Bias in causal estimates from Mendelian randomization studies with weak instruments

Mendelian randomization studies using genetic instrumental variables (IVs) are now being commonly used to estimate the causal association of a phenotype on an outcome. Even when the necessary underlying assumptions are valid, estimates from analyses using IVs are biased in finite samples. The source and nature of this bias appear poorly understood in the epidemiological field. We explain why the bias is in the direction of the confounded observational association, with magnitude relating to the statistical strength of association between the instrument and phenotype. We comment on the size of the bias, from simulated data, showing that when multiple instruments are used, although the variance of the IV estimator decreases, the bias increases. We discuss ways to analyse Mendelian randomization studies to alleviate the problem of weak instrument bias.