International journal of epidemiology
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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. ⋯ 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.