= Sensitivity analysis for unmeasured confounding
<Sensitivity analysis for unmeasured confounding> asks how an estimated <causal effect> changes under explicit departures from the assumed <conditional exchangeability>. It varies parameters describing the omitted variable's assignment imbalance and outcome effect, rather than assuming that measured <covariate balance> proves the omission harmless.
For a transparent additive <linear structural equation model>, take a pretreatment variable $U$ and
$$
Y=\tau A+\gamma U+\varepsilon,\qquad \mathbb E(\varepsilon\mid A,U)=0.
$$
Assume intervening on $A$ leaves $U$ unchanged, so the constant <treatment> effect in this model is $\tau$. Subtracting the two conditional outcome means gives
$$
D_{\rm obs}=\tau+\gamma\Delta_U,\qquad
\Delta_U=\mathbb E(U\mid A=1)-\mathbb E(U\mid A=0).
$$
Thus the adjusted effect for a hypothesized parameter pair is $\tau=D_{\rm obs}-\gamma\Delta_U$. An observed difference five would fall to three when $\gamma=2$ and $\Delta_U=1$; explaining it entirely would require $\gamma\Delta_U=5$.
The product is a bias term derived for this particular additive model. Other outcome scales and interactions need different formulas. Plausible ranges can be compared with measured pretreatment predictors or external evidence, but the observed treatment-outcome table alone cannot determine the omitted parameters. A sensitivity result quantifies a model-dependent robustness claim; it does not establish that unmeasured <confounding> is absent.
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