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(Xep)时，识别AEE(X)面临两个挑战：首先，关于Xep的可交换性不等于关于X的可交换性；其次，非差分误差假设(NDEA)在实践中可能过于严格。为解决这些问题，本文提出通过三个新概念统一可交换性与暴露及混杂因素测量误差。第一个概念——概率可交换性(PE)——指出具有Xep=e的个体结果与真实暴露于X=eT的个体结果具有概率可交换性。AEE(Xep)与AEE(X)在风险差和风险比尺度上的关系通过数学表达为概率确定性，称为可交换概率(Pe)。Pe的平方(Pe2)量化了因暴露测量误差通过非混杂机制导致AEE(Xep)与AEE(X)差异的程度。Xep对X回归中的决定系数(R2)有时足以度量Pe2。第二个概念——涌现伪混杂(EPC)——描述了暴露测量误差通过类混杂机制引入的偏倚。PE要求控制EPC，这比NDEA条件更弱。第三个概念——涌现混杂——描述了混杂因素测量误差产生偏倚的情形。对E(P)C的调整可类比混杂调整进行。本文深入阐释了AEE(Xep)何时能作为AEE(X)的合适替代指标，以及如何度量二者差异。差分误差问题可被处理，且未必损害因果推断。