Intention-to-treat analysis

An intention-to-treat analysis compares participants according to their randomized assignment, retaining that assignment even when they do not use the assigned intervention. Its causal effect is the effect of assignment under the study's actual adherence pattern, rather than the effect of perfect adherence. Randomization protects this comparison from baseline confounding; missing data can still require assumptions or additional analysis.

A treatment consequence is not interchangeable with a baseline covariate in an intention-to-treat analysis. Let randomized $Z$ be independent of $U,\epsilon$, and let actual intervention use be $D=Z+U$, with $Y=D+\epsilon$ and independent centered errors. The assignment changes the mean outcome by one. But the conditional expectation $\mathbb{E}[Y\mid Z,D]=D$ has coefficient zero on $Z$. Thus adjustment for the post-randomization variable $D$ changes the estimand even in a simple identified linear regression.