Recent causal inference literature has introduced causal effect decompositions to quantify sources of observed inequalities or disparities in outcomes but usually limiting this to pairwise comparisons. In the context of hospital profiling, comparison of hospital performance may reveal inequalities in healthcare delivery between sociodemographic groups, which may be explained by access/selection or actual effect modification. We consider the case of polytomous exposures in hospital profiling where the comparison is often to the system wide average performance, and decompose the observed variance in care delivery as the quantity of interest. For this, we formulate a new eight-way causal variance decomposition where we attribute the observed variation to components describing the main effects of hospital and group membership, modification of the hospital effect by group membership, hospital access/selection, effect of case-mix covariates and residual variance. We discuss the causal interpretation of the components, formulate parametric and nonparametric model based estimators and study the properties of these estimators through simulation. Finally, we illustrate our method by an example of cancer care delivery using data from the SEER database.

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