Average Causal Effect Estimation Via Instrumental Variables: the No Simultaneous Heterogeneity Assumption.

Area of Science:

• Epidemiology
• Biostatistics
• Econometrics

Background:

• Instrumental variables (IVs) are used to infer causal effects of treatments on outcomes.
• Standard IV assumptions (relevance, independence, exclusion) are insufficient for identifying the average causal effect (ACE).
• Existing sufficient assumptions include homogeneity of treatment effect, homogeneity of instrument association, and no effect modification.

Purpose of the Study:

• To introduce and define the "no simultaneous heterogeneity" assumption for IV analysis.
• To demonstrate that this new assumption is weaker than existing ones for ACE identification.
• To show the plausibility of identifying ACE under this relaxed assumption.

Main Methods:

• Defined "no simultaneous heterogeneity" as mean independence between heterogeneity in the causal effect and heterogeneity in the instrument association.
• Illustrated the assumption using simulation studies.
• Re-examined published studies to apply the new assumption.

Main Results:

• The "no simultaneous heterogeneity" assumption allows the Wald estimand to equal the ACE.
• This holds even when homogeneity assumptions or no effect modification are violated.
• These previously sufficient assumptions are shown to be special cases of, and thus stronger than, no simultaneous heterogeneity.

Conclusions:

• The "no simultaneous heterogeneity" assumption is sufficient for identifying the ACE using IVs.
• This weaker assumption may make ACE identification more feasible in practice.
• It provides a more plausible pathway for causal inference in observational studies.