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Abstract:
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Modern longitudinal studies feature data collected at many timepoints, often of the same order of sample size. Such studies are typically affected by dropout and positivity violations. We tackle these problems by generalizing effects of recent incremental interventions (which shift propensity scores rather than set treatment values deterministically) to accommodate multiple outcomes and subject dropout. We give an identifying expression for incremental effects when dropout is conditionally ignorable (without requiring treatment positivity), and derive the nonparametric efficiency bound for estimating such effects. Then we present efficient nonparametric estimators, showing that they converge at fast parametric rates and yield uniform inferential guarantees, even when nuisance functions are estimated flexibly at slower rates. We also study the efficiency of incremental effects relative to more conventional deterministic effects in a novel infinite time horizon setting, where the number of timepoints can grow with sample size, and show that incremental effects yield near-exponential efficiency gains. Finally, we apply our methods to study the effect of aspirin on pregnancy outcomes.
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