- [[non-compliance]]
# Idea
We can classify people based on [[potential treatment]] ($A$) and treatment assigned ($Z$). These four categories are part of the [[Neyman-Rubin causal model|Rubin causal model]] and is known as principal stratification (compliance classes are known as **principal strata**). This classification comes from pharmaceutical science.
## Each group (row) is a subpopulation
$Z$ is treatment assignment (0 or 1) and $A$ is treatment received (0 or 1).
| Z = 0 | Z = 1 | subpopulation | note |
| ------------ | ------------ | ------------- | ---------------------------------------------------------------------------------------------------------------------------------- |
| Z = 0, A = 0 | Z = 1, A = 0 | never-takers | There's no variation in treatment received. We won't learn anything about the effect of treatment. |
| Z = 0, A = 0 | Z = 1, A = 1 | compliers | Treatment is randomized. Best case scenario. |
| Z = 0, A = 1 | Z = 1, A = 0 | defiers | Do the opposite of what they're encouraged to do. Treatment is randomized, but in the opposite way. Tend to be a very small group. |
| Z = 0, A = 1 | Z = 1, A = 1 | always-takers | No variation in treatment received. |
# References
- [Compliance classes - Instrumental Variables Methods | Coursera](https://www.coursera.org/learn/crash-course-in-causality/lecture/6xNuD/compliance-classes)
- [09 - Non Compliance and LATE — Causal Inference for the Brave and True](https://matheusfacure.github.io/python-causality-handbook/09-Non-Compliance-and-LATE.html)