Incremental intervention effects in studies with dropout and many timepoints#

Kwangho Kim,Edward H. Kennedy,Ashley I. Naimi

doi:10.1515/jci-2020-0031

Kwangho Kim, Edward H. Kennedy + Show 1 more

Open Access

https://doi.org/10.1515/jci-2020-0031

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Abstract

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.

Highlights

Causal inference has long been an important scientific pursuit, and understanding causal relationships is essential across many disciplines
We showed that the incremental intervention effect adjusted for subject dropout can be identified without requiring any positivity conditions on the treatment process
Incremental interventions are a novel class of stochastic dynamic intervention where positivity assumptions can be completely avoided

Summary

Introduction

Causal inference has long been an important scientific pursuit, and understanding causal relationships is essential across many disciplines. For practical and ethical reasons, causal questions cannot always be evaluated via experimental methods (i.e., randomized trials), making observational studies the only viable alternative. When individuals can be exposed to varying treatment levels over time, collecting appropriate longitudinal data is important. Recent technological advancements that facilitate data collection are making longitudinal studies with a very large number of time points (sometimes of the same order of sample size) increasingly common (e.g. refs [1–3]). The increase in observational studies with detailed longitudinal data has introduced numerous statistical challenges that remain unaddressed.

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