9.1 Measurement bias

9.2 The structure of measurement error: dependent misclassification

9.2 The structure of measurement error: differential misclassification

9.2 The structure of measurement error: dependent & differential misclassification

Fine point 9.1

• Measurement error will result in bias
• Except if A and Y are unassociated and the measurement error is independent and nondifferential
• "The magnitude of the measurement bias depends on the magnitude of the measurement error"
• "Causal diagrams do not encode quantitative information, and therefore they cannot be used to describe the magnitude of the bias"

9.3 Mismeasured confounders

9.3 Mismeasured confounders

9.3 Mismeasured confounders

• Mismeasurement of confounders may also lead to appearance of effect modification (EMM)
• If L=0 and L=1 strata differently report $L\ast$, stratification by $L\ast$ would produce appearance of EMM

9.3 Conditioning on mismeasured collider

• Selection bias

9.4 Intention-to-treat effect: the effect of a misclassified treatment

9.5 Per-protocol effect

• Causal effect of the treatment itself and not of randomization to treatment level
• Lack of exchangeability between A=1 and A=0
• Back to observational epidemiology realm

Fine point 9.2

As-treated vs per protocol

ITT

ITT is a lower bound for per-protocol effect

• ITT is closer to null (conservative)
  • Not in safety studies
• ITT is null if there is no effect
• ITT assumes monotonicity (same direction of the effect in all individuals)

Per protocol

• Time-varying
• Report both ITT and per-protocol effects
  • trade-off between bias due to potential unmeasured confounding vs misclassification of exposure
• IV approach
• Adjustment approach

References

Hernán MA, Robins JM (2020). Causal Inference: What If. Boca Raton: Chapman & Hall/CRC (v. 31jan21)