Homogeneity in the Instrument-exposure Association and Point Estimation Using Binary Instrumental Variables

Area of Science:

• Causal inference
• Econometrics
• Epidemiology

Background:

• Instrumental variable (IV) analysis requires assumptions beyond relevance, independence, and exclusion restriction for result interpretation.
• Understanding these additional assumptions is crucial for valid causal effect estimation.

Purpose of the Study:

• To assess if instrument-exposure additive homogeneity is sufficient for equating the Wald estimand with the average derivative effect (ADE).
• To investigate this condition under specific scenarios: binary instrument and continuous exposure.

Main Methods:

• The study evaluates the condition of instrument-exposure additive homogeneity.
• It specifically examines the relationship between the Wald estimand and the average derivative effect (ADE) in a defined setting.

Main Results:

• Instrument-exposure additive homogeneity is not sufficient for ADE identification when the instrument is binary, exposure is continuous, and the exposure-outcome effect is nonlinear.
• However, for a binary exposure, the homogeneity condition is sufficient due to the inherent additive linearity of the exposure-outcome effect.

Conclusions:

• Instrument-exposure additive homogeneity adequately identifies the ADE for binary instruments when the exposure is also binary.
• When the exposure is continuous, additional assumptions, such as additive linearity of the exposure-outcome effect, are necessary for ADE identification.