Here, we explain and illustrate a geometric perspective on causal inference in cohort studies that can help epidemiologists understand the role of standardization in causal inference as well as the distinctions between confounding, effect modification, and noncollapsibility. For simplicity, we focus on a binary exposure X, a binary outcome D, and a binary confounder C that is not causally affected by X. Rothman diagrams plot risk in the unexposed on the x-axis and risk in the exposed on the y-axis. The crude risks define one point in the unit square, and the stratum-specific risks define two other points in the unit square. These three points can be used to identify confounding and effect modification, and we show briefly how these concepts generalize to confounders with more than two levels. We propose a simplified but equivalent definition of collapsibility in terms of standardization, and we show that a measure of association is collapsible if and only if all of its contour lines are straight. We illustrate these ideas using data from a study conducted in Newcastle upon Tyne, United Kingdom, where the causal effect of smoking on 20-year mortality was confounded by age. We conclude that causal inference should be taught using geometry before using regression models.

翻译：本文阐述并阐释了队列研究因果推断的几何视角，有助于流行病学家理解标准化在因果推断中的作用，以及混杂、效应修饰和不可压缩性之间的区别。为简化起见，我们聚焦于二元暴露X、二元结局D和不受X因果影响的二元混杂因子C。Rothman图以未暴露组风险为x轴、暴露组风险为y轴绘制风险值。粗风险定义单位正方形中的一个点，而层特异性风险定义单位正方形中的另外两个点。这三个点可用于识别混杂和效应修饰，并简要展示了这些概念如何推广至多水平（超过两层）的混杂因子。我们基于标准化提出一种简化但等价的压缩性定义，并证明当且仅当关联测度的所有等高线均为直线时，该测度才具有可压缩性。利用英国纽卡斯尔的一项研究数据（其中吸烟对20年死亡率的因果效应受年龄混杂）阐释上述概念。我们得出结论：因果推断的教学应先借助几何方法，而后引入回归模型。