Social scientists are often interested in estimating the marginal effects of a time-varying treatment on an end-of-study continuous outcome. With observational data, estimating these effects is complicated by the presence of time-varying confounders affected by prior treatments, which may lead to bias in conventional regression and matching estimators. In this situation, inverse-probability-of-treatment-weighted (IPTW) estimation of a marginal structural model remains unbiased if treatment assignment is sequentially ignorable and the conditional probability of treatment is correctly modeled, but this method is not without limitations. In particular, it is difficult to use with continuous treatments, and it is relatively inefficient. This article explores using an alternative regression-based method—regression-with-residuals (RWR) estimation of a constrained structural nested mean model—that may overcome some of these limitations in practice. It is unbiased for the marginal effects of a time-varying treatment if treatment assignment is sequentially ignorable, the treatment effects of interest are invariant across levels of the confounders, and a model for the conditional mean of the outcome is correctly specified. The performance of RWR estimation relative to IPTW estimation is evaluated with a series of simulation experiments and with an empirical example based on longitudinal data from the Panel Study of Income Dynamics. Results indicate that it may outperform IPTW estimation in certain situations.

中文翻译：

---

时变混杂因素的基于回归的调整

社会科学家通常对估计随时间变化的治疗对研究结束连续结果的边际影响感兴趣。对于观察数据，由于受先前治疗影响的时变混杂因素的存在，估计这些影响变得复杂，这可能导致传统回归和匹配估计量的偏差。在这种情况下，如果治疗分配顺序可忽略并且治疗的条件概率被正确建模，则边缘结构模型的逆概率治疗加权 (IPTW) 估计保持无偏，但这种方法并非没有限制。尤其是连续处理使用困难，效率相对较低。本文探讨了使用另一种基于回归的方法——约束结构嵌套均值模型的残差回归 (RWR) 估计——它可能会在实践中克服其中的一些限制。如果治疗分配顺序可忽略，感兴趣的治疗效果在混杂因素的水平上是不变的，并且正确指定了结果的条件均值模型，则时变治疗的边际效应是无偏的。RWR 估计相对于 IPTW 估计的性能通过一系列模拟实验和基于收入动态面板研究纵向数据的经验示例进行评估。结果表明，它在某些情况下可能优于 IPTW 估计。