Department of Preventive Medicine, Northwestern University, Chicago, Illinois, USA.
Department of Educational Psychology, University of Texas at Austin, Austin, Texas, USA.
Res Synth Methods. 2022 Jul;13(4):489-507. doi: 10.1002/jrsm.1558. Epub 2022 Apr 7.
Missing covariates is a common issue when fitting meta-regression models. Standard practice for handling missing covariates tends to involve one of two approaches. In a complete-case analysis, effect sizes for which relevant covariates are missing are omitted from model estimation. Alternatively, researchers have employed the so-called "shifting units of analysis" wherein complete-case analyses are conducted on only certain subsets of relevant covariates. In this article, we clarify conditions under which these approaches generate unbiased estimates of regression coefficients. We find that unbiased estimates are possible when the probability of observing a covariate is completely independent of effect sizes. When that does not hold, regression coefficient estimates may be biased. We study the potential magnitude of that bias assuming a log-linear model of missingness and find that the bias can be substantial, as large as Cohen's d = 0.4-0.8 depending on the missingness mechanism.
缺失协变量是拟合元回归模型时常见的问题。处理缺失协变量的标准做法通常涉及两种方法之一。在完全案例分析中，缺失相关协变量的效应大小从模型估计中省略。或者，研究人员采用了所谓的“转移分析单位”方法，其中仅对相关协变量的某些子集进行完全案例分析。在本文中，我们澄清了这些方法产生回归系数无偏估计的条件。我们发现，当观察协变量的概率与效应大小完全独立时，可以得到无偏估计。当这种情况不成立时，回归系数估计可能存在偏差。我们研究了在缺失的对数线性模型下的潜在偏差大小，并发现这种偏差可能很大，高达 Cohen's d = 0.4-0.8，具体取决于缺失机制。
