Cluster separation outperforms other metrics in validating multimorbidity patterns: statistical simulation study

Background and objectives Multimorbidity, defined as the presence of multiple long-term health conditions within an individual, remains a growing challenge in healthcare. Identifying frequently occurring multimorbidity clusters may help to develop targeted interventions and optimise care pathways. However, the validation of multimorbidity clusters derived from real-world data is complicated by the lack of a known "ground truth". We conducted a statistical simulation study that aimed to evaluate the performance of three common validation approaches (cluster separation, clustering stability, and strength of association with health outcomes) in assessing the quality of multimorbidity clusters, where performance was measured by agreement with known ground truth clusters. Methods Simulated datasets with predefined clusters were generated across 25 scenarios, varying parameters such as disease prevalence, sample size, and noise levels. Latent class analysis was applied to derive clusters from the simulated data, which were compared to the predefined clusters using the Adjusted Rand Index (ARI). The ARI served as our gold standard quality assessment of derived clusters. Results Cluster separation, measured by the Calinski-Harabasz Index, showed the strongest agreement with our gold standard in most scenarios (median correlation: 0.641, IQR: 0.505-0.728). Clustering stability, assessed using resampling, had mixed performance, with a median correlation of 0.421 (IQR: 0.127-0.526). The strength of association with health outcomes, assessed using Nagelkerke's R 2 , consistently showed poor agreement (median correlation: -0.424, IQR: -0.543 to -0.173) with the ARI. Conclusion Cluster separation seems to be the most reliable approach to validate multimorbidity clusters. Clustering stability can sometimes be used for validation but has limitations. Assessing the strength of association of multimorbidity clusters with health outcomes, though valuable for understanding clinical relevance, appears to not validate cluster quality despite being commonly used in published literature.