Department of Biostatistics, School of Public Health, Fudan University, Shanghai, China.
Key Laboratory of Public Health Safety of Ministry of Education, Fudan University, Shanghai, China.
BMC Med Res Methodol. 2022 Dec 28;22(1):337. doi: 10.1186/s12874-022-01822-3.
Estimating the average effect of a treatment, exposure, or intervention on health outcomes is a primary aim of many medical studies. However, unbalanced covariates between groups can lead to confounding bias when using observational data to estimate the average treatment effect (ATE). In this study, we proposed an estimator to correct confounding bias and provide multiple protection for estimation consistency.
With reference to the kernel function-based double-index propensity score (Ker.DiPS) estimator, we proposed the artificial neural network-based multi-index propensity score (ANN.MiPS) estimator. The ANN.MiPS estimator employed the artificial neural network to estimate the MiPS that combines the information from multiple candidate models for propensity score and outcome regression. A Monte Carlo simulation study was designed to evaluate the performance of the proposed ANN.MiPS estimator. Furthermore, we applied our estimator to real data to discuss its practicability.
The simulation study showed the bias of the ANN.MiPS estimators is very small and the standard error is similar if any one of the candidate models is correctly specified under all evaluated sample sizes, treatment rates, and covariate types. Compared to the kernel function-based estimator, the ANN.MiPS estimator usually yields smaller standard error when the correct model is incorporated in the estimator. The empirical study indicated the point estimation for ATE and its bootstrap standard error of the ANN.MiPS estimator is stable under different model specifications.
The proposed estimator extended the combination of information from two models to multiple models and achieved multiply robust estimation for ATE. Extra efficiency was gained by our estimator compared to the kernel-based estimator. The proposed estimator provided a novel approach for estimating the causal effects in observational studies.
估计治疗、暴露或干预对健康结果的平均效果是许多医学研究的主要目标。然而，当使用观察数据估计平均治疗效果（ATE）时，组间不平衡的协变量会导致混杂偏差。在这项研究中，我们提出了一种估计器来纠正混杂偏差，并为估计一致性提供多重保护。
我们参考基于核函数的双索引倾向评分（Ker.DiPS）估计量，提出了基于人工神经网络的多索引倾向评分（ANN.MiPS）估计量。ANN.MiPS 估计量使用人工神经网络来估计 MiPS，该 MiPS 结合了来自多个候选倾向评分和结果回归模型的信息。设计了蒙特卡罗模拟研究来评估所提出的 ANN.MiPS 估计量的性能。此外，我们将我们的估计器应用于真实数据，以讨论其实用性。
模拟研究表明，在所有评估的样本大小、治疗率和协变量类型下，如果任何一个候选模型正确指定，ANN.MiPS 估计量的偏差非常小，标准误差也相似。与基于核函数的估计量相比，当正确模型被纳入估计量时，ANN.MiPS 估计量通常会产生更小的标准误差。实证研究表明，在不同的模型规格下，ANN.MiPS 估计量的 ATE 点估计及其引导标准误差是稳定的。
所提出的估计器将来自两个模型的信息扩展到多个模型，并实现了 ATE 的多重稳健估计。与基于核的估计器相比，我们的估计器获得了额外的效率。所提出的估计器为观察性研究中的因果效应估计提供了一种新方法。
