Here we demonstrate that copy number imbalances correlate with intensity in array-CGH data thereby causing problems for conventional normalization methods. We propose a strategy to circumvent these problems by taking copy number imbalances into account during normalization, and we test the proposed strategy using several data sets from the analysis of cancer genomes. In addition, we show how the strategy can be applied to conveniently define adaptive sample-specific boundaries between balanced copy number, losses, and gains to facilitate management of variation in tissue heterogeneity when calling copy number changes.

We assumed that aCGH data from samples with a substantial amount of imbalances could be erroneously corrected using Median normalization. This problem is not unexpected and the effect is well known in corresponding cases when gene expression microarray data is normalized [18]. We investigated this issue using aCGH data derived from tiling BAC arrays comparing copy number between DNA from a normal female with karyotype 46, XX and a cell line with 47, XXX [20]. In this case, autosomes are expected to yield log ratio values of M = 0 and the X chromosome is expected to yield log ratio values of M = 0.58 corresponding to XXX/XX. By first removing Y chromosome values and then randomly omitting a varying number of values for autosomes, while retaining all X chromosome values, we could mimic cases with different percentage of gain. In this way we created mimicked data sets with 5, 10, 15, 20, 25, 30, 35, and 40 percent gain, respectively, where 5 percent gain corresponds to not omitting any autosome values. Data sets were created from raw data and then subjected to normalization using Median. After normalization we investigated ratios for autosomes and the X chromosome (Figure (Figure2).2). As a result of an increased fraction of gain, the median M for the X chromosome is shifted from 0.42 to 0.30 (Figure (Figure2a),2a), confirming our belief that normalization strategies for aCGH should account for the presence of different copy-number populations. The observed shift is a direct result of the composition of aCGH data with respect to copy number populations and can also be observed when looking at autosomes for which the median M is shifted from -0.01 to -0.13 (Figure (Figure2b).2b). When visualizing the normalized data in genome plots the shift clearly appears: M = 0 is in between the two populations (Figure (Figure2c2c).

Importantly, when creating the mimicked data sets we did not generate any simulated ratio values; rather, we formed different selections of values using real experimental data. We believe that this use of real experimental data is of significance for aCGH data. This belief is founded on that, in contrast to expression levels, copy number levels are restricted to a, by comparison, moderate dynamic range. Therefore, when a genomic region is subjected to gain or amplification, the increase of genomic material is relatively substantial. Thus, we reasoned that probes for regions of gain would yield comparably higher average intensities than those for regions of normal copy number and that this, in turn, would result in a correlation between M and A: probes measuring ratios of gain will have higher average intensities. The opposite relationship would apply for probes measuring ratios of loss. Consequently, utilizing normalization strategies based on Lowess would possibly correct for correlations between M and A related to genomic imbalances, resulting in loss of biologically relevant variation. To test this, we subjected the mimicked XXX/XX data sets to Lowess normalization. Once again, as a result of an increased fraction of gain the median M for the X chromosome is shifted, this time from 0.42 to 0.22. The shift can also be observed when looking at autosomes for which the median M is shifted from -0.01 to -0.14 (Figures (Figures2d2d and and2e).2e). Notably, the variation in M for the X chromosome increases with the fraction of gain (Figure (Figure2d).2d). The interquartile range (IQR) for X chromosome M values increases from 0.21 to 0.24, indicating that Lowess normalization is less suitable when discrete copy number populations exist. When visualizing the normalized data in genome plots the shift, as well as the increase in variation of the X chromosome, is apparent (Figure (Figure2f).2f). To illustrate the differences between how Median and Lowess fail in normalizing the data, and to explain the introduced variation, we created M-A plots for the different data sets including correction lines for the two methods (Figure (Figure3).3). With an increased fraction of gain the median M value is shifted as seen for the correction line for Median (Figures (Figures3a3a to d, yellow lines). The correction line for Lowess follows the same shift in the lower range of intensities but diverge at higher intensities (Figures (Figures3a3a to d, green lines). This divergence indicates that the X chromosome ratios yield higher average intensities and that when the percentage of gain increases an intensity bias is introduced for M. Importantly, this intensity bias is not of a technical nature but represents biologically relevant changes and is a result of inherent properties of aCGH data. In the low range of intensities the Lowess correction line is fitted to local means of M reflecting predominantly autosomes. However, at some point as intensities increase, local means are affected by the X chromosome and then reflect a mixed population of autosome and X chromosome M values, i.e., balanced copy number and gain respectively. As the intensities increase further the locally fitted line will be affected by increasing fractions of X chromosome M values and when normalization is applied this will result in differences in the corrections for X chromosome M values. Thus, this normalization introduces variation. We concluded that Lowess normalization erroneously corrects for biological gain – as gain correlates with intensity in aCGH data – resulting in suppressed ratios and increased variation within copy number populations.

