Frequentist q-values for multiple-test procedures
Roger B. Newson
National Heart and Lung Institute
Imperial College London
London, UK
[email protected]
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Abstract. Multiple-test procedures are increasingly important as technology increases
scientists’ ability to make large numbers of multiple measurements, as they
do in genome scans. Multiple-test procedures were originally defined to input a
vector of input p-values and an uncorrected critical p-value, interpreted as a familywise
error rate or a false discovery rate, and to output a corrected critical p-value
and a discovery set, defined as the subset of input p-values that are at or below the
corrected critical p-value. A range of multiple-test procedures is implemented using
the smileplot package in Stata (Newson and the ALSPAC Study Team 2003,
Stata Journal 3: 109–132; 2010, Stata Journal 10: 691–692). The qqvalue command
uses an alternative formulation of multiple-test procedures, which is also
used by the R function p.adjust. qqvalue inputs a variable of p-values and outputs
a variable of q-values that are equal in each observation to the minimum
familywise error rate or false discovery rate that would result in the inclusion of
the corresponding p-value in the discovery set if the specified multiple-test procedure
was applied to the full set of input p-values. Formulas and examples are
presented.
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Roger B. Newson
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qqvalue, smileplot, multproc, p.adjust, R, multiple-test procedure, data mining, familywise error rate, false discovery rate, Bonferroni, Sidák, Holm, Holland, Copenhaver, Hochberg, Simes, Benjamini, Yekutieli
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