Identifying and estimating effects of sustained interventions under parallel trends assumptions

TL;DR

This paper develops new methods to estimate the effects of sustained interventions over time under parallel trends assumptions, addressing limitations of existing approaches in observational studies.

Contribution

It derives identification results and proposes estimators for population effects of sustained treatments, extending difference-in-differences to more complex intervention scenarios.

Findings

Simulation studies support estimator performance at realistic sample sizes.

The methods successfully estimate effects of hypothetical interventions, demonstrated with COVID-19 stay-at-home order example.

Proposed estimators include inverse-probability weighting, outcome regression, and double robust approaches.

Abstract

Many research questions in public health and medicine concern sustained interventions in populations defined by substantive priorities. Existing methods to answer such questions typically require a measured covariate set sufficient to control confounding, which can be questionable in observational studies. Differences-in-differences relies instead on the parallel trends assumption, allowing for some types of time-invariant unmeasured confounding. However, most existing difference-in-differences implementations are limited to point treatments in restricted subpopulations. We derive identification results for population effects of sustained treatments under parallel trends assumptions. In particular, in settings where all individuals begin follow-up with exposure status consistent with the treatment plan of interest but may deviate at later times, a version of Robins' g-formula identifies the intervention-specific mean under SUTVA, positivity, and parallel trends. We develop consistent asymptotically normal estimators based on inverse-probability weighting, outcome regression, and a double robust estimator based on targeted maximum likelihood. Simulation studies confirm theoretical results and support the use of the proposed estimators at realistic sample sizes. As an example, the methods are used to estimate the effect of a hypothetical federal stay-at-home order on all-cause mortality during the COVID-19 pandemic in spring 2020 in the United States.