[The directionality of measurement bias: a directed acyclic graph-based structural perspective]

Measurement bias (MB) has been described in causal structures but is still not entirely clear. In practice, the correctness of substitution estimate (SE) of effect is a prerequisite for causal inference, usually based on a bidirectionally non-differential misclassification between the measured exposure and the measured outcome. Based on a directed acyclic graph (DAG), this paper proposes a structure for the single-variable measure, where its MB is derived from the choice of an imperfect, "input/output device-like" measurement system. The MB of the SE is influenced both by the measurement system itself and by factors outside the measurement system: while the independence or dependence mechanism of the measurement system still ensures that the MB of the SE is bidirectionally non-differential; however, the misclassification can be bidirectionally non-differential, unidirectionally differential, or bidirectionally differential resulted from the factors outside the measurement system. In addition, reverse causality should be defined at the level of measurement, where measured exposures can influence measured outcomes and vice versa. Combined with temporal relationships, DAGs help elucidate MB's structures, mechanisms, and directionality.