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Abstract:
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Instrumental variables (IVs) are commonly used to estimate effects of a treatment afflicted by unmeasured confounding, and in practice IVs are often continuous (e.g., measures of distance, or treatment preference). However, available methods for continuous IVs have important limitations: they either require restrictive parametric assumptions for identification, or else rely on modeling both the outcome and treatment process well (and require modeling effect modification by all adjustment covariates). In this work we develop the first semiparametric doubly robust estimators of the local IV effect curve, i.e., the effect among those who would take treatment for IV values above some threshold and not below. In addition to being robust to misspecification of either the IV or treatment/outcome processes, our approach also incorporates information about the IV 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 IV.
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