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.
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BibTeX
@misc{dukes2026differenceindifferences,
title = {{Difference-in-Differences for Heterogeneous Effects of General Treatment Strategies Accounting for Time-Varying Covariates}},
author = {Oliver Dukes and Zach Shahn and James Robins and Andrea Rotnitzky},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22113},
eprint = {2610.22113},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22113},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Difference-in-Differences for Heterogeneous Effects of General Treatment Strategies Accounting for Time-Varying Covariates
AU - Oliver Dukes
AU - Zach Shahn
AU - James Robins
AU - Andrea Rotnitzky
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.22113
UR - https://arxiv.org/abs/2610.22113
AB - 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.
ER -