The effect of alternative permutation testing strategies on the performance of multifactor dimensionality reduction

Multifactor Dimensionality Reduction (MDR) is a novel method developed to detect gene-gene interactions in case-control association analysis by exhaustively searching multi-locus combinations. While the end-goal of analysis is hypothesis generation, significance testing is employed to indicate statistical interest in a resulting model. Because the underlying distribution for the null hypothesis of no association is unknown, non-parametric permutation testing is used. Lately, there has been more emphasis on selecting all statistically significant models at the end of MDR analysis in order to avoid missing a true signal. This approach opens up questions about the permutation testing procedure. Traditionally omnibus permutation testing is used, where one permutation distribution is generated for all models. An alternative is n-locus permutation testing, where a separate distribution is created for each n-level of interaction tested.

In this study, we show that the false positive rate for the MDR method is at or below a selected alpha level, and demonstrate the conservative nature of omnibus testing. We compare the power and false positive rates of both permutation approaches and find omnibus permutation testing optimal for preserving power while protecting against false positives.

Omnibus permutation testing should be used with the MDR method.