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 necessity of the non-differential error assumption (NDEA), overly stringent in practice, remains uncertain. 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 (Pe.sq) 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 (R.sq) in the regression of X against Xep may sometimes be sufficient to measure Pe.sq. The second concept, Emergent Pseudo Confounding (EPC), describes the bias introduced by exposure measurement error through mechanisms akin to confounding mechanisms. PE can hold when EPC is controlled for, 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 to ensure PE. This paper provides formal justifications for using AEE(Xep) and maximum insight into potential divergence of AEE(Xep) from AEE(X) and how to measure it.

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)）时无混杂偏倚。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的可交换性并不等同于关于X的可交换性；其次，实践中过于严苛的非差分误差假设（NDEA）的必要性尚不确定。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和混杂测量误差。第一个概念——概率可交换性（PE）指出，具有Xep=e的个体结局与真实暴露于X=eT的个体结局在概率上具有可交换性。风险差和风险比尺度下AEE(Xep)与AEE(X)的关系被数学表达为概率确定性，即可交换性概率（Pe）。平方Pe（Pe.sq）量化了暴露测量误差通过非混杂机制导致AEE(Xep)偏离AEE(X)的程度。X对Xep回归中的决定系数（R.sq）在某些情况下足以度量Pe.sq。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。当控制EPC时，PE可以成立，这种条件弱于NDEA。第三个概念——涌现混杂描述了混杂测量误差导致偏倚的机制。可通过类似于混杂调整的方式调整E(P)C以确保PE。本文为利用AEE(Xep)以及深入理解AEE(Xep)与AEE(X)的潜在偏差及其度量方法提供了形式化依据。