A variance estimator for marginal Cox regression models fit to non-nested multilevel data

In health services research, researchers often use clustered data to estimate the independent association between individual outcomes and cluster-level covariates after adjusting for individual-level characteristics. Marginal generalized linear models estimated using generalized estimating equation (GEE) methods or hierarchical (or multilevel) regression models can be used when there is a single source of clustering (e.g., patients nested within hospitals). Hierarchical regression models can also be used when there are multiple sources of clustering (e.g., patients nested within surgeons who in turn are nested within hospitals). Methods for estimating marginal regression models are less well-developed when there are multiple sources of non-nested clustering (e.g., patients are clustered both within hospitals and within in neighborhoods, but neither neighborhoods or hospitals are nested in the other). Miglioretti and Heagerty developed a GEE-type variance estimator for use when fitting marginal generalized linear models to non-nested multilevel data. We propose a variance estimator for a marginal Cox regression model fit to non-nested multilevel data that combined their approach with Lin and Wei’s robust variance estimator for the Cox model. We evaluated the performance of the proposed variance estimator using an extensive set of Monte Carlo simulations. We illustrated the use of the variance estimator in a case study consisting of patients hospitalized with an acute myocardial infarction who were clustered within hospitals and who were also clustered in neighborhoods. In summary, a variance estimator motivated by that proposed by Miglioretti and Heagerty can be used with marginal Cox regression models fit to non-nested multilevel data.