QMDR solves this dilemma elegantly by collapsing all high-level genotypes and all low-level genotypes into a two level attribute. This not only makes it easier to detect higher order interaction terms, but also makes it possible to incorporate the QMDR attribute into other statistical and machine learning algorithms, such as Boosting and neural networks. This will allow researchers to build more accurate models that involve multiple genotype combinations. As we can see from real data results, QMDR successfully identifies a four-way interaction model that is strongly associated with female PAI-1 levels. This is good example of how QMDR can gain biological information above that previously obtained using a more traditional ANOVA approach. QMDR also offers a cross-validation procedure to pick the best model based on the testing score. Since high-order interactions tend to have better training scores than low-order interactions, these cross-validation procedures are necessary to limit model over-fitting. The QMDR algorithm also explores the empirical distribution of the testing score from the null models and applies it to estimate the significance of the selected model. From the simulation, we demonstrated that QMDR can detect the presence of multiplicative interaction models, even when main effects are not statistically significant. These epistatic combinations tend to be missed or dropped when using traditional linear regression approaches. Last but not least, QMDR 
is computationally efficient. One of the first algorithms developed to explore genegene interactions was the Combinatorial Partitioning Method. While elegant, its computing time increase exponentially with the number of genes examined. In contrast, QMDR’s computing time is 0 for two-way interactions. QMDR is has a nearly two-fold computational speed advantage over GMDR, as demonstrated through simulations. This increase in speed is vitally important and makes QMDR a feasible method to use when exploring large datasets such as genome-wide association studies. Despite the advantages stated above, one limitation to the approach is that the QMDR method does not have a way to It has been reported that CHOP2/2mice exhibit reduced apoptosis in response to ER stress adjust for covariate effects such as age, gender and smoking status, an often necessary step to obtain an unconfounded SNP interactionsoutcome association. Investigators can, however, first fit a model with potential confounders and the outcome of interest and then use the residuals in QMDR, as we did to adjust for SNP main effects in this paper. However, if there are too many covariates, this approach may overfit the data and sometimes fail due to limited sample size. One strength of QMDR is that it can be extended to the analysis of interactions among non-genetic variables as well as gene-environment interactions. For example, QMDR will facilitate pharmacogenomic analyses by identifying combinations of drug treatments and genotypes that affect time to progression. In summary, we demonstrate that QMDR is a promising dimension reduction method for the efficient identification of SNP interactions.