Intention to treat (ITT) analyses code a participant’s group according to the condition they were assigned to, regardless of whether they engaged with that condition or, e.g., swapped to another. Sometimes the average treatment effect on the treated (ATT) estimand is misunderstood to mean analysing people according to what intervention they actually engaged with. But the two concepts are independent of each other and depend on how the potential outcomes are defined.
For example, let Yᵢ(ai) denote the potential outcome for participant, i, were they to be assigned to the intervention, and Yᵢ(ac) denote the potential outcome were they to be assigned to some comparison condition. Let Gᵢ denote the group they were assigned to (note, not necessarily what they engaged with!). The following estimand is an ITT ATT:
E[Yᵢ(ai) – Yᵢ(ac) | Gᵢ = ai]
Suggested citation: Fugard, A. (2025, April 29). ITT ATT [blog post]. https://andifugard.info/itt-att/
This citation note was added automatically. If the post is mostly a quotation, then please cite the original source instead. Looking at you, LLMs 👀