title: Global tests of P-values for multifactor dimensionality reduction models in selection of optimal number of target genes.
abstract: BACKGROUND
  Multifactor Dimensionality Reduction (MDR) is a popular and successful data mining method developed to characterize and detect nonlinear complex gene-gene interactions (epistasis) that are associated with disease susceptibility. Because MDR uses a combinatorial search strategy to detect interaction, several filtration techniques have been developed to remove genes (SNPs) that have no interactive effects prior to analysis. However, the cutoff values implemented for these filtration methods are arbitrary, therefore different choices of cutoff values will lead to different selections of genes (SNPs).
  
  
  METHODS
  We suggest incorporating a global test of p-values to filtration procedures to identify the optimal number of genes/SNPs for further MDR analysis and demonstrate this approach using a ReliefF filter technique. We compare the performance of different global testing procedures in this context, including the Kolmogorov-Smirnov test, the inverse chi-square test, the inverse normal test, the logit test, the Wilcoxon test and Tippett's test. Additionally we demonstrate the approach on a real data application with a candidate gene study of drug response in Juvenile Idiopathic Arthritis.
  
  
  RESULTS
  Extensive simulation of correlated p-values show that the inverse chi-square test is the most appropriate approach to be incorporated with the screening approach to determine the optimal number of SNPs for the final MDR analysis. The Kolmogorov-Smirnov test has high inflation of Type I errors when p-values are highly correlated or when p-values peak near the center of histogram. Tippett's test has very low power when the effect size of GxG interactions is small.
  
  
  CONCLUSIONS
  The proposed global tests can serve as a screening approach prior to individual tests to prevent false discovery. Strong power in small sample sizes and well controlled Type I error in absence of GxG interactions make global tests highly recommended in epistasis studies.
authors.affiliation: Department of Medical Research, Children's Mercy Hospital, 2401 Gillham Road, Kansas City, MO, 64108, USA. hdai@cmh.edu.
authors.forename: Hongying
authors.initials: H
authors.lastname: Dai
authors.forename: Madhusudan
authors.initials: M
authors.lastname: Bhandary
authors.forename: Mara
authors.initials: M
authors.lastname: Becker
authors.forename: J Steven
authors.initials: JS
authors.lastname: Leeder
authors.forename: Roger
authors.initials: R
authors.lastname: Gaedigk
authors.forename: Alison A
authors.initials: AA
authors.lastname: Motsinger-Reif