Meta-analysis and Mendelian randomization: A review

Mendelian randomization (MR) uses genetic variants as instrumental variables to infer whether a risk factor causally affects a health outcome. Meta‐analysis has been used historically in MR to combine results from separate epidemiological studies, with each study using a small but select group of genetic variants. In recent years it has been used to combine genome‐wide association study (GWAS) summary data for large numbers of genetic variants. Heterogeneity amongst the causal estimates obtained from multiple genetic variants points to a possible violation of the necessary instrumental variable assumptions. In this article we provide a basic introduction to MR and the instrumental variable theory that it relies upon. We then describe how random effects models, meta‐regression and robust regression are being used to test and adjust for heterogeneity in order to improve the rigour of the MR approach.