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

Instrumental variables are commonly used to estimate effects of a treatment afflicted by unmeasured confounding, and in practice instruments are often continuous (e.g. measures of distance, or treatment preference). However, available methods for continuous instruments have important limitations: they either require restrictive parametric assumptions for identification, or else rely on modelling both the outcome and the treatment process well (and require modelling effect modification by all adjustment covariates). In this work we develop the first semiparametric doubly robust estimators of the local instrumental variable effect curve, i.e. the effect among those who would take treatment for instrument values above some threshold and not below. In addition to being robust to misspecification of either the instrument or treatment or outcome processes, our approach also incorporates information about the instrument mechanism and allows for flexible data‐adaptive estimation of effect modification. We discuss asymptotic properties under weak conditions and use the methods to study infant mortality effects of neonatal intensive care units with high versus low technical capacity, using travel time as an instrument.