  Estimation of local average treatment effects in randomized trials typically
requires an assumption known as the exclusion restriction in cases where we are
unwilling to rule out unmeasured confounding. Under this assumption, any
benefit from treatment would be mediated through the post-randomization
variable being conditioned upon, and would be directly attributable to neither
the randomization itself nor its latent descendants. Recently, there has been
interest in mobile health interventions to provide healthcare support; such
studies can feature one-way content and/or two-way content, the latter of which
allowing subjects to engage with the intervention in a way that can be
objectively measured on a subject-specific level (e.g., proportion of text
messages receiving a response). It is hence highly likely that a benefit
achieved by the intervention could be explained in part by receipt of the
intervention content and in part by engaging with/responding to it. When
seeking to characterize average causal effects conditional on
post-randomization engagement, the exclusion restriction is therefore all but
surely violated. In this paper, we propose a conceptually intuitive sensitivity
analysis procedure for this setting that gives rise to sharp bounds on local
average treatment effects. A wide array of simulation studies reveal this
approach to have very good finite-sample behavior and to recover local average
treatment effects under correct specification of the sensitivity parameter. We
apply our methodology to a randomized trial evaluating a text message-delivered
intervention for Type 2 diabetes self-care.
