Department of Epidemiology and Biostatistics, School of Public Health, Tehran University of Medical Sciences, Tehran, Iran.
Psychosocial Health Research Institute, Iran University of Medical Sciences, Tehran, Iran.
Int J Epidemiol. 2021 Mar 3;50(1):346-351. doi: 10.1093/ije/dyaa260.
All statistical estimates from data have uncertainty due to sampling variability. A standard error is one measure of uncertainty of a sample estimate (such as the mean of a set of observations or a regression coefficient). Standard errors are usually calculated based on assumptions underpinning the statistical model used in the estimation. However, there are situations in which some assumptions of the statistical model including the variance or covariance of the outcome across observations are violated, which leads to biased standard errors. One simple remedy is to use robust standard errors, which are robust to violations of certain assumptions of the statistical model. Robust standard errors are frequently used in clinical papers (e.g. to account for clustering of observations), although the underlying concepts behind robust standard errors and when to use them are often not well understood. In this paper, we demystify robust standard errors using several worked examples in simple situations in which model assumptions involving the variance or covariance of the outcome are misspecified. These are: (i) when the observed variances are different, (ii) when the variance specified in the model is wrong and (iii) when the assumption of independence is wrong.
由于抽样变异性，所有基于数据的统计估计都存在不确定性。标准误差是衡量样本估计值（例如一组观测值的平均值或回归系数）不确定性的一种方法。标准误差通常是根据用于估计的统计模型的基本假设计算得出的。但是，在某些情况下，统计模型的某些假设（包括观测值之间的结果的方差或协方差）被违反，这会导致有偏差的标准误差。一种简单的补救方法是使用稳健标准误差，它可以抵抗统计模型某些假设的违反。稳健标准误差在临床论文中经常使用（例如，用于解释观测值的聚类），尽管稳健标准误差背后的基本概念以及何时使用它们通常理解得不够好。在本文中，我们使用几个简单情况下涉及结果方差或协方差的模型假设被错误指定的工作示例来揭开稳健标准误差的神秘面纱。这些示例包括：（i）当观察到的方差不同时，（ii）当模型中指定的方差错误时，以及（iii）当独立性假设错误时。
