Applying ranked set sampling to Gaussian mixture models of Glasgow Coma Scale scores in intracerebral hemorrhage

Abstract Clinical severity scales like the Glasgow Coma Scale (GCS) exhibit heterogeneous distributions reflecting latent patient subgroups. Finite mixture models capture this heterogeneity, but component overlap limits interpretability. Ranked set sampling (RSS) incorporates auxiliary ranking information during sample selection, potentially improving separability. This empirical study evaluated whether RSS enhances component separability in Gaussian mixture models of GCS scores compared to simple random sampling (SRS). Admission GCS scores from a full consecutive cohort ( $$\:N=504$$ ) of primary intracerebral hemorrhage patients were analyzed. A retrospective ranked set subsampling ( $$\:n=300$$ ) and simple random subsampling ( $$\:n=300$$ ) were evaluated using Gaussian mixture models. A composite auxiliary variable (age and diabetes mellitus) was used for RSS ranking. Component numbers were selected via the Bayesian Information Criterion and bootstrap likelihood ratio tests. Parameters were estimated using the expectation-maximization algorithm, and separability was quantified via normalized overlap coefficients. A three-component model was selected under both schemes, aligning with established GCS severity categories. Compared to SRS, the retrospective RSS-based subsampling yielded more concentrated mixture components and substantially reduced overlap between adjacent components. A retrospective RSS-based subsampling design produced lower component overlap in Gaussian mixture models for clinical severity data without increasing model complexity. RSS represents a practical, underutilized strategy to potentially enhance mixture-based analyses of heterogeneous medical outcomes.