Mind the gap: characterizing bias due to population mismatch in two-sample Mendelian randomization

Abstract

Mendelian randomization (MR) is a statistical method for estimating causal effects using genetic variants as instrumental variables. In two sample MR (2SMR), different study samples are used to estimate genetic associations with the exposure and outcome. For valid inference, these studies must include individuals from the same population. Using studies from different populations may bias the 2SMR estimate due to differences in linkage disequilibrium or genetic effects on the exposure trait. We show that violation of the same-population assumption leads to bias in the causal estimate towards zero on average, and does not increase the rate of false positives. We verify this result in a broad survey of 2SMR estimates, comparing estimates made with matching and mismatching populations across 546 trait pairs measured in 2-7 ancestries. We find that most population-mismatched estimates are attenuated towards zero compared to their corresponding population-matched estimates, and that increasing genetic distance between study populations is associated with greater shrinkage. We observe bias even when mismatched populations have the same continental ancestry. However, we also find that, in some cases, using a larger exposure study with mismatching ancestry can improve power by dramatically increasing precision. These results show that even intra-continental population mismatch can bias 2SMR estimates, but also suggests there is potential to improve the power of 2SMR in understudied populations by properly leveraging larger, mismatching study populations.

Figure 1:

(A) Diagram depicting a 2SMR study and the calculation of the causal estimate as a weighted average of ratio estimates. (B) Two possible sources of differences between ${\beta }_{X,j,t}$ and ${\beta }_{X,j,e}$. Left, LD patterns are the same in the two populations but the causal variant has a different effect on the exposure. Right, the causal variant has the same effect in both populations, but LD structure differs. In both cases, there is a strong exposure-instrument association in population $e$, but a weaker association in population $t$.

Figure 2:

Study design of cross-population survey of 2SMR estimates. Right, example of an exposure trait-outcome study group for the effect of urate on gout with UK Biobank defining the target population. Exposure studies are color-coded based on how closely study populations match the target population: exact match (dark blue), continental match but a different subpopulation (light blue), or a continental mismatch (orange).

Figure 3:

Forest plots of 2SMR estimates of the effect of LDL cholesterol on coronary heart disease from GRAPPLE at two instrument selection p-value thresholds. Points indicate effect estimates and intervals indicate 95% confidence intervals. Color indicates if an estimate is made with exact matching (dark blue), continentally matching (light blue), or continentally mismatching (red) exposure studies. A star indicates that an estimate is significantly different than the reference estimate (FDR < 0.05), when a reference estimate is available.

Figure 4:

Population pair specific shrinkage coefficients vs approximate $F\mathit{\text{st}}$ distance between populations. Population pair specific shrinkage coefficients were estimated using SIMEX. The dashed line represents the univariable regression line from inverse-variance weighted regression of $F_{\mathit{\text{st}}}$ on estimated shrinkage coefficient. Vertical confidence intervals represent 95% confidence intervals for each shrinkage coefficient.