A comparative study on the unified model based multifactor dimensionality reduction methods for identifying gene-gene interactions associated with the survival phenotype
Authors: Lee Jung Wun , Lee Seungyeoun 
Published: March 2021

Abstract
Background
For gene-gene interaction analysis, the multifactor dimensionality reduction (MDR) method has been widely employed to reduce multi-levels of gene-gene interactions into high- or low-risk groups using a binary attribute. For the survival phenotype, the Cox-MDR method has been proposed using a martingale residual of a Cox model since Surv-MDR was first proposed using a log-rank test statistic. Recently, the KM-MDR method was proposed using the Kaplan-Meier median survival time as a classifier. All three methods used the cross-validation procedure to identify single nucleotide polymorphism (SNP) using SNP interactions among all possible SNP pairs. Furthermore, these methods require the permutation test to verify the significance of the selected SNP pairs. However, the unified model-based multifactor dimensionality reduction method (UM-MDR) overcomes this shortcoming of MDR by unifying the significance testing with the MDR algorithm within the framework of the regression model. Neither cross-validation nor permutation testing is required to identify SNP by SNP interactions in the UM-MDR method. The UM-MDR method comprises two steps: in the first step, multi-level genotypes are classified into high- or low-risk groups, and an indicator variable for the high-risk group is defined. In the second step, the significance of the indicator variable of the high-risk group is tested in the regression model included with other adjusting covariates. The Cox-UMMDR method was recently proposed by combining Cox-MDR with UM-MDR to identify gene-gene interactions associated with the survival phenotype. In this study, we propose two simple methods either by combining KM-MDR with UM-MDR, called KM-UMMDR or by modifying Cox-UMMDR by adjusting for the covariate effect in step 1, rather than in step 2, a process called Cox2-UMMDR. The KM-UMMDR method allows the covariate effect to be adjusted for in the regression model of step 2, although KM-MDR cannot adjust for the covariate effect in the classification procedure of step 1. In contrast, Cox2-UMMDR differs from Cox-UMMDR in the sense that the martingale residuals are obtained from a Cox model by adjusting for the covariate effect in step 1 of Cox2-UMMDR whereas Cox-UMMDR adjusts for the covariate effect in the regression model in step 2. We performed simulation studies to compare the power of several methods such as KM-UMMDR, Cox-UMMDR, Cox2-UMMDR, Cox-MDR, and KM-MDR by considering the effect of covariates and the marginal effect of SNPs. We also analyzed a real example of Korean leukemia patient data for illustration and a short discussion is provided.

Results
In the simulation study, two different scenarios are considered: the first scenario compares the power of the cases with and without the covariate effect. The second scenario is to compare the power of cases with the main effect of SNPs versus without the main effect of SNPs. From the simulation results, Cox-UMMDR performs the best across all scenarios among KM-UMMDR, Cox2-UMMDR, Cox-MDR and KM-MDR. As expected, both Cox-UMMDR and Cox-MDR perform better than KM-UMMDR and KM-MDR when a covariate effect exists because the former adjusts for the covariate effect but the latter cannot. However, Cox2-UMMDR behaves similarly to KM-UMMDR and KM-MDR even though there is a covariate effect. This implies that the covariate effect would be more efficiently adjusted for in the regression model of the second step rather than under the classification procedure of the first step. When there is a main effect of any SNP, Cox-UMMDR, Cox2-UMMDR and KM-UMMDR perform better than Cox-MDR and KM-MDR if the main effects of SNPs are properly adjusted for in the regression model. From the simulation results of two different scenarios, Cox-UMMDR seems to be the most robust when there is either any covariate effect adjusting for or any SNP that has a main effect on the survival phenotype. In addition, the power of all methods decreased as the censoring fraction increased from 0.1 to 0.3, as heritability increased. The power of all methods seems to be greater under MAF = 0.2 than under MAF = 0.4. For illustration, both KM-UMMDR and Cox2-UMMDR were applied to identify SNP by SNP interactions with the survival phenotype to a real dataset of Korean leukemia patients.

Conclusion
Both KM-UMMDR and Cox2-UMMDR were easily implemented by combining KM-MDR and Cox-MDR with UM-MDR, respectively, to detect significant gene-gene interactions associated with survival time without cross-validation and permutation testing. The simulation results demonstrate the utility of KM-UMMDR, Cox2-UMMDR and Cox-UMMDR, which outperforms Cox-MDR and KM-MDR when some SNPs with only marginal effects might mask the detection of causal epistasis. In addition, Cox-UMMDR, Cox2-UMMDR and Cox-MDR performed better than KM-UMMDR and KM-MDR when there were potentially confounding covariate effects.