We link and extend two approaches to estimating time-varying treatment effects on repeated continuous outcomes--time-varying Difference in Differences (DiD; see Roth et al. (2023) and Chaisemartin et al. (2023) for reviews) and Structural Nested Mean Models (SNMMs; see Vansteelandt and Joffe (2014) for a review). In particular, we show that SNMMs, which were previously only known to be nonparametrically identified under a no unobserved confounding assumption, are also identified under a generalized version of the parallel trends assumption typically used to justify time-varying DiD methods. Because SNMMs model a broader set of causal estimands, our results allow practitioners of existing time-varying DiD approaches to address additional types of substantive questions under similar assumptions. SNMMs enable estimation of time-varying effect heterogeneity, lasting effects of a `blip' of treatment at a single time point, effects of sustained interventions (possibly on continuous or multi-dimensional treatments) when treatment repeatedly changes value in the data, controlled direct effects, effects of dynamic treatment strategies that depend on covariate history, and more. Our results also allow analysts who apply SNMMs under the no unobserved confounding assumption to estimate some of the same causal effects under alternative identifying assumptions. We provide a method for sensitivity analysis to violations of our parallel trends assumption. We further explain how to estimate optimal treatment regimes via optimal regime SNMMs under parallel trends assumptions plus an assumption that there is no effect modification by unobserved confounders. Finally, we illustrate our methods with real data applications estimating effects of Medicaid expansion on uninsurance rates, effects of floods on flood insurance take-up, and effects of sustained changes in temperature on crop yields.

翻译：本文将两种估计重复连续结果上时变处理效应的方法——时变双重差分法（DiD；参见 Roth 等人（2023）和 Chaisemartin 等人（2023）的综述）与结构嵌套均值模型（SNMMs；参见 Vansteelandt 和 Joffe（2014）的综述）——联系起来并加以扩展。具体而言，我们证明，先前仅在无未观测混杂假设下被确认为非参数可识别的 SNMMs，在通常用于论证时变 DiD 方法的平行趋势假设的广义版本下同样可识别。由于 SNMMs 能够建模更广泛的因果估计量，我们的研究结果使得现有时变 DiD 方法的使用者能够在相似的假设下处理更多类型的实质性研究问题。SNMMs 支持估计时变效应异质性、单时间点“脉冲”处理的持续效应、当处理在数据中反复变化时持续干预（可能针对连续或多维处理）的效应、受控直接效应、依赖于协变量历史的动态治疗策略效应等。我们的结果也使得在无未观测混杂假设下应用 SNMMs 的分析者能够在替代的识别假设下估计部分相同的因果效应。我们提供了一种针对平行趋势假设被违反的敏感性分析方法。我们进一步解释了如何在平行趋势假设外加一个“未观测混杂因素无效应修饰”的假设下，通过最优治疗策略 SNMMs 来估计最优治疗策略。最后，我们通过实际数据应用来阐述我们的方法，包括估计医疗补助扩展对未参保率的影响、洪水对洪水保险参保率的影响，以及持续温度变化对作物产量的影响。