Robust statistical methods, utilising the vast amounts of genetic data that is now available, are required to resolve the genetic aetiology of complex human diseases including immune-mediated diseases. Essential to this process is firstly the use of genome-wide association studies (GWAS) to identify regions of the genome that determine the susceptibility to a given complex disease. Following this, identified regions can be fine-mapped with the aim of deducing the specific sequence variants that are causal for the disease of interest.

Functional genomic data is now routinely generated from high-throughput experiments. This data can reveal clues relating to disease biology, for example elucidating the functional genomic annotations that are enriched for disease-associated variants. In this thesis I describe a novel methodology based on the conditional false discovery rate (cFDR) that leverages functional genomic data with genetic association data to increase statistical power for GWAS discovery whilst controlling the FDR. I demonstrate the practical potential of my method through applications to asthma and type 1 diabetes (T1D) and validate my results using the larger, independent, UK Biobank data resource.

Fine-mapping is used to derive credible sets of putative causal variants in associated regions from GWAS. I show that these sets are generally over-conservative due to the fact that fine-mapping data sets are not randomly sampled, but are instead sampled from a subset of those with the largest effect sizes. I develop a method to derive credible sets that contain fewer variants whilst still containing the true causal variant with high probability. I use my method to improve the resolution of fine-mapping studies for T1D and ankylosing spondylitis. This enables a more efficient allocation of resources in the expensive functional follow-up studies that are used to elucidate the true causal variants from the prioritised sets of variants.

Whilst GWAS investigate genome-wide patterns of association, it is likely that studying a specific biological factor using a variety of data sources will give a more detailed perspective on disease pathogenesis. Taking a more holistic approach, I utilise a variety of genetic and functional genomic data in a range of statistical genetics techniques to try and decipher the role of the Ikaros family of transcription factors in T1D pathogenesis. I find that T1D-associated variants are enriched in Ikaros binding sites in immune-relevant cell types, but that there is no evidence of epistatic effects between causal variants residing in the Ikaros gene region and variants residing in genome-wide binding sites of Ikaros, thus suggesting that these sets of variants are not acting synergistically to influence T1D risk.

Together, in this thesis I develop and examine a range of statistical methods to aid understanding of the genetic basis of complex human diseases, with application specifically to immune-mediated diseases.