Instrumental Variable Analyses and Selection Bias

Abstract

Instrumental variables (IV) are used to draw causal conclusions about the effect of exposure E on outcome Y in the presence of unmeasured confounders. IV assumptions have been well described: (1) IV affects E; (2) IV affects Y only through E; (3) IV shares no common cause with Y. Even when these assumptions are met, biased effect estimates can result if selection bias allows a noncausal path from E to Y. We demonstrate the presence of bias in IV analyses on a sample from a simulated dataset, where selection into the sample was a collider on a noncausal path from E to Y. By applying inverse probability of selection weights, we were able to eliminate the selection bias. IV approaches may protect against unmeasured confounding but are not immune from selection bias. Inverse probability of selection weights used with IV approaches can minimize bias.

Figure 1

Directed Acyclic Graph (DAG) depicting the association between exposure E and outcome Y with unmeasured confounder U. Selecting on binary selection variable, S, induces a non-causal pathway between the instrumental variable (IV) and Y through E→[S]←C→Y.