@article{BlanchardDickhausRoquainetal.2014,
  author    = {Blanchard, Gilles and Dickhaus, Thorsten and Roquain, Etienne and Villers, Fanny},
  title     = {On least favorable configurations for step-up-down tests},
  series = {Statistica Sinica},
  volume    = {24},
  journal   = {Statistica Sinica},
  number    = {1},
  publisher = {Statistica Sinica, Institute of Statistical Science, Academia Sinica},
  address   = {Taipei},
  issn      = {1017-0405},
  doi       = {10.5705/ss.2011.205},
  pages     = {1 -- U31},
  year      = {2014},
  language  = {en}
}
@article{MiethKloftRodriguezetal.2016,
  author    = {Mieth, Bettina and Kloft, Marius and Rodriguez, Juan Antonio and Sonnenburg, Soren and Vobruba, Robin and Morcillo-Suarez, Carlos and Farre, Xavier and Marigorta, Urko M. and Fehr, Ernst and Dickhaus, Thorsten and Blanchard, Gilles and Schunk, Daniel and Navarro, Arcadi and M{\"u}ller, Klaus-Robert},
  title     = {Combining Multiple Hypothesis Testing with Machine Learning Increases the Statistical Power of Genome-wide Association Studies},
  series = {Scientific reports},
  volume    = {6},
  journal   = {Scientific reports},
  publisher = {Nature Publ. Group},
  address   = {London},
  issn      = {2045-2322},
  doi       = {10.1038/srep36671},
  pages     = {14},
  year      = {2016},
  abstract  = {The standard approach to the analysis of genome-wide association studies (GWAS) is based on testing each position in the genome individually for statistical significance of its association with the phenotype under investigation. To improve the analysis of GWAS, we propose a combination of machine learning and statistical testing that takes correlation structures within the set of SNPs under investigation in a mathematically well-controlled manner into account. The novel two-step algorithm, COMBI, first trains a support vector machine to determine a subset of candidate SNPs and then performs hypothesis tests for these SNPs together with an adequate threshold correction. Applying COMBI to data from a WTCCC study (2007) and measuring performance as replication by independent GWAS published within the 2008-2015 period, we show that our method outperforms ordinary raw p-value thresholding as well as other state-of-the-art methods. COMBI presents higher power and precision than the examined alternatives while yielding fewer false (i.e. non-replicated) and more true (i.e. replicated) discoveries when its results are validated on later GWAS studies. More than 80\% of the discoveries made by COMBI upon WTCCC data have been validated by independent studies. Implementations of the COMBI method are available as a part of the GWASpi toolbox 2.0.},
  language  = {en}
}