Objective: The identification of gene-gene interactions has been limited by small sample size and large number of potential interactions between genes. To address this issue, Ritchie et al.  have proposed multifactor dimensionality reduction (MDR) method to detect polymorphisms associated with the disease risk. The MDR reduces the dimension of the genetic factors by classifying them into high-risk and low-risk groups. The strong point in favor of MDR is that it can detect interactions in absence of significant main effects. However, it often suffers from the sparseness of the cells in high-dimensional contingency tables, since it cannot classify an empty cell as high risk or low risk. Method: We propose a pair-wise multifactor dimensionality reduction (PWMDR) approach to address the issue of MDR in classifying sparse or empty cells. Instead of looking at the higher dimensional contingency table, we score each pair-wise interaction of the genetic factors involved and combine the scores of all such pairwise interactions. Results: Simulation studies showed that the PWMDR generally had greater power than MDR to detect third order interactions for polymorphisms with low allele frequencies. The PWMDR also outperformed the MDR in detecting gene-gene interaction on a kidney transplant dataset. Conclusion: The PWMDR outperformed the MDR to detect polymorphisms with low frequencies.
- Case-control study
- Gene-gene interaction
- Multifactor dimensionality reduction
- Nonparametric approach