Zhang Min, Yu Youfei, Wang Shikun, Salvatore Maxwell, G Fritsche Lars, He Zihuai, Mukherjee Bhramar
Department of Biostatistics, University of Michigan School of Public Health, Ann Arbor, Michigan.
Department of Biostatistics, MD Anderson Cancer Center, Houston, Texas.
Stat Med. 2020 May 20;39(11):1675-1694. doi: 10.1002/sim.8505. Epub 2020 Feb 26.
The statistical practice of modeling interaction with two linear main effects and a product term is ubiquitous in the statistical and epidemiological literature. Most data modelers are aware that the misspecification of main effects can potentially cause severe type I error inflation in tests for interactions, leading to spurious detection of interactions. However, modeling practice has not changed. In this article, we focus on the specific situation where the main effects in the model are misspecified as linear terms and characterize its impact on common tests for statistical interaction. We then propose some simple alternatives that fix the issue of potential type I error inflation in testing interaction due to main effect misspecification. We show that when using the sandwich variance estimator for a linear regression model with a quantitative outcome and two independent factors, both the Wald and score tests asymptotically maintain the correct type I error rate. However, if the independence assumption does not hold or the outcome is binary, using the sandwich estimator does not fix the problem. We further demonstrate that flexibly modeling the main effect under a generalized additive model can largely reduce or often remove bias in the estimates and maintain the correct type I error rate for both quantitative and binary outcomes regardless of the independence assumption. We show, under the independence assumption and for a continuous outcome, overfitting and flexibly modeling the main effects does not lead to power loss asymptotically relative to a correctly specified main effect model. Our simulation study further demonstrates the empirical fact that using flexible models for the main effects does not result in a significant loss of power for testing interaction in general. Our results provide an improved understanding of the strengths and limitations for tests of interaction in the presence of main effect misspecification. Using data from a large biobank study "The Michigan Genomics Initiative", we present two examples of interaction analysis in support of our results.
在统计和流行病学文献中，使用两个线性主效应和一个乘积项来对交互作用进行建模的统计方法极为常见。大多数数据建模者都知道，主效应的错误设定可能会在交互作用检验中导致严重的I型错误膨胀，从而导致交互作用的虚假检测。然而，建模实践并没有改变。在本文中，我们关注模型中的主效应被错误设定为线性项的具体情况，并描述其对统计交互作用常用检验的影响。然后，我们提出了一些简单的替代方法，以解决由于主效应错误设定而在检验交互作用时潜在的I型错误膨胀问题。我们表明，当对具有定量结果和两个独立因素的线性回归模型使用三明治方差估计量时，Wald检验和得分检验在渐近意义上都能保持正确的I型错误率。然而，如果独立性假设不成立或结果是二元的，使用三明治估计量并不能解决问题。我们进一步证明，在广义相加模型下灵活地对主效应进行建模，可以在很大程度上减少或常常消除估计中的偏差，并且无论独立性假设如何，对于定量和二元结果都能保持正确的I型错误率。我们表明，在独立性假设下且对于连续结果，相对于正确设定的主效应模型，过度拟合和灵活地对主效应进行建模在渐近意义上不会导致检验效能的损失。我们的模拟研究进一步证明了一个经验事实，即一般来说，使用灵活的主效应模型不会导致检验交互作用时的效能显著损失。我们的结果有助于更好地理解在存在主效应错误设定的情况下交互作用检验的优势和局限性。利用来自大型生物样本库研究“密歇根基因组计划”的数据，我们给出了两个交互作用分析的例子来支持我们的结果。
