One goal of personal genomics is to use information about genomic variation to predict who is at risk for various common diseases. Technological advances in genotyping have spawned several personal genetic testing services that market genotyping services directly to the consumer. An important goal of consumer genetic testing is to provide health information along with the genotyping results. This has the potential to integrate detailed personal genetic and genomic information into healthcare decision making. Despite the potential importance of these advances, there are some important limitations. One concern is that much of the literature that is used to formulate personal genetics reports is based on genetic association studies that consider each genetic variant independently of the others. It is our working hypothesis that the true value of personal genomics will only be realized when the complexity of the genotype-to-phenotype mapping relationship is embraced, rather than ignored. We focus here on complexity in genetic architecture due to epistasis or nonlinear gene-gene interaction. We have previously developed a multifactor dimensionality reduction (MDR) algorithm and software package for detecting nonlinear interactions in genetic association studies. In most prior MDR analyses, the permutation testing strategy used to assess statistical significance was unable to differentiate MDR models that captured only interaction effects from those that also detected independent main effects. Statistical interpretation of MDR models required post-hoc analysis using entropy-based measures of interaction information. We introduce here a novel permutation test that allows the effects of nonlinear interactions between multiple genetic variants to be specifically tested in a manner that is not confounded by linear additive effects. We show using data simulated across 35 different epistasis models with varying effect sizes (heritabilities = 0.01, 0.025, 0.05, 0.1, 0.2, 0.3, 0.4) and sample sizes (n = 400, 800, 1600) that the power to detect interactions using the explicit test of epistasis is no different than a standard permutation test. We also show that the test has the appropriate size or type I error rate of approximately 0.05. We then apply MDR with the new explicit test of epistasis to a large genetic study of bladder cancer (n=914) and show that a previously reported nonlinear interaction between two XPD gene polymorphisms is indeed significant (P = 0.005), even after considering the strong additive effect of smoking in the model. Finally, we evaluated the power of the explicit test of epistasis to detect the nonlinear interaction between two XPD gene polymorphisms by simulating data from the MDR model of bladder cancer susceptibility. We show that the power to detect the interaction alone was 1.00 while the power to detect the independent effect of smoking alone was 0.06 which is close to the expected type I error rate of 0.05. Importantly, the power to detect the interaction with smoking in the model was 0.94. The results of this study provide for the first time a simple method for explicitly testing epistasis or gene-gene interaction effects in genetic association studies. An important advantage of the method is that it can be combined with any modeling approach. The explicit test of epistasis brings us a step closer to the type of routine gene-gene interaction analysis that is needed if we are to enable personal genomics.