An empirical fuzzy multifactor dimensionality reduction method for detecting gene-gene interactions

Background: Detection of gene-gene interaction (GGI) is a key challenge towards solving the problem of missing heritability in genetics. The multifactor dimensionality reduction (MDR) method has been widely studied for detecting GGIs. MDR reduces the dimensionality of multi-factor by means of binary classification into high-risk (H) or low-risk (L) groups. Unfortunately, this simple binary classification does not reflect the uncertainty of H/L classification. Thus, we proposed Fuzzy MDR to overcome limitations of binary classification by introducing the degree of membership of two fuzzy sets H/L. While Fuzzy MDR demonstrated higher power than that of MDR, its performance is highly dependent on the several tuning parameters. In real applications, it is not easy to choose appropriate tuning parameter values. Result: In this work, we propose an empirical fuzzy MDR (EF-MDR) which does not require specifying tuning parameters values. Here, we propose an empirical approach to estimating the membership degree that can be directly estimated from the data. In EF-MDR, the membership degree is estimated by the maximum likelihood estimator of the proportion of cases(controls) in each genotype combination. We also show that the balanced accuracy measure derived from this new membership function is a linear function of the standard chi-square statistics. This relationship allows us to perform the standard significance test using p-values in the MDR framework without permutation. Through two simulation studies, the power of the proposed EF-MDR is shown to be higher than those of MDR and Fuzzy MDR. We illustrate the proposed EF-MDR by analyzing Crohn's disease (CD) and bipolar disorder (BD) in the Wellcome Trust Case Control Consortium (WTCCC) dataset. Conclusion: We propose an empirical Fuzzy MDR for detecting GGI using the maximum likelihood of the proportion of cases(controls) as the membership degree of the genotype combination. The program written in R for EF-MDR is available at http://statgen.snu.ac.kr/software/EF-MDR.