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Estimation of local average treatment effects in randomized trials typicallyrequires an assumption known as the exclusion restriction in cases where we areunwilling to rule out unmeasured confounding. Under this assumption, anybenefit from treatment would be mediated through the post-randomizationvariable being conditioned upon, and would be directly attributable to neitherthe randomization itself nor its latent descendants. Recently, there has beeninterest in mobile health interventions to provide healthcare support; suchstudies can feature one-way content and/or two-way content, the latter of whichallowing subjects to engage with the intervention in a way that can beobjectively measured on a subject-specific level (e.g., proportion of textmessages receiving a response). It is hence highly likely that a benefitachieved by the intervention could be explained in part by receipt of theintervention content and in part by engaging with/responding to it. Whenseeking to characterize average causal effects conditional onpost-randomization engagement, the exclusion restriction is therefore all butsurely violated. In this paper, we propose a conceptually intuitive sensitivityanalysis procedure for this setting that gives rise to sharp bounds on localaverage treatment effects. A wide array of simulation studies reveal thisapproach to have very good finite-sample behavior and to recover local averagetreatment effects under correct specification of the sensitivity parameter. Weapply our methodology to a randomized trial evaluating a text message-deliveredintervention for Type 2 diabetes self-care.

Bounding the local average treatment effect in an instrumental variable analysis of engagement with a mobile intervention