Difference-in-Differences for Heterogeneous Effects of General Treatment Strategies Accounting for Time-Varying Covariates

Abstract

We introduce a class of marginal Structural Nested Mean Models (mSNMMs) that enable modeling time-varying effect modification by a subset of covariates required as adjustment variables. We focus on identifiability and estimation under conditional parallel trends assumptions, so mSNMMs are applicable in settings where time-varying Difference-in-Differences (DiD) methods are typically applied. Modeling effect modification by lower dimensional covariates reduces the risk of model misspecification and can improve interpretability relative to previously developed `full SNMMs'. mSNMMs enjoy two key advantages over alternative time-varying DiD methods. First, the parallel trends assumptions that they require are more plausible in the presence of time-varying confounding. Second, they are able to model effects of \textit{sustained} interventions even when treatment switches on and off in the data. We illustrate the methodology by applying mSNMMs to estimate how the effects of Medicaid expansion (a time-varying treatment) on local uninsurance rates vary with unemployment rate prior to expansion (a time-varying covariate), adjusting for additional time-varying demographic and economic variables.