Confounding

Confounding is distortion of an exposure-outcome association by common causes or associated background variables.

Case mix describes the distribution of patient characteristics affecting prognosis, such as age, severity, comorbidity and urgency. Comparing provider outcomes without accounting for case mix may confuse differences in patients with differences in care. Adjustment requires comparable, reliably measured baseline variables and does not remove all possible confounding.

A risk-adjusted provider comparison contrasts observed outcomes with outcomes expected from a prespecified patient-risk model, or standardizes providers to a common patient population. For individual fitted risks $p_i$, the expected event count is ${\sum }_i{p}_i$. Patient selection, model calibration, omitted risk factors, small samples and dependence between outcomes can still affect interpretation. Funnel plots display precision differences that an ordered league table can obscure.

A comparison can have the same direction within every background stratum but reverse after pooling strata with different group compositions. For example, let unexposed event risks be $0.001$ in a low-risk stratum and $0.05$ in a high-risk stratum, and multiply the odds by $2.7$ for exposure within each stratum. The exposed risks are then approximately $0.002695$ and $0.124424$. If 80% of unexposed subjects but only 1% of exposed subjects belong to the high-risk stratum, the pooled unexposed risk is $0.0402$ while the pooled exposed risk is about $0.003913$. Every conditional odds ratio is above one, yet the pooled exposed risk is smaller. The differing background distributions create the reversal; this example does not identify a causal effect without assumptions on how exposure was assigned.

A confounder predicts both treatment assignment and outcome and can create a noncausal association.