Transplant matching for donor and recipient is traditionally based on various clinical aspects, and any genetic matching focuses only on the major histocompatibility complex (MHC) of the genome, which codes for a large set of immune genes. Due to a lack of improvement in long-term transplant outcomes over the years, there has been a recent push to look beyond the MHC at other genomic regions that may be important for donor/recipient matching. Unfortunately, no clear definition of genetic matching distance between a donor/recipient pair has been established in the field, and association results may differ based on what measure is used for analysis. In this work, we focus on establishing and testing various statistical methods that can be applied to paired donor/recipient genetic data. First, we focus on genetic matching at a single genetic variant, examining four different genetic matching scores. Our work shows that jointly testing the recipient genotype variant and matching score is a powerful preliminary screening method to discover transplant outcome related variants. Following-up with marginal testing can then lead to more insight on potential biological mechanisms behind transplant outcomes. Application of these methods to liver transplant data analysis found various genetic variants where a genetic matching score was associated with time to acute rejection. Building on this work, we then propose a multi-marker Joint Score Test (JST) to jointly test for association between recipient genotypes and a gene-based donor/recipient matching score with transplant outcome. Extensive simulation studies show JST is competitive when compared with existing methods, especially when the associated variants are in low linkage disequilibrium with the rest of the variants in the region. Applying JST to paired kidney transplant data gave insight into gene regions that are potentially associated with acute rejection outcome. Lastly, focusing on association testing of genetic matching score only, we investigated the performance of four existing high-dimensional data methods that allow us to account for a potentially large number of recipient genotype variant effects.