion of single individuals being the second highest and married individuals the third highest among the clusters. The largest share of individuals resided in region of south Denmark (24.6%), followed by Capital Region of Denmark (23.9%) and Central Denmark Region (23.7%). This cluster had the highest proportion of individuals in employment (42.4%), while the share of retired individuals was the lowest (35.4%). It also had the highest level of higher educational attainment (28.6%). Additionally, income was the highest, with 34.1% falling within the third and fourth quartiles.

Conclusion: This cluster consisted of the youngest individuals, with a high proportion of women (75.6%). It was characterized by mental disorders such as depression and anxiety, as well as hypertension and high cholesterol. While it had the lowest average number of chronic conditions, it had a high burden on psychologist visits. This cluster had the highest social position in terms of education and income.

Cluster size: The cluster consisted of 918,901 individuals, accounting for 77.59% of all individuals with multimorbidity, making it the largest cluster.

Utilization of healthcare services: Medication usage (5.57), hospitalizations (0.048), bed days (0.14), general practitioner visits (3.19), specialist doctor visits (0.46), psychologist consultations (0.0062), and outpatient visits (0.47) were the lowest in this cluster.

Chronic conditions in the cluster: This cluster had the second lowest average number of chronic conditions (3.08). The three most prevalent chronic conditions were hypertension (68.11%), high cholesterol (43.88%), and osteoarthritis (22.08%), while the least prevalent were personality disorder (0.28%), schizophrenia (0.50%), and Parkinson Disease (0.66%). A higher prevalence than expected was only observed for multiple sclerosis (O/E:1.03, corresponding to a 3% increase).

Combinations of chronic conditions in the cluster: Hypertension and high cholesterol were prominent in combinations of two, three, and four chronic conditions (Table 4). When excluding the risk factors (Table 5 in appendix), osteoarthritis, COPD, and allergies emerged as the most prevalent conditions in these combinations.

Sociodemographic characteristics: The average age in this cluster was 64.4 years, making it the third highest among the clusters. A higher proportion of men (54.2%) than women was observed. The percentage of married individuals (52.1%) was the highest among the clusters, while the prevalence of single individuals was the lowest at 39.6%. Most individuals resided in the Capital Region of Denmark (25.7%), followed by the Region of Southern Denmark (23.9%) and the Central Denmark Region (23.1%). The proportion of retired individuals was the second lowest (53.2%), whereas the proportion of employed individuals was the second highest (27.7%) among the clusters. This cluster had the second-highest level of higher educational attainment (14.7%) and the second-highest income (30.6%) when combining the third and fourth quartiles.

Conclusion: This cluster included chronic conditions such as hypertension, high cholesterol, and osteoarthritis. It had a higher proportion of men (54.2%) than women. This cluster had the lowest utilization of healthcare services and the second-highest social position in terms of education and income.

Cluster size: This cluster comprised 236,381 individuals, representing 19.96% of the multimorbid population and ranking as the second largest cluster.

Utilization of healthcare services: General practitioner (23.1) and specialist doctor (6.1) were the highest in this cluster. Additionally, medication usage (8.1), hospitalization (0.52), and outpatient visits (3.6) were the second highest, while bed days (1.61) and psychologist visits (0.024) were the second lowest among the clusters.

Chronic conditions in the cluster: The cluster had the second-highest average number of chronic conditions (3.85). Hypertension (78.56%), high cholesterol (51.78%), and osteoarthritis (27.29%) were considered the three most prevalent chronic conditions in the cluster, while personality disorder (0.27%), schizophrenia (0.53%), and multiple sclerosis (0.68%) were the three least prevalent. An observed/expected ratio above 1 was identified for 24 of the 33 chronic conditions. The most notable increases were observed for atrial fibrillation (O/E:1.51, corresponding to a 51% increase), heart failure (1.46; 46%), and Parkinson disease (1.39; 39%). The rest can be seen in Table 2.

Combinations of chronic conditions in the cluster: Hypertension was most prominent in combinations of two conditions, whereas both hypertension and high cholesterol were observed in all combinations of three and four (Table 4). When risk factors were excluded (Table 5 in appendix), osteoarthritis was the most prominent, followed by COPD and allergies.

Sociodemographic characteristics: The average age of the cluster is 69.2 years, which was the highest among the clusters. Additionally, a higher proportion of men (56.2%) than women was observed. In terms of family type, 50.7% were married, while 42.6% were single, which was the second-lowest among the clusters. Individuals in this cluster primarily resided in the Capital Region of Denmark (25.7%) followed by the Region of South Denmark (24.9%) and the Central Denmark Region (22.8%). The proportion of retired was 67.8%, which was the highest among the clusters. In contrast, individuals in employment were the second-lowest (15.19%). It was also noted that the cluster had the second-lowest level of higher educational attainment (12.33%). Income was also the second-lowest (24.4%), when combining the third and fourth quartiles.

Conclusion: This cluster included the oldest individuals, with a higher proportion of men (56.2%) than women. The individuals were primarily affected by hypertension, high cholesterol, and osteoarthritis. It had the highest proportion of retired individuals (67.8%). The cluster showed high healthcare utilization, particularly in terms of General Practitioner and specialist doctor visits. Additionally, it had the second-lowest social position based on education and income.

To assess the robustness and stability of the clustering solution, a sensitivity analysis was performed. This investigated whether the results were sensitive to the relationship between chronic conditions and healthcare utilization. In this analysis, the weight between the two data segments, chronic conditions and healthcare utilization, was adjusted. This allowed healthcare utilization to be weighted more or less in the clustering process, relative to the chronic conditions. The lower limit was set to 0.5*W and the upper limit to 2*W, where W is the weight. This range was chosen to reflect meaningful but realistic perturbations, with the aim of assessing robustness of the clustering solution rather than optimizing the weighting scheme. Figure 3 illustrates the weight adjustments and their impact on cluster formation through confusion matrices.

Illustrates two confusion matrices. The left compares the original solution with the lower limit (0.5*W), while the one on the right compares the original solution with the upper limit (2*W)

As shown in Fig. 3, two confusion matrices were presented, comparing the original solution to the lower limit (0.5*W) and the upper limit (2*W), respectively. The two matrices were identical, as both limits resulted in the same clustering solution. In both matrices, most observations were located along the diagonal (98.3%), indicating a general similarity between the cluster assignments. Notable deviations were observed in clusters 3 and 4, minor discrepancies in cluster 1, and complete consistency in cluster 2. The results indicated that the clustering solution is reasonably stable within the examined range of weight, with only minor deviations observed.