Department of Biostatistics, Yale School of Public Health, New Haven, USA.
Center for Methods in Implementation and Prevention Science, Yale School of Public Health, New Haven, USA.
BMC Med Res Methodol. 2021 Nov 20;21(1):253. doi: 10.1186/s12874-021-01425-4.
The natural indirect effect (NIE) and mediation proportion (MP) are two measures of primary interest in mediation analysis. The standard approach for mediation analysis is through the product method, which involves a model for the outcome conditional on the mediator and exposure and another model describing the exposure-mediator relationship. The purpose of this article is to comprehensively develop and investigate the finite-sample performance of NIE and MP estimators via the product method.
With four common data types with a continuous/binary outcome and a continuous/binary mediator, we propose closed-form interval estimators for NIE and MP via the theory of multivariate delta method, and evaluate its empirical performance relative to the bootstrap approach. In addition, we have observed that the rare outcome assumption is frequently invoked to approximate the NIE and MP with a binary outcome, although this approximation may lead to non-negligible bias when the outcome is common. We therefore introduce the exact expressions for NIE and MP with a binary outcome without the rare outcome assumption and compare its performance with the approximate estimators.
Simulation studies suggest that the proposed interval estimator provides satisfactory coverage when the sample size ≥500 for the scenarios with a continuous outcome and sample size ≥20,000 and number of cases ≥500 for the scenarios with a binary outcome. In the binary outcome scenarios, the approximate estimators based on the rare outcome assumption worked well when outcome prevalence less than 5% but could lead to substantial bias when the outcome is common; in contrast, the exact estimators always perform well under all outcome prevalences considered.
Under samples sizes commonly encountered in epidemiology and public health research, the proposed interval estimator is valid for constructing confidence interval. For a binary outcome, the exact estimator without the rare outcome assumption is more robust and stable to estimate NIE and MP. An R package mediateP is developed to implement the methods for point and variance estimation discussed in this paper.
自然间接效应（NIE）和中介比例（MP）是中介分析中两个主要关注的指标。中介分析的标准方法是通过乘积法，该方法涉及到一个关于中介变量和暴露因素的结果模型，以及另一个描述暴露-中介关系的模型。本文的目的是通过乘积法全面发展和研究 NIE 和 MP 估计量的有限样本性能。
对于一个连续/二项结果和一个连续/二项中介变量的四种常见数据类型，我们通过多元 delta 方法理论提出了 NIE 和 MP 的闭式区间估计，并相对于自举法评估了它们的经验性能。此外，我们观察到，当结果为常见时，在具有二项结果的情况下，为了近似 NIE 和 MP，经常使用稀有结果假设，但这种近似可能会导致不可忽略的偏差。因此，我们在没有稀有结果假设的情况下引入了具有二项结果的 NIE 和 MP 的精确表达式，并比较了它们的性能与近似估计量的性能。
模拟研究表明，对于连续结果的情况，当样本量≥500 时，对于二项结果的情况，当样本量≥20000 且病例数≥500 时，所提出的区间估计提供了令人满意的覆盖范围。在二项结果的情况下，基于稀有结果假设的近似估计量在结果流行率小于 5%时效果良好，但在结果常见时可能会导致较大的偏差；相比之下，精确估计量在所有考虑的结果流行率下始终表现良好。
在流行病学和公共卫生研究中常见的样本量下，所提出的区间估计对于构建置信区间是有效的。对于二项结果，没有稀有结果假设的精确估计量更稳健且更稳定，可用于估计 NIE 和 MP。已经开发了一个 R 包 mediateP 来实现本文中讨论的点估计和方差估计的方法。
