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 not akin to confounding mechanisms. In realistic settings, the coefficient of determination (R.sq) in the regression of X against Xep may be sufficient to measure Pe.sq. The second concept, Emergent Pseudo Confounding (EPC), describes the bias introduced by exposure measurement error, 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 justifies for using AEE(Xep) and maximum insight into potential divergence of AEE(Xep) from AEE(X) and its measurement. Differential errors do not necessarily compromise causal inference.

翻译：关于连续暴露变量X的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)面临两大挑战：首先，针对Xep的交换性不等同于针对X的交换性；其次，实践中过度严苛的非差分误差假设（NDEA）的必要性仍不明确。为解决这些问题，本文提出三个新概念以统一交换性、暴露及混杂测量误差。第一个概念"概率交换性（PE）"指出，具有Xep=e的对象的结局与真实暴露于X=eT的对象的结局在概率上具有交换性。AEE(Xep)与AEE(X)在风险差与风险比尺度上的关系以概率确定性形式表达，称为交换性概率（Pe）。平方交换性概率（Pe.sq）量化了因暴露测量误差（不同于混杂机制）导致的AEE(Xep)与AEE(X)的差异程度。在实际场景中，X对Xep回归的决定系数（R.sq）足以衡量Pe.sq。第二个概念"涌现伪混杂（EPC）"描述了由暴露测量误差引入的偏倚（类似于混杂机制）。当控制EPC时，PE可成立，且该条件弱于NDEA。第三个概念"涌现混杂"描述了混杂测量误差导致偏倚的情形。可像调整混杂因素一样调整E(P)C以确保PE。本文为使用AEE(Xep)提供了理论依据，并深入揭示了AEE(Xep)偏离AEE(X)及其测量值的潜在机制。差分误差未必会损害因果推断。