Table 2

Definitions of different types of treatment effect

 Effect Potential outcome notation Description Average treatment effect (ATE) The difference between the average outcome when everyone is exposed, and the average outcome when nobody is. Average treatment effect in the treated (ATT) The ATE in the subpopulation of individuals who were actually exposed. Average treatment effect in the untreated (ATU/ATUT) The ATE in the subpopulation of individuals who were actually unexposed. Intention-to-treat effect (ITT) Average effect of being assigned to (but not necessarily receiving) the exposure. Complier average causal effect (CACE) or local average treatment effect (LATE) The ATE among the ‘compliers’, that is, the subpopulation whose exposure status was affected by the assignment mechanism.
• A denotes actual exposure status (a=1 for exposed, a=0 for unexposed). Z denotes assignment to the exposure, which may or may not have been adhered to (z=1 for assignment to the exposure, z=0 for assignment away from the exposure).