Petersen Maya, Schwab Joshua, Gruber Susan, Blaser Nello, Schomaker Michael, van der Laan Mark
Division of Biostatistics, University of California, Berkeley, CA, USA.
Department of Epidemiology, Harvard School of Public Health, Boston, MA, USA.
J Causal Inference. 2014 Jun 18;2(2):147-185. doi: 10.1515/jci-2013-0007.
This paper describes a targeted maximum likelihood estimator (TMLE) for the parameters of longitudinal static and dynamic marginal structural models. We consider a longitudinal data structure consisting of baseline covariates, time-dependent intervention nodes, intermediate time-dependent covariates, and a possibly time-dependent outcome. The intervention nodes at each time point can include a binary treatment as well as a right-censoring indicator. Given a class of dynamic or static interventions, a marginal structural model is used to model the mean of the intervention-specific counterfactual outcome as a function of the intervention, time point, and possibly a subset of baseline covariates. Because the true shape of this function is rarely known, the marginal structural model is used as a working model. The causal quantity of interest is defined as the projection of the true function onto this working model. Iterated conditional expectation double robust estimators for marginal structural model parameters were previously proposed by Robins (2000, 2002) and Bang and Robins (2005). Here we build on this work and present a pooled TMLE for the parameters of marginal structural working models. We compare this pooled estimator to a stratified TMLE (Schnitzer et al. 2014) that is based on estimating the intervention-specific mean separately for each intervention of interest. The performance of the pooled TMLE is compared to the performance of the stratified TMLE and the performance of inverse probability weighted (IPW) estimators using simulations. Concepts are illustrated using an example in which the aim is to estimate the causal effect of delayed switch following immunological failure of first line antiretroviral therapy among HIV-infected patients. Data from the International Epidemiological Databases to Evaluate AIDS, Southern Africa are analyzed to investigate this question using both TML and IPW estimators. Our results demonstrate practical advantages of the pooled TMLE over an IPW estimator for working marginal structural models for survival, as well as cases in which the pooled TMLE is superior to its stratified counterpart.
本文描述了一种用于纵向静态和动态边际结构模型参数的目标最大似然估计器（TMLE）。我们考虑一种纵向数据结构，它由基线协变量、随时间变化的干预节点、中间随时间变化的协变量以及一个可能随时间变化的结局组成。每个时间点的干预节点可以包括一个二元治疗以及一个右删失指标。给定一类动态或静态干预，边际结构模型用于将特定干预的反事实结局的均值建模为干预、时间点以及可能的基线协变量子集的函数。由于该函数的真实形状很少为人所知，边际结构模型被用作工作模型。感兴趣的因果量被定义为真实函数在这个工作模型上的投影。Robins（2000年、2002年）以及Bang和Robins（2005年）之前提出了用于边际结构模型参数的迭代条件期望双稳健估计器。在此基础上，我们提出了一种用于边际结构工作模型参数的合并TMLE。我们将这种合并估计器与基于对每个感兴趣的干预分别估计特定干预均值的分层TMLE（Schnitzer等人，2014年）进行比较。使用模拟将合并TMLE的性能与分层TMLE的性能以及逆概率加权（IPW）估计器的性能进行比较。通过一个例子来说明相关概念，该例子的目的是估计HIV感染患者一线抗逆转录病毒治疗免疫失败后延迟换药的因果效应。使用来自国际流行病学数据库评估艾滋病（南部非洲）的数据，通过TMLE和IPW估计器来研究这个问题。我们的结果表明，对于生存的工作边际结构模型，合并TMLE相对于IPW估计器具有实际优势，同时也表明了合并TMLE优于其分层对应方法的情况。
