Consistent testing for recurrent genomic aberrations

We consider the detection and identification of recurrent departures from stationary behaviour in genomic or similarly arranged data containing measurements at an ordered set of variables. Our primary focus is on departures that occur only at a single variable, or within a small window of contiguous variables, but involve more than one sample. This encompasses the identification of aberrant markers in genome-wide measurements of DNA copy number and DNA methylation, as well as meta-analyses of genome-wide association studies. We propose and analyse a cyclic shift-based procedure for testing recurrent departures from stationarity. Our analysis establishes the consistency of cyclic shift p-values for datasets with a fixed set of samples as the number of observed variables tends to infinity, under the assumption that each sample is an independent realization of a stationary Markov chain. Our results apply to any test statistic satisfying a simple invariance condition.