Abstract
Mendelian randomisation (MR) estimates causal effects of modifiable phenotypes on an outcome by using genetic variants as instrumental variables, but its validity relies on the assumption of no pleiotropy, that is, genes influence the outcome only through the given phenotype. Excluding pleiotropy is difficult, but the use of multiple instruments can indirectly address the issue: if all genes represent valid instruments, their MR estimates should vary only by chance. The Sargan test detects pleiotropy when individual phenotype, outcome and genotype data are measured in the same subjects. We propose an alternative approach to be used when only summary genetic data are available or data on gene-phenotype and gene-outcome come from different subjects. The presence of pleiotropy is investigated using the between-instrument heterogeneity Q test (together with the I(2) index) in a meta-analysis of MR Wald estimates, derived separately from each instrument. For a continuous outcome, we evaluate the approach through simulations and illustrate it using published data. For the scenario where all data come from the same subjects, we compare it with the Sargan test. The Q test tends to be conservative in small samples. Its power increases with the degree of pleiotropy and the sample size, as does the precision of the I(2) index, in which case results are similar to those of the Sargan test. In MR studies with large sample sizes based on summary data, the between-instrument Q test represents a useful tool to explore the presence of heterogeneity due to pleiotropy or other causes.