Measurement errors are pervasive. A deeper understanding of measurement error impacts on research is critical for causal inference. Exchangeability concerning a continuous exposure or treatment, X, may be assumed to identify average exposure/treatment effects of X, AEE(X). When X is measured with error (Xep), exchangeability issues arise, a topic remains largely understudied. First, exchangeability regarding Xep does not equal exchangeability regarding X. Second, there is no formal justification for using AEE(Xep) to estimate AEE(X) under the potential outcomes framework. Third, a definition of exchangeability that implies that AEE(Xep) can differ from AEE(X) is lacking. Fourth, the non-differential error assumption (NDEA) could be overly stringent in practice. Fifth, while confounders or exposure mixtures may be measured with error, raising concerns about residual confounding, methods to correct for measurement errors in both exposures and confounders remain lacking. To address them, first, this article proposes unifying exchangeability and exposure/confounder measurement errors through three concepts. First, Probabilistic Exchangeability (PE) is an exchangeability assumption that allows for the difference between AEE(Xep) and AEE(X). The second, Emergent Pseudo Confounding (EPC), describes the bias introduced by exposure measurement error through mechanisms like confounding mechanisms. The third, Emergent Confounding (EC), describes when bias due to confounder measurement error arises. Second, this article develops correction theories for differential exposure measurement error and confounder measurement error to estimate AEE(X) under PE. This paper provides comprehensive insight into when AEE(Xep) is a surrogate of AEE(X). Differential errors can be addressed, which may not compromise causal inference.

翻译：测量误差普遍存在。深入理解测量误差对研究的影响对因果推断至关重要。为识别连续暴露或处理X的平均暴露/处理效应AEE(X)，通常假设关于X的可交换性成立。当X存在测量误差（记为Xep）时，可交换性问题随之产生，而这一主题目前尚未得到充分研究。首先，关于Xep的可交换性不等于关于X的可交换性。其次，在潜在结果框架下使用AEE(Xep)估计AEE(X)缺乏正式的理论依据。第三，目前缺乏能够解释AEE(Xep)与AEE(X)存在差异的可交换性定义。第四，实践中非差分误差假设可能过于严格。第五，虽然混杂因素或暴露混合物可能存在测量误差并引发残余混杂问题，但目前仍缺乏同时校正暴露与混杂因素测量误差的方法。为解决这些问题，本文首先提出通过三个概念统一可交换性与暴露/混杂因素测量误差的框架。第一，概率可交换性是一种允许AEE(Xep)与AEE(X)存在差异的可交换性假设。第二，涌现伪混杂描述了暴露测量误差通过类混杂机制引入的偏倚。第三，涌现混杂描述了混杂因素测量误差产生偏倚的情形。其次，本文发展了在概率可交换性下校正差分暴露测量误差与混杂因素测量误差以估计AEE(X)的理论。本研究系统阐明了AEE(Xep)何时能作为AEE(X)的有效替代指标，并证明差分误差问题可被解决而不影响因果推断的有效性。