Identification of dynamic treatment effects when treatment histories are partially observed

This paper proposes a class of methods for identifying and estimating dynamic treatment effects when outcomes depend on the entire treatment path and treatment histories are only partially observed. We advocate for the approach which we refer to as `robust' that identifies path-dependent treatment effects for different mover subpopulations under misspecification of any one of three models involved (outcome, propensity score, or missing data models). Our approach can handle fixed, absorbing, sequential, or simultaneous treatment regimes where missing treatment histories may obfuscate identification of causal effects. Numerical experiments demonstrate how the proposed estimator compares to traditional complete-case methods. We find that the missingness-adjusted estimates have negligible bias compared to their complete-case counterparts. As an illustration, we apply the proposed class of adjustment methods to estimate dynamic effects of COVID-19 on voter turnout in the 2022 U.S. general elections. We find that counties that experienced above-average number of cases in 2020 and 2021 had a statistically significant reduction in voter turnout compared to those that did not.