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

TL;DR

This paper develops a sensitivity analysis method to bound the local average treatment effect in randomized trials where post-randomization engagement may violate the exclusion restriction, especially relevant for mobile health interventions.

Contribution

It introduces a novel sensitivity analysis procedure that provides sharp bounds on treatment effects when the exclusion restriction is potentially violated due to engagement.

Findings

Method shows good finite-sample performance in simulations.

Recovers local average treatment effects under correct sensitivity parameter specification.

Applied successfully to a diabetes self-care mobile intervention trial.

Abstract

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.