title: A fast algorithm for determining bounds and accurate approximate p-values of the rank product statistic for replicate experiments.
abstract: BACKGROUND
  The rank product method is a powerful statistical technique for identifying differentially expressed molecules in replicated experiments. A critical issue in molecule selection is accurate calculation of the p-value of the rank product statistic to adequately address multiple testing. Both exact calculation and permutation and gamma approximations have been proposed to determine molecule-level significance. These current approaches have serious drawbacks as they are either computationally burdensome or provide inaccurate estimates in the tail of the p-value distribution.
  
  
  RESULTS
  We derive strict lower and upper bounds to the exact p-value along with an accurate approximation that can be used to assess the significance of the rank product statistic in a computationally fast manner. The bounds and the proposed approximation are shown to provide far better accuracy over existing approximate methods in determining tail probabilities, with the slightly conservative upper bound protecting against false positives. We illustrate the proposed method in the context of a recently published analysis on transcriptomic profiling performed in blood.
  
  
  CONCLUSIONS
  We provide a method to determine upper bounds and accurate approximate p-values of the rank product statistic. The proposed algorithm provides an order of magnitude increase in throughput as compared with current approaches and offers the opportunity to explore new application domains with even larger multiple testing issue. The R code is published in one of the Additional files and is available at http://www.ru.nl/publish/pages/726696/rankprodbounds.zip .
authors.affiliation: Institute for Computing and Information Sciences, Radboud University Nijmegen, Nijmegen, The Netherlands. t.heskes@science.ru.nl.
authors.forename: Tom
authors.initials: T
authors.lastname: Heskes
authors.affiliation: Department of Social Science Research Methods, Radboud University Nijmegen, Nijmegen, The Netherlands. r.eisinga@maw.ru.nl.
authors.forename: Rob
authors.initials: R
authors.lastname: Eisinga
authors.affiliation: Manchester Institute of Biotechnology, Faculty of Life Sciences, University of Manchester, Manchester, UK. rainer.breitling@manchester.ac.uk.
authors.forename: Rainer
authors.initials: R
authors.lastname: Breitling
mesh_terms: D000375:Aging / Q000235:genetics*; D000465:Algorithms; D015415:Biomarkers / Q000032:analysis*; D030541:Databases, Genetic; D020869:Gene Expression Profiling / Q000379:methods*; D006801:Humans; D011336:Probability
chemical_list: D015415:Biomarkers