= Baseline covariate
A baseline covariate is measured before treatment assignment or exposure. A prognostic baseline covariate predicts the outcome. Adjusting for such variables in a <randomized controlled trial> can improve <statistical efficiency> without conditioning on a treatment consequence. For example, if $Y=\tau Z+\gamma X+\varepsilon$ with randomized $Z$ independent of $X$, adjustment for $X$ reduces the unexplained <variance> from $\gamma^2\operatorname{Var}(X)+\operatorname{Var}(\varepsilon)$ to $\operatorname{Var}(\varepsilon)$. This precision role of prognostic baseline adjustment is described in https://www.fda.gov/media/148910/download[the FDA statistical guidance on covariate adjustment].
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