Estimating the arm-wise false discovery rate in array comparative genomic hybridization experiments

Array Comparative Genomic Hybridization (aCGH) is an array-based technology which provides simultaneous spot assays of relative genetic abundance (RGA) levels at multiple sites across the genome. These spot assays are spatially correlated with respect to genomic location and, as a result, the univariate tests conducted using data generated from these spot assays are also spatially correlated. In the context of multiple hypothesis testing, this spatial correlation complicates the question of how best to define a 'discovery' and consequently, how best to estimate the false discovery rate (FDR) corresponding to a given rejection region. One can quantify the number of discoveries as the total number of spots for which the spot-based univariate test statistic falls within a given rejection region. Under this spot-based method, separate but correlated discoveries are identified. We show via a simulation study that the method of Benjamini and Hochberg (1995) can provide a reasonable estimate of the spot-wise FDR, but these results require that the simulated spot assays are categorized as true or false discoveries in a particular way. However, laboratory researchers may actually be interested in estimating a 'regional' FDR, rather than a 'local' spot-wise FDR. We describe an example of such circumstances, and present a method for estimating the (chromosome) arm-wise False Discovery Rate. In this framework, one can quantify the number of discoveries as the total number of chromosome arms for which at least one spot-based test statistic falls into a given rejection region. Defining the discoveries in this way, both the biological and testing objectives coincide. We provide results from a series of simulations which involved the analysis of preferentially re-sampled spot assay values from a real aCGH dataset.