Multivariate Cluster-Based Multifactor Dimensionality Reduction to Identify Genetic Interactions for Multiple Quantitative Phenotypes

Abstract

To understand the pathophysiology of complex diseases, including hypertension, diabetes, and autism, deleterious phenotypes are unlikely due to the effects of single genes, but rather, gene-gene interactions (GGIs), which are widely analyzed by multifactor dimensionality reduction (MDR). Early MDR methods mainly focused on binary traits. More recently, several extensions of MDR have been developed for analyzing various traits such as quantitative traits and survival times. Newer technologies, such as genome-wide association studies (GWAS), have now been developed for assessing multiple traits, to simultaneously identify genetic variants associated with various pathological phenotypes. It has also been well demonstrated that analyzing multiple traits has several advantages over single trait analysis. While there remains a need to find GGIs for multiple traits, such studies have become more difficult, due to a lack of novel methods and software. Herein, we propose a novel multi-CMDR method, by combining fuzzy clustering and MDR, to find GGIs for multiple traits. Multi-CMDR showed similar power to existing methods, when phenotypes followed bivariate normal distributions, and showed better power than others for skewed distributions. The validity of multi-CMDR was confirmed by analyzing real-life Korean GWAS data.

Figure 1

Summary of the multi-CMDR algorithm in the case of 10-fold and 2^nd-order gene-gene interactions.

Figure 2

Hit-ratios for a multivariate normal distribution and multivariate gamma distribution. MCMDR (multi-CMDR), MCMDR2 (multi-CMDR without trimming, MCMDR3 (multi-CMDR, without membership score), MQMDR (multi-QMDR), QMDR.Y1 (QMDR with Y₁), and QMDR.Y2 (QMDR with Y₂).

Figure 3

(Left) Scatter plots, histograms, and correlations between phenotypes. (Right) Box plots of phenotypes.

Pseudocode 1

Pseudocode of multi-CMDR.