Credible Mendelian randomization studies: approaches for evaluating the instrumental variable assumptions

Abstract

As with other instrumental variable (IV) analyses, Mendelian randomization (MR) studies rest on strong assumptions. These assumptions are not routinely systematically evaluated in MR applications, although such evaluation could add to the credibility of MR analyses. In this article, the authors present several methods that are useful for evaluating the validity of an MR study. They apply these methods to a recent MR study that used fat mass and obesity-associated (FTO) genotype as an IV to estimate the effect of obesity on mental disorder. These approaches to evaluating assumptions for valid IV analyses are not fail-safe, in that there are situations where the approaches might either fail to identify a biased IV or inappropriately suggest that a valid IV is biased. Therefore, the authors describe the assumptions upon which the IV assessments rely. The methods they describe are relevant to any IV analysis, regardless of whether it is based on a genetic IV or other possible sources of exogenous variation. Methods that assess the IV assumptions are generally not conclusive, but routinely applying such methods is nonetheless likely to improve the scientific contributions of MR studies.

Figure 1.

Causal structures in which fat mass and obesity-associated (FTO) genotype provides a valid instrumental variable (IV) with which to estimate the effect of body mass index (BMI) on the risk of mental disorder (MD). In these diagrams, dotted lines indicate the hypothesized causal pathway of primary research interest: the effect of BMI on MD. The solid arrows represent hypothesized causal pathways, and the absence of an arrow connecting 2 variables represents the assumption that these variables do not affect one another. Whenever 2 variables in the diagram share a common cause, that relation is shown in the diagram (even if the specific common cause is unknown or unmeasured (U)). Thus, the directed acyclic graph (DAG) in part A represents the assumptions that FTO and U both affect BMI, U affects MD, there is no direct effect of FTO on MD, and there is no common prior cause of FTO and MD. The DAG in part B introduces linkage disequilibrium (LD) between FTO and the KIAA1005 gene. Under the assumptions shown in part B, KIAA1005 would be a valid IV with which to estimate the effect of BMI on MD, and because there are no other pathways connecting FTO and MD, FTO is also a valid IV. The DAG in part C is similar to that in part A, but U has been eliminated; thus, part C represents the assumption that there are no confounders of BMI and MD.

Figure 2.

Causal structures in which fat mass and obesity-associated (FTO) genotype is not a valid instrumental variable (IV) with which to estimate the effect of body mass index (BMI) as measured on the risk of mental disorder (MD). FTO would not be a valid instrument for estimating the effect of BMI on MD if FTO and MD shared an unmeasured common cause such as population group (G), sometimes called population stratification (as in part A), or if there is a causal pathway from FTO to MD that is not mediated by BMI, as with pleiotropy (shown in part B). In part C, FTO influences abdominal adiposity but not thigh fat. Both thigh fat and abdominal adiposity influence BMI, but only thigh fat affects MD. The Mendelian randomization effect estimate based on FTO would not correspond to the effect of thigh fat on MD. If, as in the directed acyclic graph (DAG) shown in part D, BMI as measured is not the causal version of BMI, then the IV estimate based on measured BMI would correspond to the causal effect only under special circumstances. In the DAG shown in part E, MD affects BMI, rather than vice versa, and the IV estimate would not correspond to the effect of BMI on MD.

Figure 3.

Directed acyclic graph showing that positive confounding arises from the association between counterfactuals. BMI(FTO) represents the set of counterfactual values of body mass index (BMI) for all possible values of fat mass and obesity-associated (FTO) genotype. MD(BMI) represents the set of counterfactual values of mental disorder (MD) for all possible values of BMI. An unmeasured trait (U) does not affect FTO, but U does affect the value BMI would take for any specific value of FTO.

Figure 4.

Causal structure in which the effect of fat mass and obesity-associated (FTO) genotype on body mass index (BMI) is silenced among women. In part A, FTO is a valid instrument and the association between FTO and mental disorder (MD) is silenced among women because the variable Male × FTO is zero among women (modified from Figure 1C). In part B, FTO is not a valid instrument, and the biasing pathway linking FTO and MD would create a statistical association between FTO and MD even among women (this is a modification of Figure 2B). In part C, FTO is not a valid instrument, but the biasing pathway linking FTO and MD would not create a statistical association between FTO and MD even among women, because the biasing pathway with the unmeasured phenotype originates after the Male × FTO interaction. In this diagram, the variable M represents a mediator which is influenced by Male × FTO interaction and affects both BMI and the unmeasured phenotype (this is also a modification of Figure 2B).