# Incremental Intervention Effects in Studies with Dropout and Many Timepoints

## TL;DR

This paper extends incremental intervention effects to longitudinal studies with dropout and many timepoints, providing new estimators and theoretical guarantees for efficient inference in complex settings.

## Contribution

It generalizes incremental intervention effects to handle multiple outcomes and dropout, deriving identifying expressions and efficient estimators with strong theoretical properties.

## Key findings

- Estimators converge at fast parametric rates.
- Incremental effects offer near-exponential gains in precision.
- Methods are validated through simulations and applied to aspirin study.

## 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.