In health and social sciences, research questions often involve systematic assessment of the modification of treatment causal effect by patient characteristics. In longitudinal settings, time-varying or post-intervention effect modifiers are also of interest. In this work, we investigate the robust and efficient estimation of the Counterfactual-History-Adjusted Marginal Structural Model (van der Laan MJ, Petersen M. Statistical learning of origin-specific statically optimal individualized treatment rules. Int J Biostat. 2007;3), which models the conditional intervention-specific mean outcome given a counterfactual modifier history in an ideal experiment. We establish the semiparametric efficiency theory for these models, and present a substitution-based, semiparametric efficient and doubly robust estimator using the targeted maximum likelihood estimation methodology (TMLE, e.g. van der Laan MJ, Rubin DB. Targeted maximum likelihood learning. Int J Biostat. 2006;2, van der Laan MJ, Rose S. Targeted learning: causal inference for observational and experimental data, 1st ed. Springer Series in Statistics. Springer, 2011). To facilitate implementation in applications where the effect modifier is high dimensional, our third contribution is a projected influence function (and the corresponding projected TMLE estimator), which retains most of the robustness of its efficient peer and can be easily implemented in applications where the use of the efficient influence function becomes taxing. We compare the projected TMLE estimator with an Inverse Probability of Treatment Weighted estimator (e.g. Robins JM. Marginal structural models. In: Proceedings of the American Statistical Association. Section on Bayesian Statistical Science, 1-10. 1997a, Hernan MA, Brumback B, Robins JM. Marginal structural models to estimate the causal effect of zidovudine on the survival of HIV-positive men. EPIDEMIOLOGY 2000;11:561-570), and a non-targeted G-computation estimator (Robins JM. A new approach to causal inference in mortality studies with sustained exposure periods - application to control of the healthy worker survivor effect. Math Modell. 1986;7:1393-1512.). The comparative performance of these estimators is assessed in a simulation study. The use of the projected TMLE estimator is illustrated in a secondary data analysis for the Sequenced Treatment Alternatives to Relieve Depression (STAR*D) trial where effect modifiers are subject to missing at random.

中文翻译：

---

具有反事实效应修饰符的边际结构模型。

在健康和社会科学中，研究问题通常涉及通过患者特征对治疗因果效应的修正进行系统评估。在纵向设置中，时变或干预后效应修饰符也很有趣。在这项工作中，我们研究了反事实历史调整边际结构模型的稳健和有效估计（van der Laan MJ，Petersen M. Statistical learning of origin-specific statically optimal individualized treatment rules. Int J Biostat. 2007;3） ，它模拟了在理想实验中给定反事实修饰符历史的条件干预特定平均结果。我们为这些模型建立了半参数效率理论，并提出了一个基于替代的，使用目标最大似然估计方法（TMLE，例如 van der Laan MJ，Rubin DB。目标最大似然学习。Int J Biostat。2006；2，van der Laan MJ，Rose S。目标学习：因果inference for observational and experimental data, 1st ed. Springer Series in Statistics. Springer, 2011). 为了便于在影响修饰符是高维的应用程序中实现，我们的第三个贡献是投影影响函数（和相应的投影 TMLE 估计器），它保留了其高效对等体的大部分稳健性，并且可以在使用的应用程序中轻松实现有效的影响函数变得繁重。我们将预测的 TMLE 估计器与治疗加权估计器的逆概率（例如 Robins JM. 边际结构模型。在：美国统计协会会刊。贝叶斯统计科学部分，1-10。1997a，Hernan MA，Brumback B，Robins JM。估计齐多夫定对 HIV 阳性男性生存的因果影响的边际结构模型。EPIDEMIOLOGY 2000;11:561-570) 和非目标 G 计算估计量（Robins JM。持续暴露期死亡率研究中因果推断的新方法 - 用于控制健康工人幸存者效应的应用。Math Modell。 1986;7:1393-1512）。这些估计器的比较性能在模拟研究中进行评估。预测 TMLE 估计量的使用在用于缓解抑郁症的顺序治疗替代方案 (STAR*D) 试验的二次数据分析中得到了说明，其中效果修饰符可能会随机缺失。