• Mendelian randomization;
  • meta-analysis;
  • multivariate models;
  • methylene tetrahydrofolate reductase (MTHFR) gene;
  • instrumental variables


In traditional epidemiological studies the association between phenotype (risk factor) and disease is often biased by confounding and reverse causation. As a person's genotype is assigned by a seemingly random process, genes are potentially useful instrumental variables for adjusting for such bias. This type of adjustment combines information on the genotype–disease association and the genotype–phenotype association to estimate the phenotype–disease association and has become known as Mendelian randomization. The information on genotype–disease and genotype–phenotype may well come from a meta-analysis. In such a synthesis, a multivariate approach needs to be used whenever some studies provide evidence on both the genotype–phenotype and genotype–disease associations. This paper presents two multivariate meta-analytical models, which differ in their treatment of the heterogeneities (between-study variances). Heterogeneities on the genotype–phenotype and genotype–disease associations may be highly correlated, but a multivariate model that parameterizes the heterogeneity directly is difficult to fit because that correlation is poorly estimated. We advocate an alternative model that treats the heterogeneities on genotype–phenotype and phenotype–disease as being independent. This model fits readily and implicitly defines the correlation between the heterogeneities on genotype–phenotype and genotype–disease. We show how either maximum likelihood or a Bayesian approach with vague prior distributions can be used to fit the alternative model. Copyright © 2005 John Wiley & Sons, Ltd.