In Mendelian randomization a carefully selected gene is used as an instrumental variable in the estimation of the association between a biological phenotype and a disease. A study using Mendelian randomization will have information on an individual's disease status, the genotype and the phenotype. The phenotype must be on the causal pathway between gene and disease for the instrumental-variable analysis to be valid. For a biallelic polymorphism there are three possible genotypes with which to compare disease risk. Existing methods select two of the three possible genotypes for use in a Mendelian randomization analysis. Multivariate meta-analysis models for Mendelian randomization case-control studies are proposed, which extend previous methods by estimating the pooled phenotype-disease association across both genotype comparisons by using the gene-disease log odds ratios and differences in mean phenotypes. The methods are illustrated using a meta-analysis of the effect of a gene related to collagen production on bone mineral density and osteoporotic fracture.