对撞偏差与对数可加尺度上交互作用之间的关系
Relationship between Collider Bias and Interactions on the Log-Additive Scale
AI总结：
本文研究了对撞偏差与对数可加尺度上交互作用之间的关系，证明在逻辑、线性和泊松回归下对撞偏差大小均与交互作用强度成比例，并指出即使模型误设，交互作用项仍可提示对撞偏差大小，对逆概率加权等校正方法具有重要启示。
摘要：
当以两个变量 $X$、$Y$ 的共同结果（对撞变量）为条件时，就会产生对撞偏差。在本手稿中，我们量化了由选择暴露和结局的一个二值对撞变量 $S$ 的某个取值所诱导的、暴露 $X$ 与结局 $Y$ 之间估计关联中的对撞偏差。在逻辑回归情形下，已知暴露-结局回归系数中对撞偏差的大小与对撞变量的对数可加模型中 $X$ 和 $Y$ 之间的交互作用强度 $δ_3$ 成比例：$\mathbb{P} (S = 1 | X, Y) = \exp \left\{ δ_0 + δ_1 X + δ_2 Y + δ_3 X Y \right\}$。我们证明，在暴露-结局关联的线性回归或泊松回归模型下，这一结果同样成立。随后，我们通过模拟说明，即使带交互作用的对数可加模型并非对撞变量的真实模型，该模型中的交互作用项仍然能够提供关于对撞偏差大小的信息。最后，我们讨论了这些发现对试图校正对撞偏差的方法的意义，例如逆概率加权法，该方法在实施时通常不在加权模型中包含变量之间的交互作用。
英文摘要：
Collider bias occurs when conditioning on a common effect (collider) of two variables $X, Y$. In this manuscript, we quantify the collider bias in the estimated association between exposure $X$ and outcome $Y$ induced by selecting on one value of a binary collider $S$ of the exposure and the outcome. In the case of logistic regression, it is known that the magnitude of the collider bias in the exposure-outcome regression coefficient is proportional to the strength of interaction $δ_3$ between $X$ and $Y$ in a log-additive model for the collider: $\mathbb{P} (S = 1 | X, Y) = \exp \left\{ δ_0 + δ_1 X + δ_2 Y + δ_3 X Y \right\}$. We show that this result also holds under a linear or Poisson regression model for the exposure-outcome association. We then illustrate by simulation that even if a log-additive model with interactions is not the true model for the collider, the interaction term in such a model is still informative about the magnitude of collider bias. Finally, we discuss the implications of these findings for methods that attempt to adjust for collider bias, such as inverse probability weighting which is often implemented without including interactions between variables in the weighting model.
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