Adjusting treatment effect for crossover type of non adherence in a two arm trial

[Venkata Ganesh]

Dear statalist,
I have a dataset from a trial where subjects were allocated to either standard of care (SOC) or to experimental treatment (ET). However, some of the subjects (20%) who were randomized to receive ET ended up receiving SOC. This switch was due to a continuous variable x and a binary categorical variable y. The outcome variable is a continuous variable. How do I adjust the treatment effect (ATE, ATET, which needs to be expressed as a mean difference with 95% CI) to arrive at a causal inference? Which would be the best method to choose: ivregress, ivtreatreg, eteffects or etregress? Is there any other better method that I need to look into?

[Fei Wang]

Venkata, you may regress outcome on actual locations of subjects and covariates, and instrument the actual location with the initial random assignment of subjects -- -ivregress- works for this case.

[Venkata Ganesh]

Dear Fei,
Thank you for the answer. If my variables were as follows
sid = continuous outcome variable
age ph = continuous covariates
gender = categorical covariate
treat (0/1) = actual treatment received (0 = SOC and 1 = ET)
alloc (0/1) = initial random allocation

then is the following command correct?

ivregress 2sls sid age ph i.gender (i.treat = i.alloc ph)

[Fei Wang]

Almost correct, Venkata, "ph" is a covariate rather than an excluded IV. Moreover, I would make another correction as both "treat" and "alloc" are 0-1 variables. You may also need to cluster SE at some level -- but I'd stop suggesting at this point as I'm unfamiliar with the experiment design. You may check how literature with similar designs clusters their SEs.

ivregress 2sls sid age ph i.gender (treat = alloc)

[Venkata Ganesh]

Thank you very much for clearing up my doubts.