title: A novel fuzzy set based multifactor dimensionality reduction method for detecting gene-gene interaction.
abstract: Gene-gene interaction (GGI) is one of the most popular approaches for finding the missing heritability of common complex traits in genetic association studies. The multifactor dimensionality reduction (MDR) method has been widely studied for detecting GGIs. In order to identify the best interaction model associated with disease susceptibility, MDR compares all possible genotype combinations in terms of their predictability of disease status from a simple binary high(H) and low(L) risk classification. However, this simple binary classification does not reflect the uncertainty of H/L classification.
  
  
  
  We regard classifying H/L as equivalent to defining the degree of membership of two risk groups H/L. By adopting the fuzzy set theory, we propose Fuzzy MDR which takes into account the uncertainty of H/L classification. Fuzzy MDR allows the possibility of partial membership of H/L through a membership function which transforms the degree of uncertainty into a [0,1] scale. The best genotype combinations can be selected which maximizes a new fuzzy set based accuracy measure.
  
  
  
  Two simulation studies are conducted to compare the power of the proposed Fuzzy MDR with that of MDR. Our results show that Fuzzy MDR has higher power than MDR. We illustrate the proposed Fuzzy MDR by analysing bipolar disorder (BD) trait of the WTCCC dataset to detect GGI associated with BD.
  
  
  
  We propose a novel Fuzzy MDR method to detect gene-gene interaction by taking into account the uncertainly of H/L classification and show that it has higher power than MDR. Fuzzy MDR can be easily extended to handle continuous phenotypes as well. The program written in R for the proposed Fuzzy MDR is available at https://statgen.snu.ac.kr/software/FuzzyMDR.
authors.affiliation: Faculty of Liberal Education, Seoul National University, Seoul, 08826, South Korea. Electronic address: hyjunglove@snu.ac.kr.
authors.forename: Hye-Young
authors.initials: HY
authors.lastname: Jung
authors.affiliation: Department of Statistics, Seoul National University, Seoul, 08826, South Korea. Electronic address: leemss@snu.ac.kr.
authors.forename: Sangseob
authors.initials: S
authors.lastname: Leem
authors.affiliation: Interdisciplinary Program of Bioinformatics, Seoul National University, Seoul, 08826, South Korea. Electronic address: biznok@gmail.com.
authors.forename: Sungyoung
authors.initials: S
authors.lastname: Lee
authors.affiliation: Department of Statistics, Seoul National University, Seoul, 08826, South Korea; Interdisciplinary Program of Bioinformatics, Seoul National University, Seoul, 08826, South Korea. Electronic address: tspark@stats.snu.ac.kr.
authors.forename: Taesung
authors.initials: T
authors.lastname: Park
mesh_terms: D004843:Epistasis, Genetic; D017143:Fuzzy Logic; D006801:Humans
keywords: Fuzzy classifier; Fuzzy set theory; Gene-gene interaction; Multifactor dimensionality reduction; Uncertainty