Structural Mean Effects of Noncompliance

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Abstract
A randomized, placebo-controlled blood pressure (BP) reduction trial has recorded compliance measures by electronic monitoring. Causal questions regarding dose effects are of interest, but one often wants to avoid the assumption that compliance quantiles on both randomized arms are comparable. Structural mean models (SMMs) do avoid this assumption; however, they do not allow for interaction effects between variables observed on different randomized arms. Such an interaction between observed exposure on the treatment arm and latent treatmentfree response (i. e., placebo response) was suggested by the data. Building on structural models, we propose an approach that makes this possible. To allow for a structural interaction effect with potential placebo response, we invoke a compliance selection model. It turns out that SMMs imply identifiable selection models; hence the secondary model is testable. Next, to assess the amount of variation explained by the structural model, we identify separate variance compo...

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