= Conditional average treatment effect
{title2=CATE}
The <conditional average treatment effect> at pretreatment covariates $X=x$ is $\tau(x)=\mathbb E[Y(1)-Y(0)\mid X=x]$. It describes average effect variation between strata rather than identifying a particular individual effect. If $\tau(x)=2$ in one equally common stratum and $-1$ in another, the <average treatment effect> is $1/2$. Under <conditional exchangeability>, <consistency in causal inference> and <positivity>, conditional outcome means identify $\tau(x)$. A predictor measured after treatment cannot simply be substituted for a pretreatment covariate without changing the causal question.
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