Instrumental variables are routinely used to recover a consistent estimator of an exposure causal effect in the presence of unmeasured confounding. Instrumental variable approaches to account for non-ignorable missing data also exist, but are less familiar to epidemiologists. Like instrumental variables for exposure causal effects, instrumental variables for missing data rely on exclusion restriction and instrumental variable relevance assumptions. Yet these two conditions alone are insufficient for point identification. For estimation, researchers have invoked a third assumption, typically involving fairly restrictive parametric constraints. Inferences can be sensitive to these parametric assumptions, which are typically not empirically testable. The purpose of our paper is to discuss another approach for leveraging a valid instrumental variable. Although the approach is insufficient for nonparametric identification, it can nonetheless provide informative inferences about the presence, direction, and magnitude of selection bias, without invoking a third untestable parametric assumption. An important contribution of this paper is an Excel spreadsheet tool that can be used to obtain empirical evidence of selection bias and calculate bounds and corresponding Bayesian 95% credible intervals for a non-identifiable population proportion. For illustrative purposes, we used the spreadsheet tool to analyze HIV prevalence data collected by the 2007 Zambia Demographic and Health Survey (DHS).
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