Covariate

A covariate is an observed explanatory variable used to model the conditional distribution of a response. A vector of covariates can enter a linear predictor, a treatment-effect adjustment or a hazard multiplier. Conditioning on a covariate does not itself establish that its effect is causal.

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 $Y=\tau Z+\gamma X+\epsilon$ with randomized $Z$ independent of $X$, adjustment for $X$ reduces the unexplained variance from ${\gamma }^2\mathrm{Var}(X)+\mathrm{Var}(\epsilon )$ to $\mathrm{Var}(\epsilon )$. This precision role of prognostic baseline adjustment is described in the FDA statistical guidance on covariate adjustment.