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arXiv · 2107.01070

Homogeneity in the instrument-treatment association is not sufficient for the Wald estimand to equal the average causal effect for a binary instrument and a continuous exposure

Fernando Pires Hartwig·Linbo Wang·George Davey Smith·Neil Martin Davies
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Abstract

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 non-linear 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.

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Fernando Pires Hartwig, Linbo Wang, George Davey Smith, Neil Martin Davies. 2021-07-02. Homogeneity in the instrument-treatment association is not sufficient for the Wald estimand to equal the average causal effect for a binary instrument and a continuous exposure. https://arxiv.org/abs/2107.01070

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