Exchangeability concerning a continuous exposure, X, implies no confounding bias when identifying average exposure effects of X, AEE(X). When X is measured with error (Xep), two challenges arise in identifying AEE(X). Firstly, exchangeability regarding Xep does not equal exchangeability regarding X. Secondly, the non-differential error assumption (NDEA) could be overly stringent in practice. To address them, this article proposes unifying exchangeability and exposure and confounder measurement errors with three novel concepts. The first, Probabilistic Exchangeability (PE), states that the outcomes of those with Xep=e are probabilistically exchangeable with the outcomes of those truly exposed to X=eT. The relationship between AEE(Xep) and AEE(X) in risk difference and ratio scales is mathematically expressed as a probabilistic certainty, termed exchangeability probability (Pe). Squared Pe (Pe2) quantifies the extent to which AEE(Xep) differs from AEE(X) due to exposure measurement error through mechanisms not akin to confounding mechanisms. The coefficient of determination (R2) in the regression of Xep against X may sometimes be sufficient to measure Pe2. The second concept, Emergent Pseudo Confounding (EPC), describes the bias introduced by exposure measurement error through mechanisms akin to confounding mechanisms. PE requires controlling for EPC, which is weaker than NDEA. The third, Emergent Confounding, describes when bias due to confounder measurement error arises. Adjustment for E(P)C can be performed like confounding adjustment. This paper provides maximum insight into when AEE(Xep) is an appropriate surrogate of AEE(X) and how to measure the difference between these two. Differential errors could be addressed and may not compromise causal inference.

翻译：关于连续暴露变量X的可交换性意味着在识别X的平均暴露效应（AEE(X)）时不存在混杂偏倚。当X存在测量误差（记为Xep）时，识别AEE(X)面临两个挑战：其一，Xep的可交换性并不等同于X的可交换性；其二，非差异误差假设（NDEA）在实际应用中可能过于严格。为解决这些问题，本文提出三个新概念以统一可交换性与暴露及混杂测量误差。第一个概念"概率可交换性"（PE）指出，具有Xep=e观测值的个体的结局与真实暴露于X=eT个体的结局具有概率可交换性。AEE(Xep)与AEE(X)在风险差和风险比尺度上的关系以概率确定性形式数学表达，称为可交换性概率（Pe）。平方概率（Pe²）量化了AEE(Xep)因暴露测量误差而与AEE(X)产生差异的程度，其作用机制不同于混杂机制。在某些情况下，Xep对X回归中的决定系数（R²）足以度量Pe²。第二个概念"涌现伪混杂"（EPC）描述了暴露测量误差通过类似于混杂机制引入的偏倚。PE要求控制EPC，该条件弱于NDEA。第三个概念"涌现混杂"描述了因混杂测量误差产生偏倚的情景。对E(P)C的调整可如同混杂调整一样进行。本文为判断AEE(Xep)何时可作为AEE(X)的合适替代指标，以及如何量化两者差异提供了最大化的理论洞见。差异误差问题可被妥善处理，且不会损害因果推断的有效性。