Measurement bias and "noncausal" diagrams¶
Measurement Bias¶
Measurement bias is caused by errors in measuring values of variables, i.e. \(A^* \not = A\). Measurement error is defined as the difference between the measured value and the true value of a variable, \(e_A = A^* - A\). Taken measurement error into consideration, the causal diagram is modified as follows:
Measurement error follow two properties:
- Indepedence: \(e_A \perp e_Y\).
- Nondifferentiality: \(e_A \perp Y\) and \(e_Y \perp A\).
Lack of either property will bring extra association and lead to bias.
- Edge \(Y\ra U_A\) will introduce recall bias.
- Edge \(A\ra U_Y\) will introduce reverse causation bias.
- Edge \(U_A\la U_{AY}\ra U_Y\) will introduce independent measurement error.
Correcting for measurement error usually requires additional validated non-biased samples.
"Noncausal" Diagrams¶
A causal graph requires that all of the edges in the graph can be interpreted causally, together with well-defined intervention. For graphs with non-causal edges, adjustments might fail to remove bias, as the adjusted variable is not on the true causal path.
