The false discovery rate (q-value, left axis) and score (A′ and D′, right axis) for amplification and deletion (positive and negative respectively, labeled) on the 22 autosomes in genomic coordinates (chromosomes indicated at bottom and in plot by alternating colors, centromere in red). The threshold for significance determines the alterations subject to ROI detection (green). Maximum observed scores of A′ and D′ unattainable by permutation p-value (parentheses, right axis).

(a) In a noisy system, a soft discriminator (red) is juxtaposed to a hard threshold (black); both of which assign points either continuous or binary values respectively (parentheses) for confidently copy-neutral or amplified loci (black) and for challenging cases at the margin of signal (green). This indicates the benefit of soft discrimination. (b) The functional form of the soft discriminator; a sigmoid function with parameters for location (E) and slope (β). (c) Individual-tumor approach to detecting gain and loss; the multi-component model parameterized for two tumors (red and blue) indicating that tumor-specific features produce different discriminators for single-copy gain and loss (solid), amplification (dot-dash), and homozygous deletion (dotted). Parameterization selects values for E and β such that their magnitude (unsigned) moves in the direction indicated (legend).

Input is a set of patients; tumor DNA, (un) matched non-tumor DNA, and an unrelated reference normal cohort. Tumor and non-tumor samples are quantified, normalized, and subject to quality control. In the assessment phase, individual samples are segmented and a multi-component model is parameterized for each; this produces a detector for single-copy gain, amplification, hemizygous loss, and homozygous deletion. Across all tumors, a unified breakpoint profile (UBP) is derived from the ensemble of segmentation breakpoints, and each region is scored for gain and loss. A background model of random aberrations is constructed with supplemental cleavage and permutation of genomic regions, and p-values are assigned and corrected for multiple hypothesis testing. In the output phase, RAE determines genomic boundaries for regions of interest (ROI), controls for germline and population copy-number variation, and reports statistically significant alterations.

(a) The density of human recombination hotspots (top; median distance between hotspots is ∼55 kb) spans segmentation (red) of probe-level data (dark blue) in a ∼5 mb region of 13q14.13-3 in four pleomorphic liposarcomas. The unique tumor-associated breakpoints (black arrows) define the UBP (regions r_1–6; bottom), the smallest of which (r₃) spans four genes including the tumor suppressor RB1 (direction of transcription indicated). (b) On chromosome 1p, the density distribution of predicted recombination hotspots (red) at a width equal to the median distance between all p-arm hotspots (56 kb), and the distribution of their randomization (blue). The sampling procedure respects the shape of the original distribution and therefore the sequence features that underlie it. (c) Size distribution of regions derived from segmentation and subsequently defined by the unified breakpoint profile (UBP; gray), and those hotspot-cleaved regions of the same permuted during null model generation (as indicated, blue).

Deletion of RB1 at 13q14.2–q14.3 in pleomorphic liposarcoma demonstrates features of ROI detection in RAE. (a) Heatmap of copy number in a small region of 13q in 24 pleomorphic liposarcomas (tumors are rows, markers are columns; color scale as indicated), and (b) From segmentation, the extent of genomic deletion in a subset of tumors with either hemizygous loss (thin) or homozygous deletion (thick) (c) Inset, the regions of the UBP at this locus (filled circles), and their summary score (D′, left axis). The combination of analytical error (error bars) and two thresholds (FDR and peak detection, green) determine the sensitivity of ROI detection. The detected peak (identified by red plus) is merged with physically adjacent regions that fall inside its error interval (red filled circles and error bars) and define the 5 and 3′ boundaries of the ROI (gray). Statistical significance (q-value) corresponding to summary scores such that permutation is unable to resolve a p-value smaller than 1/(N_p+1) (dotted line, right axis) indicates the necessity for resolving ROIs in the space of the summary score D′. Regional and peak boundaries define the ROI (at bottom; mb) spanning 20 and two genes respectively, the latter including RB1 (direction of transcription indicated). Note, the region detected as the peak is void of genic content, emphasizing the necessity for incorporating a measure of uncertainty on its score.