The objective of the study was to identify interacting genes contributing to rheumatoid arthritis (RA) susceptibility and identify SNPs that discriminate between RA patients who were anti-cyclic citrullinated protein positive and healthy controls. We analyzed two independent cohorts from the North American Rheumatoid Arthritis Consortium. A cohort of 908 RA cases and 1,260 controls was used to discover pairwise interactions among SNPs and to identify a set of single nucleotide polymorphisms (SNPs) that predict RA status, and a second cohort of 952 cases and 1,760 controls was used to validate the findings. After adjusting for HLA-shared epitope alleles, we identified and replicated seven SNP pairs within the HLA class II locus with significant interaction effects. We failed to replicate significant pairwise interactions among non-HLA SNPs. The machine learning approach "random forest" applied to a set of SNPs selected from single-SNP and pairwise interaction tests identified 93 SNPs that distinguish RA cases from controls with 70% accuracy. HLA SNPs provide the most classification information, and inclusion of non-HLA SNPs improved classification. While specific gene-gene interactions are difficult to validate using genome-wide SNP data, a stepwise approach combining association and classification methods identifies candidate interacting SNPs that distinguish RA cases from healthy controls.

An SIR epidemiological community-structured model is constructed to investigate the effects of clustered distributions of unvaccinated individuals and the distribution of the primary case relative to vaccination levels. The communities here represent groups such as neighborhoods within a city or cities within a region. The model contains two levels of mixing, where individuals make more intra-group than inter-group contacts. Stochastic simulations and analytical results are utilized to explore the model. An extension of the effective reproduction ratio that incorporates more spatial information by predicting the average number of tertiary infections caused by a single infected individual is introduced to characterize the system. Using these methods, we show that both the vaccination coverage and the variation in vaccination levels among communities affect the likelihood and severity of epidemics. The location of the primary infectious case and the degree of mixing between communities are also important factors in determining the dynamics of outbreaks. In some cases, increasing the efficacy of a vaccine can in fact increase the effective reproduction ratio in early generations, due to the effects of population structure on the likely initial location of an infection.