There is increasing interest in comparing healthcare providers in terms of performance indicators that capture processes or outcomes showing variation between the providers/hospitals. We consider quantifying how much of the crude between hospital variation in the outcomes at patient level is explained by the differences in patient case-mix, and further, how the variance in the outcomes can be decomposed into that explained by the hospital adjusting for case-mix, the case-mix itself, and residual variation. This contributes to the development of performance indicators that differentiate between hospitals and identifying patient populations where the indicators reflect differences in performance. For this purpose, we derive three-way variance decompositions, with particular attention to their causal interpretation, and consider alternative model-based estimators. The interpretation of the decompositions and the properties of the estimation methods are illustrated through simulations.