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

BACKGROUND: Instrumental variables (IVs) can be used to provide evidence as to whether a treatment has a causal effect on an outcome . Even if the instrument satisfies the three core IV assumptions of relevance, independence, and exclusion restriction, further assumptions are required to identify the average causal effect (ACE) of on . Sufficient assumptions for this include homogeneity in the causal effect of on ; homogeneity in the association of with ; and no effect modification. METHODS: We describe the no simultaneous heterogeneity assumption, which requires the heterogeneity in the - causal effect to be mean independent of (i.e., uncorrelated with) both and heterogeneity in the - association. This happens, for example, if there are no common modifiers of the - effect and the - association, and the - effect is additive linear. We illustrate the assumption of no simultaneous heterogeneity using simulations and by re-examining selected published studies. RESULTS: Under no simultaneous heterogeneity, the Wald estimand equals the ACE even if both homogeneity assumptions and no effect modification (which we demonstrate to be special cases of-and therefore stronger than-no simultaneous heterogeneity) are violated. CONCLUSIONS: The assumption of no simultaneous heterogeneity is sufficient for identifying the ACE using IVs. Since this assumption is weaker than existing assumptions for ACE identification, doing so may be more plausible than previously anticipated.

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

BACKGROUND: Interpreting instrumental variable results often requires further assumptions in addition to the core assumptions of relevance, independence, and the exclusion restriction. METHODS: We assess whether instrument-exposure additive homogeneity renders the Wald estimand equal to the average derivative effect (ADE) in the case of a binary instrument and a continuous exposure. RESULTS: Instrument-exposure additive homogeneity is insufficient for ADE identification when the instrument is binary, the exposure is continuous, and the effect of the exposure on the outcome is nonlinear on the additive scale. For a binary exposure, the exposure-outcome effect is necessarily additive linear, so the homogeneity condition is sufficient. CONCLUSIONS: For binary instruments, instrument-exposure additive homogeneity identifies the ADE if the exposure is also binary. Otherwise, additional assumptions (such as additive linearity of the exposure-outcome effect) are required.