Towards more plausible point-identifying assumptions in two-sample Mendelian randomization

Two-sample Mendelian randomization (MR) is a widely applied methodology in epidemiology. In two-sample MR, summary data (typically, regression coefficients and standard errors) quantifying the association between multiple genetic variants and the exposure and the outcome are used in an instrumental variable framework aimed at estimating the causal effect of the exposure on the outcome. Most two-sample MR methods were developed under data-generating models where the association of for each candidate genetic instrument with the exposure, as well as the causal effect of the exposure on the outcome, are constant in the additive scale. These assumptions are useful because they imply that, had all genetic variants been valid IVs, they would all estimate the same causal parameter - namely, the constant causal effect. We refer to this condition as summary-level homogeneity. However, these are rather strong homogeneity conditions which may raise concerns about the plausibility of these methods in practice. In this paper, we show that summary-level homogeneity is implied by the following conditions: the causal effect is additive linear, but not necessarily constant across, all strata of the population; and uncorrelatedness between heterogeneity in the causal effect and in the association between each genetic variant and the exposure. Under these conditions, typical two-sample MR methods can be interpreted as estimators of the average causal effect. These results clarify that point-identifying assumptions required for two-sample MR methods are weaker than previously anticipated, which contributes to their plausibility and interpretation in at least some practical applications.