Gene–gene interaction (GGI) is one of the most popular approaches for finding and explaining the missing heritability of common complex traits in genome-wide association studies. The multifactor dimensionality reduction (MDR) method has been widely studied for detecting GGI effects. However, there are several disadvantages of the existing MDR-based approaches, such as the lack of an efficient way of evaluating the significance of multi-locus models and the high computational burden due to intensive permutation. Furthermore, the MDR method does not distinguish marginal effects from pure interaction effects.


We propose a two-step unified model based MDR approach (UM-MDR), in which, the significance of a multi-locus model, even a high-order model, can be easily obtained through a regression framework with a semi-parametric correction procedure for controlling Type I error rates. In comparison to the conventional permutation approach, the proposed semi-parametric correction procedure avoids heavy computation in order to achieve the significance of a multi-locus model. The proposed UM-MDR approach is flexible in the sense that it is able to incorporate different types of traits and evaluate significances of the existing MDR extensions.


The simulation studies and the analysis of a real example are provided to demonstrate the utility of the proposed method. UM-MDR can achieve at least the same power as MDR for most scenarios, and it outperforms MDR especially when there are some single nucleotide polymorphisms that only have marginal effects, which masks the detection of causal epistasis for the existing MDR approaches.


UM-MDR provides a very good supplement of existing MDR method due to its efficiency in achieving significance for every multi-locus model, its power and its flexibility of handling different types of traits.

Availability and implementation

A R package “umMDR” and other source codes are freely available at


[email protected]

Supplementary information

Supplementary data are available at Bioinformatics online.

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