Table 3.
Examples of measurement error bias
| Structural Representation of Measurement Error Bias | ||
|---|---|---|
| Bias | Causal Diagram | |
| 1 | Uncorrelated errors under sharp null: no treatment effect: Under sharp null, assuming confounders are not measured with error, uncorrelated measurement errors are generally not expected to lead to bias |  |
| 2 | Uncorrelated errors under treatment effect: Outside sharp null, uncorrelated measurement errors distort targeted effects |  |
| 3 | Correlated errors: Related, systematic errors in A and Y measurements that are related |  |
| 4 | Directed error: exposure effects error of outcome: A affects Y's measurement error |  |
| 5 | Directed error: outcome affects error of exposure: Y affects A's measurement error |  |
| 6 | Correlated/directed error: Both systematic and correlated errors in A and Y measurements are from an unmeasured source of dependency |  |
Key: A denotes the treatment; Y denotes the outcome; U denotes an unmeasured confounder; L denotes measured confounders; 
asserts causality; 
indicates a latent variable X measured by proxy X′; 
indicates a path for bias linking A to Y absent causation; 
biased path for treatment effect in the target population; 
indicates that conditioning on X introduces bias; 
indicates that the error in a measured variable X′ modifies the effect of A → Y, such that the 
.