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Instrumental variables are commonly used to estimate effects of a treatmentafflicted by unmeasured confounding, and in practice instruments are oftencontinuous (e.g., measures of distance, or treatment preference). However,available methods for continuous instruments have important limitations: theyeither require restrictive parametric assumptions for identification, or elserely on modeling both the outcome and treatment process well (and requiremodeling effect modification by all adjustment covariates). In this work wedevelop the first semiparametric doubly robust estimators of the localinstrumental variable effect curve, i.e., the effect among those who would taketreatment for instrument values above some threshold and not below. In additionto being robust to misspecification of either the instrument ortreatment/outcome processes, our approach also incorporates information aboutthe instrument mechanism and allows for flexible data-adaptive estimation ofeffect modification. We discuss asymptotic properties under weak conditions,and use the methods to study infant mortality effects of neonatal intensivecare units with high versus low technical capacity, using travel time as aninstrument.

Robust causal inference with continuous instruments using the local instrumental variable curve