- [[intent-to-treat]], [[potential treatment]], [[compliance classes]] # Idea In a [[randomized controlled trial]], we can assign subjects to treatment, $Z$. But not everyone assigned treatment will actually receive the treatment, which we denote with $A$. And let $Y$ be the outcome. Example: We randomly assign Twitter users to either treatment or control group ($Z$). We want the treatment to be whether they were shown ads on Twitter ($A$), and we measure the effects of ads on their behavior on Twitter ($Y$). ![[s20220517_084119.png]] With [[non-compliance]], a randomized trial looks like an observational study. There could be confounding based on treatment received—there are common causes $X$ that might influence whether treatment was received $A$ and the outcome $Y$. But because it's a randomized trial, we can assume that treatment assignment $Z$ does not directly affect $Y$ (and thus, $Z$ is an [[instrumental variables|instrument]]). # References - [Randomized trials with noncompliance - Instrumental Variables Methods | Coursera](https://www.coursera.org/learn/crash-course-in-causality/lecture/I21jb/randomized-trials-with-noncompliance)