# Robust methods for Mendelian randomization

Genetic confounding (e.g., due to horizontal pleiotropy) and limited power are the most important limitations typically faced in an MR study. Practical strategies and novel methods have been proposed for dealing with these limitations and for enhancing causal inference

**Assessment of association with measured confounders**

In an MR analysis, the association between the genetic instrument or instruments and a wide range of potential confounders can be assessed. The MR assumptions can be viewed as plausible when the number of associations is no greater than expected by chance, as is generally observed empirically (70). An exclusive association with the target exposure provides further evidence supporting the MR assumptions..

**Exclusion of nonspecific genetic instruments**

Nonspecific genetic instruments (e.g., SNPs associated with nontarget exposures as well as the target exposure) can be excluded in a sensitivity analysis (18). If a genetic instrument remains associated with an outcome of interest after excluding nonspecific SNPs, evidence for causality may be strengthened..

**Detecting and correcting for pleiotropy by statistical and graphical tests**

The use of multiple genetic polymorphisms as instruments makes it easier to detect evidence of pleiotropy by statistical and graphical tests. If the estimate of the causal effect is of a consistent magnitude (e.g. homogeneous) across multiple independent instruments, then pleiotropy is considerably less likely to account for the results, as is observed in MR studies of LDL cholesterol (12). On the other hand, if the causal effects are not consistent (i.e. heterogeneous) across independent instruments (e.g., with some genetic instruments showing unexpectedly large or small effects on the outcome, given the magnitude of their exposure effect), this could be indicative of pleiotropy.

Figure 4. Pleiotropy robust tools for sensitivity analysis (MR-Egger regression and the Weighted Median) shown as slopes on the scatter plot.

Pleiotropy can be is also detectable by performing MR-Egger regression test (72), a regression of the gene-outcome on the gene-exposure associations with the intercept unconstrained. (see Figure 4). The intercept from MR-Egger regression provides a formal statistical test for the presence of directional (bias inducing) pleiotropy, because when the gene-exposure association is zero the gene-outcome association should also be zero. MR-Egger regression is relies on the assumption that the strength of the gene-exposure association should not correlate with the strength the pleiotropic effects across instruments [the so-called Instrument Strength Independent of Direct Effect (InSIDE) assumption (72)]. Another pleiotropy robust tool is the weighted median estimator. This is defined as the median (50th percentile) of the weighted empirical distribution function of ratio estimates. It is a consistent estimate of the causal effect if at least 50% of the weight in the analysis stems from variants that are valid instruments (i.e. not pleiotropic) - See Figure 4.

Unfortunately, MR-Egger regression suffers from a lack of power, and a susceptibility to weak instrument bias. Both MR-Egger and the Weighted Median should be considered as a tools for sensitivity analysis rather than as a primary analysis tool.