Instrumental variable (IV) analysis is used to address unmeasured confounding when comparing two nonrandomized treatment groups. The local average treatment effect (LATE) is a causal estimand that can be identified by an IV. The LATE approach is appealing because its identification relies on weaker assumptions than those in other IV approaches requiring a homogeneous treatment effect assumption. If the instrument is confounded by some covariates, then one can use a weighting estimator, for which the outcome and treatment are weighted by instrumental propensity scores. The weighting estimator for the LATE has a large variance when the IV is weak and the target population, i.e., the compliers, is relatively small. We propose a truncated LATE that can be estimated more reliably than the regular LATE in the presence of a weak IV. In our approach, subjects who contribute substantially to the weak IV are identified by their probabilities of being compliers, and they are removed based on a pre-specified threshold. We discuss interpretation of the proposed estimand and related inference method. Simulation and real data experiments demonstrate that the proposed truncated LATE can be estimated more precisely than the standard LATE.
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