Measuring variability between clusters by subgroup: An extension of the median odds ratio

Investigating clustered data requires consideration of the variation across clusters, including consideration of the component of the total individual variance that is at the cluster level. The median odds ratio and analogues are useful intuitive measures available to communicate variability in outcomes across clusters using the variance of random intercepts from a multilevel regression model. However, the median odds ratio cannot describe variability across clusters for different patient subgroups because the random intercepts do not vary by subgroup. To empower investigators interested in equity and other applications of this scenario, we describe an extension of the median odds ratio to multilevel regression models employing both random intercepts and random coefficients. By example, we conducted a retrospective cohort analysis of variation in care limitations (goals of care preferences) according to ethnicity in patients admitted to intensive care. Using mixed-effects logistic regression clustered by hospital, we demonstrated that patients of non-Caucasian ethnicity were less likely to have care limitations but experienced similar variability across hospitals. Limitations of the extended median odds ratio include the large sample sizes and computational power needed for models with random coefficients. This extension of the median odds ratio to multilevel regression models with random coefficients will provide insight into cluster-level variability for researchers interested in equity and other phenomena where variability by patient subgroup is important.