A number of sophisticated estimators of longitudinal effects have been proposed for estimating the intervention-specific mean outcome. However, there is a relative paucity of research comparing these methods directly to one another. In this study, we compare various approaches to estimating a causal effect in a longitudinal treatment setting using both simulated data and data measured from a human immunodeficiency virus cohort. Six distinct estimators are considered: (i) an iterated conditional expectation representation, (ii) an inverse propensity weighted method, (iii) an augmented inverse propensity weighted method, (iv) a double robust iterated conditional expectation estimator, (v) a modified version of the double robust iterated conditional expectation estimator, and (vi) a targeted minimum loss-based estimator. The details of each estimator and its implementation are presented along with nuisance parameter estimation details, which include potentially pooling the observed data across all subjects regardless of treatment history and using data adaptive machine learning algorithms. Simulations are constructed over six time points, with each time point steadily increasing in positivity violations. Estimation is carried out for both the simulations and applied example using each of the six estimators under both stratified and pooled approaches of nuisance parameter estimation. Simulation results show that double robust estimators remained without meaningful bias as long as at least one of the two nuisance parameters were estimated with a correctly specified model. Under full misspecification, the bias of the double robust estimators remained better than that of the inverse propensity estimator under misspecification, but worse than the iterated conditional expectation estimator. Weighted estimators tended to show better performance than the covariate estimators. As positivity violations increased, the mean squared error and bias of all estimators considered became worse, with covariate-based double robust estimators especially susceptible. Applied analyses showed similar estimates at most time points, with the important exception of the inverse propensity estimator which deviated markedly as positivity violations increased. Given its efficiency, ability to respect the parameter space, and observed performance, we recommend the pooled and weighted targeted minimum loss-based estimator.

中文翻译：

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纵向治疗效果的双重稳健有效估计器：模拟和案例研究中的比较性能

已经提出了许多复杂的纵向效应估计器来估计干预特定的平均结果。然而，将这些方法直接相互比较的研究相对较少。在这项研究中，我们使用模拟数据和人类免疫缺陷病毒队列测量的数据比较了估计纵向治疗环境中因果效应的各种方法。考虑了六个不同的估计量：（i）迭代条件期望表示，（ii）逆倾向加权方法，（iii）增强逆倾向加权方法，（iv）双重稳健迭代条件期望估计，（v）修改双鲁棒迭代条件期望估计器的版本，以及 (vi) 基于目标最小损失的估计器。每个估计器及其实现的细节与令人讨厌的参数估计细节一起呈现，其中包括可能汇集所有受试者的观察数据，而不管治疗历史如何，并使用数据自适应机器学习算法。模拟是在六个时间点上构建的，每个时间点的阳性违规率稳步增加。在有害参数估计的分层和合并方法下，使用六个估计量中的每一个对模拟和应用示例进行估计。模拟结果表明，只要使用正确指定的模型估计两个有害参数中的至少一个，双重稳健估计量就不会出现有意义的偏差。在完全错误的规格下，双稳健估计量的偏差在错误指定下仍然优于逆倾向估计量，但比迭代条件期望估计量差。加权估计量往往比协变量估计量表现出更好的性能。随着阳性违规的增加，所考虑的所有估计量的均方误差和偏差变得更糟，基于协变量的双重稳健估计量特别容易受到影响。应用分析在大多数时间点显示出类似的估计，除了逆倾向估计量随着阳性违规增加而显着偏离。鉴于其效率、尊重参数空间的能力和观察到的性能，我们建议使用池化加权目标最小损失估计器。