Studying complex diseases, such as autoimmune diseases, can lead to the detection of pleiotropic loci with otherwise small effects. Through the detection of pleiotropic loci the genetic architecture of these complex diseases can be better defined, allowing for subsequent improvements in their treatment and prevention efforts. Here, we investigate the genetic relatedness of complex diseases through the detection and quantification of simultaneous disease-associated genetic variants using genome-wide association study (GWAS) data. We propose two max-type statistics, with and without an added level of dependency on the directions of the genetic effects, that globally test whether a pair of complex diseases shares at least one disease-associated genetic variant. The proposed global tests are based on the simultaneity of complex disease-associated genetic variants, allowing for the determination of exact p-values from a permutation distribution assuming independence. While an independence assumption is often imposed on genetic variants, we propose a perturbation procedure for evaluating the statistical significance of one of the proposed global tests, preserving the inherent dependency structure among genetic variants. We extend that global test beyond the detection of genetic relatedness at identical genetic variants to the detection of genetic relatedness within dependency-defined windows across the genome. With the proposed methods we identify pairs of pediatric autoimmune diseases (pAIDs) that exhibit evidence of genetic sharing, such as Crohn's disease and ulcerative colitis. We then characterize the detected genetic sharing between a pair of complex diseases through the quantification of shared disease-associated genetic variants using GWAS data. We develop a quantification measure as a function of standardized variant effect sizes, adjusted for the total number of genetic variants and varied GWAS sample size. The quantification measure acts as an estimate of the genetic correlation among shared disease-associated genetic variants. We use a bootstrapping procedure to estimate the properties of our quantification measure. In applying the developed measure to pAID GWAS we observe similar trends in relatedness among pAIDs pairs.