Measurement bias: a structure perspective

Objectives: To propose new causal structures to clarify the structures and mechanisms of measurement bias (MB). Methods: We propose a new structure for measuring one singleton variable firstly, and then extend it into clarifying the effect between an exposure and an outcome, aided by the Directed Acyclic Graphs (DAGs). Results: The MB for one singleton variable arises in the selection of an imperfect I/O device-like measurement system only. For effect estimation, however, extra source of MB arises from any redundant association between a measured exposure and a measured outcome. The misclassification will be bidirectionally differential for a common outcome, unidirectionally differential for a causal relation, and non-differential for a common cause or an independence, between the measured exposure and the measured outcome. The measured exposure can actually affect the measured outcome, or vice versa. Reverse causality is a concept defined at the level of measurement. Conclusions: Measurement extends the causality from real world to human thinking. MB has two origins: an imperfect measurement system and any redundant association at the measurement level. Our new DAGs have clarified the structures and mechanisms of MB.