A Robust Multifactor Dimensionality Reduction Method for Detecting Gene-Gene Interactions with Application to the Genetic Analysis of Bladder Cancer Susceptibility

TLDR

Human genetics aims to identify susceptibility genes for common diseases, but modeling gene–gene interactions (epistasis) remains challenging; the multifactor dimensionality reduction (MDR) method was introduced as a machine‑learning alternative to logistic regression for detecting such interactions without significant marginal effects. This study proposes Robust Multifactor Dimensionality Reduction (RMDR), which applies constructive induction using Fisher’s Exact Test instead of a fixed threshold to reduce dimensionality in genotype combination analysis. RMDR performs constructive induction with Fisher’s Exact Test, evaluates only statistically significant genotype combinations, and was tested via simulations that show higher success rates when few combinations are significant, and applied to bladder‑cancer genotype data from a New Hampshire population study. Simulations demonstrate that RMDR increases MDR success when few genotype combinations are significant, while maintaining performance when many are significant, and the method limits analysis to only statistically significant combinations.

Abstract

A central goal of human genetics is to identify susceptibility genes for common human diseases. An important challenge is modelling gene–gene interaction or epistasis that can result in nonadditivity of genetic effects. The multifactor dimensionality reduction (MDR) method was developed as a machine learning alternative to parametric logistic regression for detecting interactions in the absence of significant marginal effects. The goal of MDR is to reduce the dimensionality inherent in modelling combinations of polymorphisms using a computational approach called constructive induction. Here, we propose a Robust Multifactor Dimensionality Reduction (RMDR) method that performs constructive induction using a Fisher's Exact Test rather than a predetermined threshold. The advantage of this approach is that only statistically significant genotype combinations are considered in the MDR analysis. We use simulation studies to demonstrate that this approach will increase the success rate of MDR when there are only a few genotype combinations that are significantly associated with case-control status. We show that there is no loss of success rate when this is not the case. We then apply the RMDR method to the detection of gene–gene interactions in genotype data from a population-based study of bladder cancer in New Hampshire.