The Mendelian randomization approach is concerned with the causal pathway between a gene, an intermediate phenotype and a disease. The aim of the approach is to estimate the causal association between the phenotype and the disease when confounding or reverse causation may affect the direct estimate of this association. The approach represents the use of genes as instrumental variables in epidemiological research and is justified through Mendel's second law.\ud \ud Instrumental variable analysis was developed in econometrics as an alternative to regression analyses affected by confounding and reverse causation. Methods such as two-stage least squares are appropriate for instrumental variable analyses where the phenotype and disease are continuous. However, case-control and cohort studies typically report binary outcomes and instrumental variable methods for these studies are less well developed.\ud \ud For a binary outcome study three estimators of the phenotype-disease log odds ratio are compared. An adjusted instrumental variable estimator is shown to have the least bias compared with the other two estimators. However, significance tests of the adjusted estimator are shown to have an inflated type I error rate, so the standard estimator, which had the correct type I error rate, could be used for testing.\ud \ud A single study may not have adequate statistical power to detect a causal association in a Mendelian randomization analysis. Meta-analysis models that extend existing approaches are investigated. The ratio of coefficients approach is applied within the meta-analysis models and a Taylor series approximation is used to investigate its finite sample bias.\ud \ud The increasing awareness of the Mendelian randomization approach has made researchers aware of the need for instrumental variable methods appropriate for epidemiological study designs. The work in this thesis viewed in the context of the research into instrumental variable analysis in other areas of biostatistics such as non-compliance in clinical trials and other subject areas such as econometrics and causal inference contributes to the development of methods for Mendelian randomization analyses
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