Introduction and aims: Methodology and software for the analysis of genome-wide association studies (GWAS) have focused on binary phenotypes and quantitative traits. However, the impact of single nucleotide polymorphisms (SNPs) on time-to-event (TTE) outcomes is understudied, particularly for pharmacogenetic GWAS. Statistical methodology and computational tools to design and analyse GWAS with TTE outcomes are not well developed, due to the scale and complexity of data, particularly when analysing rare variants. This thesis aims to develop statistical methodology and a variety of computational tools to aid the design and analysis of both GWAS of common and rare variants with TTE outcomes. Methods: This thesis compares existing methodology such as the Cox proportional hazards, logistic and Weibull regression models using simulations based on a range of pharmacogenetic GWAS designs with TTE outcomes. This thesis also presents new statistical methodologies for the analysis of rare variants using a combination of gene-based tests of association and TTE regression models. Results: Examination of the literature provided an overview of the methods and software used for analysing GWAS with TTE outcomes. One approach taken due to lack of software availability was to dichotomise event times at a fixed time-point and analyse the binary outcome using existing GWAS software. A simulation study was conducted comparing alternative regression models under pharmacogenetic TTE study designs. This simulation study demonstrated that dichotomisation of the TTE outcome would result in a loss of statistical power. Hence, the thesis outlines three user-friendly computational tools specific to TTE GWAS. The first is SurvivalGWAS_Power, which performs power calculations and generates sample pharmacogenetic data across a range of design scenarios, allowing for censoring and interactions. Second, SurvivalGWAS_- SV, software capable of analysing large-scale imputed GWAS data, offering a variety of survival analysis models. Third, rareSurvival, a command line application, which implements gene-based burden tests for the analysis of rare variants with TTE outcomes. SurvivalGWAS_SV and rareSurvival have been evaluated through simulation studies as well as application to a GWAS investigating the pharmacogenetics of acute coronary syndrome (PhACS). The single variant and gene discovery analyses of the PhACS study identified novel loci associated with time to recurrence of a cardiovascular event including rs56045815 located in the CTNNA2 gene. Conclusions: This thesis introduces three novel computational tools for GWAS with TTE outcomes. SurvivalGWAS_SV and rareSurvival are compatible with highperformance computing clusters and are available on Linux, Windows and Mac OSX operating systems. SurvivalGWAS_SV and rareSurvival were applied to the PhACS data, identifying significantly associated SNPs and functional units for further followup. With their particular relevance to pharmacogenetic GWAS, SurvivalGWAS_Power, SurvivalGWAS_SV and rareSurvival, will help in the design of studies and identification of genetic biomarkers of patient response to treatment, with the ultimate goal of personalising therapeutic interventions.