Am J Epidemiol. 2022 Sep 28;191(10):1813-1819. doi: 10.1093/aje/kwac103.
Previous papers have mentioned that conditioning on a binary collider would introduce an association between its causes in at least 1 stratum. In this paper, we prove this statement and, along with intuitions, formally examine the direction and magnitude of the associations between 2 risk factors of a binary collider using interaction contrasts. Among level one of the collider, 2 variables are independent, positively associated, and negatively associated if multiplicative risk interaction contrast is equal to, more than, and less than 0, respectively; the same results hold for the other level of the collider if the multiplicative survival interaction contrast, equal to multiplicative risk interaction contrast minus the additive risk interaction contrast, is compared with 0. The strength of the association depends on the magnitude of the interaction contrast: The stronger the interaction is, the larger the magnitude of the association will be. However, the common conditional odds ratio under the homogeneity assumption will be bounded. A figure is presented that succinctly illustrates our results and helps researchers to better visualize the associations introduced upon conditioning on a collider.
先前的论文提到，在二元混杂因素上进行条件化会导致其至少在 1 个层上的原因之间产生关联。在本文中，我们证明了这一说法，并通过交互对比，从直观上正式检验了二元混杂因素的 2 个风险因素之间关联的方向和大小。在混杂因素的第一层中，如果乘法风险交互对比等于、大于和小于 0，则两个变量是相互独立的、正相关的和负相关的；如果比较的是乘法生存交互对比，即乘法风险交互对比减去加法风险交互对比，并且是混杂因素的另一层，则会得到相同的结果。关联的强度取决于交互对比的大小：交互越强，关联的幅度就越大。然而，同质性假设下的常见条件优势比将受到限制。本文提供了一个简明的图表，直观地说明了我们的结果，并帮助研究人员更好地可视化在混杂因素上进行条件化后引入的关联。
