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The Use of Multiplicity Corrections, Order Statistics and Generalized Family-Wise
Statistics with Application to Genome-Wide Studies
#MMPMID27128491
Schrodi SJ
PLoS One
2016[]; 11
(4
): e0154472
PMID27128491
show ga
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-?idāk 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-?idāk 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.
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