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Confounding occurs when the compared treatment groups differ in relevant potential outcomes, so their observed outcome contrast mixes the causal effect with differences in baseline prognosis. In a binary-treatment model, absence of confounding is expressed through ignorability, $Y(a)\perp A$ for each compared $a$, or through conditional exchangeability after a sufficient pretreatment adjustment set is specified.

For a causal directed acyclic graph, $A\leftarrow U\to Y$ is the simplest backdoor path: the common cause changes both assignment and outcome. Confounding by indication is a practical example when baseline severity influences which treatment is received. Outcome standardization, matching and inverse probability weighting can address measured confounding under their identification assumptions.

A changed adjusted estimate does not, by itself, prove that confounding was removed. Noncollapsibility of the odds ratio can produce different marginal and conditional odds ratios even without confounding; adjustment for an inappropriate variable can introduce collider bias. Causal structure and the target effect must guide the adjustment choice.^[ref]