Table 7.

Uncorrelated/Undirected Measurement Error in Single-World Intervention Graph. There is no ‘action at a distance’: all measurement errors have causes; errors entering reporters of the treatment and outcome clarify that the treatment reporter induces collider bias, and the outcome reporter induces effect modification during estimation

Measurement Error Bias: Non-directional Uncorrelated Measurement Errors
Bias in Treatment Reporter Off-The-Null
1.1
1.2
1.3
Bias in Outcome Reporter Off-The-Null
2.1
2.2
2.3
Measurement Error On The Null: No Bias
1.4
2.4

Key: denotes the the true outcome; a denotes the true treatment. denotes the mismeasured treatment; denotes the mismeasured outcome; E^A: unmeasured variable(s) that, together with cause measurement: ; E^Y Unmeasured variable(s) that, together with cause measurement: ; Shaded nodes are unobserved. Treatment reporter bias: ; Outcome reporter bias: .