Incremental Intervention Effects in Studies with Dropout and Many Timepoints

Abstract

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.

arXiv comment52 pages

References in corpus (10)

• Nonparametric methods for doubly robust estimation of continuous treatment effects
• Breaking the Curse of Horizon: Infinite-Horizon Off-Policy Estimation
• On Inverse Probability Weighting for Nonmonotone Missing at Random Data
• Minimax-optimal nonparametric regression in high dimensions
• Instrumental Variables: An Econometrician's Perspective
• Additive Approximations in High Dimensional Nonparametric Regression via the SALSA
• Minimax-optimal rates for sparse additive models over kernel classes via convex programming
• Uniformly Valid Post-Regularization Confidence Regions for Many Functional Parameters in Z-Estimation Framework
• Sequential Double Robustness in Right-Censored Longitudinal Models
• Local average causal effects and superefficiency

Cited by in corpus (1)

• Assessing the causal effects of a stochastic intervention in time series data: Are heat alerts effective in preventing deaths and hospitalizations?