# Causal variance decompositions for institutional comparisons in healthcare

## TL;DR

This paper introduces a causal variance decomposition method to analyze and compare healthcare institutions based on disease-specific quality indicators, focusing on overall variation and causal effects rather than pairwise hospital comparisons.

## Contribution

It develops a novel three-way variance decomposition framework with causal interpretation, including model-based estimators for analyzing hospital performance variations.

## Key findings

- Effective in decomposing variation into causal components
- Model estimators perform well in simulations
- Applied successfully to real healthcare data

## Abstract

There is increasing interest in comparing institutions delivering healthcare in terms of disease-specific quality indicators (QIs) that capture processes or outcomes showing variations in the care provided. Such comparisons can be framed in terms of causal models, where adjusting for patient case-mix is analogous to controlling for confounding, and exposure is being treated in a given hospital, for instance. Our goal here is to help identifying good QIs rather than comparing hospitals in terms of an already chosen QI, and so we focus on the presence and magnitude of overall variation in care between the hospitals rather than the pairwise differences between any two hospitals. We consider how the observed variation in care received at patient level can be decomposed into that causally explained by the hospital performance adjusting for the case-mix, the case-mix itself, and residual variation. For this purpose, we derive a three-way variance decomposition, with particular attention to its causal interpretation in terms of potential outcome variables. We propose model-based estimators for the decomposition, accommodating different link functions and either fixed or random effect models. We evaluate their performance in a simulation study and demonstrate their use in a real data application.