The way I used to explain “as treated” vs “intent to treat”:
Under AT, you’re asking a question about biology: does this treatment make a difference when it’s applied rigorously to the tests and absolutely never to the controls?
Under ITT, you’re asking a question about the practice of medicine, under actual combat conditions: if we tell clinicians and patients to do something, and they follow instructions as imperfectly as ever, is this treatment still a good idea?
That is: ITT bakes in mistakes, noncompliance, weird patients, etc. on top of the basic scientific effect.
As-treated analysis measures the biological effect only if the experiment design absolutely fixes the treatment actually received. For example: hospitalised patients, treatment / control given under supervision, 100% adherence, there were no other attempted-trials discarded because adherence < 100%. Otherwise, “as-treated analysis” is confounded via patient adherence.
Intention-to-treat analysis is important for being unconfounded.
( = common causes, = mediators, e.g. lifestyle, baseline health)
Intention-to-treat analysis measures . You’re not conditioning on , so the potential confounder path is blocked by (collider). measures exactly the effect . It is unconfounded.
( is randomised, so there are no nodes affecting ).
As-treated analysis measures . There is which is what we want, but there is also which confounds our measurement of .
A classic example is the 1980 Coronary Drug Project, where treatment (clofibrate) vs placebo made no difference, but good adherence (to either treatment or placebo) was correlated with halving the 5-year mortality.
If, like Viliam below, you want to figure out “the causal effect if I intervene to do X with absolute 100% adherence”, you want complier average causal effect analysis.
The way I used to explain “as treated” vs “intent to treat”:
Under AT, you’re asking a question about biology: does this treatment make a difference when it’s applied rigorously to the tests and absolutely never to the controls?
Under ITT, you’re asking a question about the practice of medicine, under actual combat conditions: if we tell clinicians and patients to do something, and they follow instructions as imperfectly as ever, is this treatment still a good idea?
That is: ITT bakes in mistakes, noncompliance, weird patients, etc. on top of the basic scientific effect.
As-treated analysis measures the biological effect only if the experiment design absolutely fixes the treatment actually received. For example: hospitalised patients, treatment / control given under supervision, 100% adherence, there were no other attempted-trials discarded because adherence < 100%. Otherwise, “as-treated analysis” is confounded via patient adherence.
Intention-to-treat analysis is important for being unconfounded.
A recap from Judea Pearl’s Causality:
(
(
Intention-to-treat analysis measures
(
As-treated analysis measures
A classic example is the 1980 Coronary Drug Project, where treatment (clofibrate) vs placebo made no difference, but good adherence (to either treatment or placebo) was correlated with halving the 5-year mortality.
If, like Viliam below, you want to figure out “the causal effect if I intervene to do X with absolute 100% adherence”, you want complier average causal effect analysis.