Controlling time-varying confounding in difference-in-differences studies using the time-varying treatments framework.

Abstract

This article clarifies how the biostatistical literature on time-varying treatments (TVT) can provide tools for dealing with time-varying confounding in difference-in-differences (DiD) studies. I use a simulation study to compare the bias and standard error of inverse probability weighting estimators from the TVT framework, a DiD framework, and hybrid approaches that combine ideas from both frameworks. I simulated longitudinal data with treatment effect heterogeneity over multiple time points using linear and logistic models. Simulation settings looked at both time-invariant confounders and time-varying confounders affected by prior treatment. Estimators that combined ideas from both frameworks had lower bias than standard TVT and DiD estimators when assumptions were unmet. The TVT framework provides estimation tools that can complement DiD tools in a wide range of applied settings. It also provides alternate estimands for consideration in policy settings.