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Article
The Use of Multiplicity Corrections, Order Statistics and Generalized Family-Wise Statistics with Application to Genome-Wide Studies
PLoS One (2016)
  • Steven J Schrodi
Abstract
The most important decision faced by large-scale studies, such as those presently encountered
in human genetics, is to distinguish between those tests that are true positives from
those that are not. In the context of genetics, this entails the determination of genetic markers
that actually underlie medically-relevant phenotypes from a vast number of makers typically
interrogated in genome-wide studies. A critical part of these decisions relies on the
appropriate statistical assessment of data obtained from tests across numerous markers.
Several methods have been developed to aid with such analyses, with family-wise
approaches, such as the Bonferroni and Dunn-Šidàk corrections, being popular. Conditions
that motivate the use of family-wise corrections are explored. Although simple to implement,
one major limitation of these approaches is that they assume that p-values are i.i.d. uniformly
distributed under the null hypothesis. However, several factors may violate this
assumption in genome-wide studies including effects from confounding by population stratification,
the presence of related individuals, the correlational structure among genetic markers,
and the use of limiting distributions for test statistics. Even after adjustment for such
effects, the distribution of p-values can substantially depart from a uniform distribution
under the null hypothesis. In this work, I present a decision theory for the use of family-wise
corrections for multiplicity and a generalization of the Dunn-Šidàk correction that relaxes the
assumption of uniformly-distributed null p-values. The independence assumption is also
relaxed and handled through calculating the effective number of independent tests. I also
explicitly show the relationship between order statistics and family-wise correction procedures.
This generalization may be applicable to multiplicity problems outside of genomics.
Publication Date
April 29, 2016
Citation Information
Steven J Schrodi. "The Use of Multiplicity Corrections, Order Statistics and Generalized Family-Wise Statistics with Application to Genome-Wide Studies" PLoS One (2016)
Available at: http://works.bepress.com/steve_schrodi/48/