  Genomic aberrations, such as somatic copy number alterations, are frequently
observed in tumor tissue. Recurrent aberrations, occurring in the same region
across multiple subjects, are of interest because they may highlight genes
associated with tumor development or progression. A number of tools have been
proposed to assess the statistical significance of recurrent DNA copy number
aberrations, but their statistical properties have not been carefully studied.
Cyclic shift testing, a permutation procedure using independent random shifts
of genomic marker observations on the genome, has been proposed to identify
recurrent aberrations, and is potentially useful for a wider variety of
purposes, including identifying regions with methylation aberrations or
overrepresented in disease association studies. For data following a
countable-state Markov model, we prove the asymptotic validity of cyclic shift
$p$-values under a fixed sample size regime as the number of observed markers
tends to infinity. We illustrate cyclic shift testing for a variety of data
types, producing biologically relevant findings for three publicly available
datasets.
