Model-based multifactor dimensionality reduction for detecting epistasis in case-control data in the presence of noise

Abstract

Analyzing the combined effects of genes and/or environmental factors on the development of complex diseases is a great challenge from both the statistical and computational perspective, even using a relatively small number of genetic and nongenetic exposures. Several data-mining methods have been proposed for interaction analysis, among them, the Multifactor Dimensionality Reduction Method (MDR) has proven its utility in a variety of theoretical and practical settings. Model-Based Multifactor Dimensionality Reduction (MB-MDR), a relatively new MDR-based technique that is able to unify the best of both nonparametric and parametric worlds, was developed to address some of the remaining concerns that go along with an MDR analysis. These include the restriction to univariate, dichotomous traits, the absence of flexible ways to adjust for lower order effects and important confounders, and the difficulty in highlighting epistatic effects when too many multilocus genotype cells are pooled into two new genotype groups. We investigate the empirical power of MB-MDR to detect gene-gene interactions in the absence of any noise and in the presence of genotyping error, missing data, phenocopy, and genetic heterogeneity. Power is generally higher for MB-MDR than for MDR, in particular in the presence of genetic heterogeneity, phenocopy, or low minor allele frequencies.

Figure 1. Graphical overview of major MB-MDR steps

Figure 2. Penetrance functions of simulated data of (Ritchie et al., 2003)

Multilocus penetrance functions and MAFs used to simulate case-control data exhibiting gene-gene interactions in the absence of main effects.

Figure 3. MB-MDR and MDR power with different sources of noise, excluding genetic heterogeneity

The 6 plots display MB-MDR power estimates to identify the correct interacting pair for models 1-6, for different p-value cut-offs p_c = 0.05,0.1,0.2,0.5 and 1. The color coding is as follows: error-free data (black), data with induced missingness (red), genotyping errors (green) and phenocopy (blue). The line types refer to the different MB-MDR testing strategies used: T = |T_H/L| (solid line), max (|T_H/LO|,|T_L/HO|) (dashed line) and max (|T_H/L|,|T_H/LO|,|T_L/HO|) (dot-dashed line). MDR power estimates of screening over 1-5 order models are also shown (bullets at p_c=1).

Figure 4. MB-MDR and MDR power in the presence of genetic heterogeneity

The 6 plots display MB-MDR power estimates for models 1-6, for different p-value cut-offs P_c = 0.05,0.1,0.2,0.5 and 1. The color coding is as follows: power to identify both interacting pairs (black), the first interacting pair (red), and at least one of the interacting pairs (green). The line types refer to the different MB-MDR testing strategies used: T = |T_H/L| (solid line), max (|T_H/LO|,|T_L/HO|) (dashed line) and max (|T_H/L|,|T_H/LO|,|T_L/HO|) (dot-dashed line). MDR power estimates of screening over 1-5 order models are also shown (bullets at P_c=1).