  The Wisconsin Smoker's Health Study (WSHS2) was a longitudinal trial
conducted to compare the effectiveness of two commonly used smoking cessation
treatments, varenicline and combination nicotine replacement therapy (cNRT)
with the less intense standard of care, nicotine patch. The main outcome of the
WSHS2 study was that all three treatments had equivalent treatment effects.
However, in-depth analysis of the compliance data collected via ecological
momentary assessment (EMA) were not analyzed. Compliance to the treatment
regimens may represent a confounder as varenicline and cNRT are more intense
treatments and would likely have larger treatment effects if all subjects
complied. In order to estimate the causal compliance effect, we view the
counterfactual, the outcome that would have been observed if the subject was
allocated to the treatment counter to the fact, as a missing data problem and
proceed to impute the counterfactual. Our contribution to the methodological
literature lies in the extension of this idea to a more general analytic
approach that includes mediators and confounders of the mediator-outcome
relationship. Simulation results suggest that our method works well and
application to the WSHS2 data suggest that the treatment effect of nicotine
patch, varenicline, and cNRT are equivalent after accounting for differences in
treatment compliance.

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