Bayesian methods for instrumental variable analysis with genetic instruments ('Mendelian randomization'): example...

The 'Mendelian randomization' approach uses genotype as an instrumental variable to distinguish between causal and non-causal explanations of biomarker-disease associations. Classical methods for instrumental variable analysis are limited to linear or probit models without latent variables or missing data, rely on asymptotic approximations that are not valid for weak instruments and focus on estimation rather than hypothesis testing. We describe a Bayesian approach that overcomes these limitations, using the JAGS program to compute the log-likelihood ratio (lod score) between causal and non-causal explanations of a biomarker-disease association. To demonstrate the approach, we examined the relationship of plasma urate levels to metabolic syndrome in the ORCADES study of a Scottish population isolate, using genotype at six single-nucleotide polymorphisms in the urate transporter gene SLC2A9 as an instrumental variable. In models that allow for intra-individual variability in urate levels, the lod score favouring a non-causal over a causal explanation was 2.34. In models that do not allow for intra-individual variability, the weight of evidence against a causal explanation was weaker (lod score 1.38). We demonstrate the ability to test one of the key assumptions of instrumental variable analysis--that the effects of the instrument on outcome are mediated only through the intermediate variable--by constructing a test for residual effects of genotype on outcome, similar to the tests of 'overidentifying restrictions' developed for classical instrumental variable analysis. The Bayesian approach described here is flexible enough to deal with any instrumental variable problem, and does not rely on asymptotic approximations that may not be valid for weak instruments. The approach can easily be extended to combine information from different study designs. Statistical power calculations show that instrumental variable analysis with genetic instruments will typically require combining information from moderately large cohort and cross-sectional studies of biomarkers with information from very large genetic case-control studies.