Sensitivity analysis

To further investigate the causal estimates found in the standard (IVW) MR analyses and to evaluate the validity of the analysed genetic instruments, MR-Egger⁴⁹ and weighted median MR⁵⁰ methods were used to overcome and accommodate for potential violations of the core MR assumptions. These complementary methods help to support the causal effects found with IVW, as a single method cannot account for all biological and statistical properties that may impact MR estimates. A variety of recommended⁷⁸ specialised sensitivity tests was also applied.

To assess overall horizontal pleiotropy (violation of assumption 3), the intercept in the MR-Egger regression⁴⁹ was evaluated, and the heterogeneity among the genetic variants was quantified using Cochran’s Q-statistic⁷⁹. The intercept term in MR-Egger regression is a useful indication of whether directional horizontal pleiotropy is driving the results of an MR analysis. When the Egger intercept is close to zero (e.g., < 0.002) and the P-value is large, this can be interpreted as no evidence of a substantial directional (horizontal) pleiotropic effect. When the Q-statistic for heterogeneity (difference in individual ratio estimates) is high and the corresponding p-value is small, this suggests evidence for heterogeneity and possibly horizontal pleiotropy. A high Q-statistic can be also used as an indicator of one or more variant outliers in the analysis, which may also be violating the MR assumptions.

Additionally, scatter plots of SNP effects from exposure and outcome fitted by all tested MR methods were evaluated for any deviations which would also be indicative of heterogeneity and violations of MR assumptions. Single SNP forest plots were used to summarise the effect of the exposure on the outcome due to each SNP separately, which is a helpful approach for visualising SNPs heterogeneity. Next, funnel plots were used to visually evaluate the direction of pleiotropy, which, if present, would be characterised by asymmetry in the plot. Finally, the sensitivity of causal inference to any individual genetic variant was tested by leave-one-out analysis, which is used to identify outliers.

In MVMR analyses, conditional F-statistics were used to evaluate the instrument strength⁷⁶, with F > 10 indicating suitable strength for the analysis. However, as in univariable MR, heterogeneity may be indicative of horizontal pleiotropy that does not act through one of the exposures. In MVMR, heterogeneity is quantified by Q_A-statistic (also a further modification of Cochran’s Q), and small Q_A indicates a lack of directional pleiotropic effect⁷⁶.

To calculate both statistic measures, a phenotypic correlation matrix for each MVMR test had to be constructed. This was done by applying the method for phenotypic matrix construction from GWAS summary data, available from metaCCA⁸⁰ R package. This is an alternative approach to using individual-level data for matrix construction. The method was only applied in cases when both exposures in MVMR were from the same sample (i.e., UK Biobank). When data samples were different, the default settings for F and Q_A statistics were used (i.e., gencov parameter set to zero)⁷⁶.

In the cases where MVMR sensitivity tests indicated the presence of weak instruments and potential pleiotropy via heterogeneity, Q-minimisation approach (Q-het) for estimating causal association was used to supplement the estimated of MVMR-IVW approach⁷⁶.