k-FWER Control without p -value Adjustment, with Application to Detection of Genetic Determinants of Multiple Sclerosis in Italian Twins


  • L. Finos,

    Corresponding author
    1. Department of Statistical Sciences, University of Padua, Padua, Italy and Department of Medical Statistics and Bioinformatics, Leiden University Medical Center, The Netherlands
    Search for more papers by this author
  • A. Farcomeni

    Corresponding author
    1. Department of Hygiene and Public Health Sapienza—University of Rome, Rome, Italy
    Search for more papers by this author




Summary We show a novel approach for k-FWER control which does not involve any correction, but only testing the hypotheses along a (possibly data-driven) order until a suitable number of p-values are found above the uncorrected α level. p-values can arise from any linear model in a parametric or nonparametric setting. The approach is not only very simple and computationally undemanding, but also the data-driven order enhances power when the sample size is small (and also when k and/or the number of tests is large). We illustrate the method on an original study about gene discovery in multiple sclerosis, in which were involved a small number of couples of twins, discordant by disease. The methods are implemented in an R package (someKfwer), freely available on CRAN.