Incremental Intervention Effects in Studies with Dropout and Many Timepoints
This work addresses methodological challenges in causal inference for longitudinal data, offering improved precision for researchers in fields like epidemiology, though it is incremental as it builds on existing incremental intervention frameworks.
The authors tackled the problem of estimating causal effects in longitudinal studies with many timepoints, dropout, and positivity violations by generalizing incremental interventions to handle multiple outcomes and dropout, showing that their estimators converge at parametric rates and yield near-exponential gains in statistical precision in infinite time horizon settings.
Modern longitudinal studies collect feature data 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 intervention 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 variance ratio of incremental intervention 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 intervention effects yield near-exponential gains in statistical precision in this setup. Finally we conclude with simulations and apply our methods in a study of the effect of low-dose aspirin on pregnancy outcomes.