Frequentist Q-values for Multiple-test Procedures

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.