The global randomization test: A Mendelian randomization falsification test for the exclusion restriction assumption

Mendelian randomization may give biased causal estimates if the instrument affects the outcome not solely via the exposure of interest (violating the exclusion restriction assumption). We demonstrate use of a global randomization test as a falsification test for the exclusion restriction assumption. Using simulations, we explored the statistical power of the randomization test to detect an association between a genetic instrument and a covariate set due to a) selection bias or b) horizontal pleiotropy, compared to three approaches examining associations with individual covariates: i) Bonferroni correction for the number of covariates, and ii) correction for the effective number of independent covariates and iii) an r2 permutation-based approach. We conducted proof-of-principle analyses in UK Biobank, using CRP as the exposure and coronary heart disease (CHD) as the outcome. In simulations, power of the randomization test was higher than the other approaches for detecting selection bias when the correlation between the covariates was low (R2< 0.1), and at least as powerful as the other approaches across all simulated horizontal pleiotropy scenarios. In our applied example, we found strong evidence of selection bias using all approaches (e.g., global randomization test p<0.002). We identified 51 of the 58 CRP genetic variants as horizontally pleiotropic, and estimated effects of CRP on CHD attenuated somewhat to the null when excluding these from the genetic risk score (OR=0.956 [95% CI: 0.918, 0.996] versus 0.970 [95% CI: 0.900, 1.046] per 1-unit higher log CRP levels). The global randomization test can be a useful addition to the MR researcher s toolkit.