The interaction among multiple genes and environmental factors can affect an individual's susceptibility to disease. Some genes may not show strong marginal associations when they affect disease risk through interactions with other genes. As a result, these genes may not be identified by single-marker methods that are widely used in genome-wide association studies. To explore this possibility in real data, we carried out a two-stage model selection procedure of joint single-nucleotide polymorphism (SNP) analysis to detect genes associated with rheumatoid arthritis (RA) using Genetic Analysis Workshop 16 genome-wide association study data. In the first stage, the genetic markers were screened through an exhaustive two-dimensional search, through which promising SNP and SNP pairs were identified. Then, LASSO was used to choose putative SNPs from the candidates identified in the first stage. We then use the RA data collected by the Wellcome Trust Case Control Consortium to validate the putative genetic factors. Balancing computational load and statistical power, this method detects joint effects that may fail to emerge from single-marker analysis. Based on our proposed approach, we not only replicated the identification of important RA risk genes, but also found novel genes and their epistatic effects on RA. To our knowledge, this is the first two-dimensional scan based analysis for a real genome-wide association study.