I’ve seen a general trend (and this comes from mainly speaking to people and random readings, so nothing I can point to) to use blanket statements such as: if you have missing data then “intention to treat requires imputation” and “if you do not use imputation then your analyses are per protocol” - I strongly disagree, but I would like somebody to either tell me I’m wrong or to confirm/adjust my thinking below:
As I see it, ITT and PP are not even on the same spectrum. ITT is the effect of being allocated to treatment, in do-calculus it is p(Y | do(A = 1)) versus p(Y | do(A = 0)). PP is generally undefined, as it is entirely subjective depending on what researchers define as being compliant to the protocol. It is dependent on what we observe rather than what we do, and is therefore potentially confounded (by factors such as patient preference etc.). It would be something like p(Y | C = 1) versus p(Y | C = 0) where C = 1 is when we observe somebody being compliant and C = 0 not.
If we decide that we want to estimate ITT, and have missing data, it may mean that our ITT is biased. If MCAR, we lose some power but the ITT is unbiased. If data is MAR we could be helped by imputation. If data is MNAR we could also be helped by imputation if we allow for assumptions. My point is that in neither case does the ITT estimate suddenly become a PP estimate. It may be a really bad ITT estimate, but it is still an attempt to estimate ITT.
What I’m trying to fight against are blanket statements which suggest that something should “always be done” - surely we must look at each study uniquely and sometimes we may decide that imputation is the way to go, and sometimes not, and yet still talk about ITT estimates. In some cases we may prefer a non-imputed ITT estimate with a thorough attrition/sensitivity analysis to understand the potential risk of bias. Using imputation as a way to “hide bias under the rug” is in my eyes worse, I would rather researchers did a proper assessment of the risk of bias than show me what MICE produced (with all due respect to MICE which is a pretty fantastic).
Tell me I’m wrong (or not).