Doubly robust (DR) estimators are an important class of statistics derived from a theory of semiparametric efficiency. They have become a popular tool in causal inference, including applications to dynamic treatment regimes. The doubly robust estimators for the mean response to a dynamic treatment regime may be conceived through the augmented inverse probability weighted (AIPW) estimating function, defined as the sum of the inverse probability weighted (IPW) estimating function and an augmentation term. The IPW estimating function of the causal estimand via marginal structural model is defined as the complete-case score function for those subjects whose treatment sequence is consistent with the dynamic regime in question divided by the probability of observing the treatment sequence given the subject's treatment and covariate histories. The augmentation term is derived by projecting the IPW estimating function onto the nuisance tangent space and has mean-zero under the truth. The IPW estimator of the causal estimand is consistent if (i) the treatment assignment mechanism is correctly modeled and the AIPW estimator is consistent if either (i) is true or (ii) nested functions of intermediate and final outcomes are correctly modeled. Hence, the AIPW estimator is doubly robust and, moreover, the AIPW is semiparametric efficient if both (i) and (ii) are true simultaneously. Unfortunately, DR estimators can be inferior when either (i) or (ii) is true and the other false. In this case, the misspecified parts of the model can have a detrimental effect on the variance of the DR estimator. We propose an improved DR estimator of causal estimand in dynamic treatment regimes through a technique originally developed by [4] which aims to mitigate the ill-effects of model misspecification through a constrained optimization. In addition to solving a doubly robust system of equations, the improved DR estimator simultaneously minimizes the asymptotic variance of the estimator under a correctly specified treatment assignment mechanism but misspecification of intermediate and final outcome models. We illustrate the desirable operating characteristics of the estimator through Monte Carlo studies and apply the methods to data from a randomized study of integrilin therapy for patients undergoing coronary stent implantation. The methods proposed here are new and may be used to further improve personalized medicine, in general.

中文翻译：

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动态制度边际均值模型的改进双稳健估计

双稳健（DR）估计量是从半参数效率理论衍生而来的一类重要的统计量。它们已成为因果推理中的流行工具，包括在动态治疗方案中的应用。可以通过增强的逆概率加权（AIPW）估计函数来构想针对动态治疗方案的平均响应的双稳健估计量，该增强的逆估计概率加权函数被定义为逆概率加权（IPW）估计函数与增加项之和。通过边际结构模型将因果估计的IPW估计函数定义为那些受试者的完整病例评分函数，这些受试者的治疗顺序与所讨论的动态方案一致，除以观察到给定受试者治疗的治疗顺序的概率，并对其进行协变量历史。扩展项是通过将IPW估计函数投影到有害切线空间而得出的，并且在真实情况下均值为零。如果（i）正确地建立了治疗分配机制，并且（i）是正确的，或者（ii）中间和最终结果的嵌套函数被正确地建模，则因果估计的IPW估计器是一致的，而AIPW估计器是一致的。因此，AIPW估计器具有双重鲁棒性，此外，如果同时（i）和（ii）都为真，则AIPW是半参数有效的。不幸的是，当（i）或（ii）为真而另一个为假时，DR估计量可能会较差。在这种情况下，模型的错误指定部分可能会对DR估算器的方差产生不利影响。我们提出了一种改进的因果估计，通过动态治疗方案中的因果估计的DR估计，该技术最初由[4]开发，旨在通过约束优化来减轻模型错误指定的不良影响。除了求解方程组的双重健壮性之外，改进的DR估计器在正确指定的治疗分配机制下还会使估计器的渐近方差最小，而中间和最终结果模型的规格不正确。我们通过蒙特卡洛研究说明了估计器的理想操作特性，并将该方法应用于来自整体药物治疗冠状动脉支架植入患者的整体研究的数据。此处提出的方法是新方法，通常可用于进一步改进个性化医学。