Correct illustration of assumptions in Mendelian randomization

Abstract

Mendelian randomization (MR) is a genetic epidemiological tool which aims to identify causal effects, first proposed in 1986 by Katan.1 The method is built on the foundations of instrumental variable analyses in econometrics, which uses an exogenous variable to proxy a modifiable exposure of interest. In MR, genetic variants randomly allocated at meiosis are implemented as instrumental variables for a phenotype of interest. Under three core assumptions, using an instrumental variable (IV) should yield valid causal estimates that are less prone to bias by confounding and reverse causality2: IV1: genetic variants are strongly associated with the exposure (relevance assumption); IV2: no confounding of the relationship between the instruments and the outcome (independence assumption); IV3: no alternative pathway between the instrument and the outcome, other than via the exposure (exclusion-restriction criteria, commonly known as no horizontal pleiotropy). MR has gained popularity in causal inference research to identify risk factors for a disease,3 in drug discovery and repurposing,4 and to identify downstream effects or biomarkers of disease.5 It is commonplace to accompany an MR analysis with a causal diagram. However, as an increasing number of MR analyses are published, we have noticed incorrectly drawn causal diagrams.6–9 MR causal diagrams are typically used to illustrate: (i) the analyses being conducted, e.g. the exposure(s) and outcome(s) of interest; and (ii) the MR assumptions required for valid inference. Thus, they often present both causal effect arrows, and arrows depicting the absence of causal effects in accordance with MR assumptions. These causal diagrams are often drawn with an incorrect arrow (or no arrow) representing IV2. This is potentially due to a misconception about what IV2 assumes. IV2 specifically assumes no confounders of the genetic variant and the outcome. This means there can be no directed arrow from the confounder (C) to the genetic variants (G): dashed red arrow in panel (b) of Figure 1. MR assumptions diagrams. Panel (a) shows an incorrect causal diagram. Panel (b) shows a correct causal diagram. G represents genetic variants. X represents the exposure. Y represents the outcome. C represents confounders. IV1, IV2 and IV3 represent the three core MR assumptions. Dashed arrows represent where there should be an absence of a causal effect for IV2 and IV3 assumptions to be valid. The dashed red arrow illustrates the correct direction for IV2. MR, Mendelian randomization; IV, instrumental variable In practice, it is common to falsify IV2 by examining whether there is an association between the genetic instruments and a suite of phenotypic variables, with the objective of ensuring that the instruments are unconfounded. However, this does not mean ‘unconfounded’ in the traditional sense, for example by lifestyle or biological factors such as adiposity or smoking. The instruments, by definition, cannot be confounded by those variables. Genes are randomly allocated at meiosis, and nothing downstream of them (e.g. adiposity or smoking) can be a confounder, as those variables lie on the causal pathway between the gene and the exposure or outcome. Rather, the objective is to ensure the instrument-outcome association is unconfounded by factors that can affect the likelihood of inheriting a genetic variant, such as population stratification or assortative mating. It is often assumed that because C (typically used to represent conventional lifestyle/biological factors) cannot cause the genetic variant, that the directed arrow should go from G to C: dashed blue arrow in panel (a) of Figure 1. This, however, would simply illustrate an example of a horizontal pleiotropy pathway (i.e. an effect of G on Y, through a pathway other than X). Confounding due to population structure or assortative mating is challenging to examine directly. Instead, we leverage the fact that bias due to these phenomena can cause spurious associations to arise between the instruments and confounders. If there is no evidence in our data that the instrument is associated with confounders, we can be more confident that IV2 is less likely to have been violated. If associations are observed between the instrument and confounders, there are at least two plausible explanations. First, IV2 has been violated (e.g. by population stratification or assortative mating) and has induced spurious associations between two otherwise uncorrelated variables. Second, that there are pleiotropic pathways from the instrument to the outcome, which operate through those specific confounders tested. Disentangling those two possible underlying mechanisms can be challenging. Methods now exist to address violations of both IV2 (e.g. adjusting for principle components of ancestry10 or performing within-family MR11) and IV3 (e.g. MR-Egger6 or multivariable MR adjusting for potential pleiotropic pathways12), and these methods are discussed extensively in the literature. Comparing results from those methods may provide evidence for which mechanism is most likely. Last, it is worth noting that associations between instruments and confounders can only be examined in individual-level data MR studies (i.e. one-sample MR), not summary-level MR studies (i.e. two-sample MR). In summary, it remains important to consider whether IV2 may be violated and to correctly illustrate this assumption in MR causal diagrams. We encourage all MR practitioners to revise the core assumptions and ensure causal diagrams are correctly drawn and described. A.R.C. and E.L.A. conceived the idea for the letter. E.L.A. wrote the first draft of the manuscript. A.R.C. provided critical comments. E.L.A. is funded by a UKRI Future Leaders Fellowship (MR/W011581/1). E.L.A. has no conflicts of interest to declare. A.R.C. works for Novo Nordisk Research Centre in Oxford, but Novo Nordisk have not been involved in the writing or publishing of this research.

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