Once data is stratified into sets of enriched copy number populations we can select one, e.g., the largest, to perform Lowess normalization on. The generated correction curve must be generalized to cover the full range of A allowing for correction of all M values (Figure (Figure6e).6e). This procedure will ensure that the lowess derived correction line trails one population and remains unaffected by adjacent ones. We refer to this action as popLowess-o (where the letter o is a mnemonic for one) as it makes use of one population to derive a correction line for all data. The complete procedure of data stratification and popLowess normalization is shown in figure figure5,5, steps 1–8. Naturally, once data is stratified alternative variants of calculating normalization corrections are imaginable. For example, one could fit lowess lines to each population and correct them individually or one could individually center populations and then use the combined data to create a lowess derived correction line. We refer to these alternatives as popLowess-i (where the letter i is a mnemonic for individual) and popLowess-c (where the letter c is a mnemonic for common) respectively. The latter alternative has the added advantage of reducing the degree to which the correction line needs to be extrapolated to cover the full range of A. Both alternatives require an additional step to center a selected copy number population at M = 0. The variants popLowess-o and popLowess-c rely on that the intensity-based curvature in M-A space is reasonably shared between populations.

The normalization procedure presented herein will center a population with unknown copy number at M = 0. The rationale for selecting an appropriate population for this purpose can differ depending on samples analyzed and the aim of a project. For instance, in the field of cytogenetics, gains and losses in tumors are by convention described as net changes relative to intrinsic balanced copy number, i.e., relative ploididy. As the number of centromeres determines ploidity, a parallel rationale would be to relate imbalances relative to the largest identified population and therefore center this population at M = 0. However, in some applications it might be more appropriate to relate imbalances to a normal diploid state. Thus, selecting a population to center data at can include using prior knowledge about regions with known copy number or selecting the middle population out of three, if present. Irrespectively of preferences of how data best be centered, the proposed popLowess procedure will alleviate the normalization problems related to mixed copy number populations. Importantly, when performing focused aCGH with specialized arrays that do not cover the entire genome, or comprise probes with a disproportioned focus on specific genomic regions, even CNAs that affect a minor part of the genome can introduce a significant correlation between copy number and intensity, and can result in misinterpretations of how a given ratio level relate to copy number.

All data sets were loaded into BioArray Software Environment (BASE) [28] for analysis. Positive and non-saturated spots were background corrected using the median foreground minus the median background signal intensity for each channel and log ratios (M) were calculated from the background corrected intensities. In all analysis we used M = log₂(int1/int2) and A = log₁₀(sqrt(int1*int2)), where int1 and int2 are background corrected intensities from the investigated sample and reference, respectively. Data sets 1–4 and 7–8 were filtered for signal-to-noise ratio for each spot in both channels according to published reports and the remaining data sets for signal-to-noise ratio > 5 in both channels before BASE implemented software plug-ins of the different normalization strategies were employed. A lowess smooth factor of 0.33, delta of 0.1, and four iterations were used for standard Lowess, popLowess and block-based lowess normalization. Block group size was set to 1 for all block-based normalizations.

A schematic overview of the proposed popLowess normalization strategy is shown in figure figure5.5. The approach is applied on a per sample basis starting with genomic mapping and raw intensities (int1 and int2) for N probe IDs (step 1, Figure Figure5).5). The probes are sorted according to genomic position and M and A are calculated for each probe (step 2, Figure Figure5).5). Next, a standard deviation in M is calculated for each probe in sliding windows of user-defined size along the genome. The resulting distribution of N standard deviations is subjected to a cut-off criterion generating K probes with standard deviations < cut-off for continued population analysis (step 3, Figure Figure5).5). A moving window size of 11 probes was used and the median of the standard deviation distribution was used as cut-off value. This selection criterion is sample adaptive avoiding problems with using a global cut-off criterion. The K selected probes are next segmented on a per chromosome basis using, e.g., the CGHplotter algorithm [14] or the faster circular binary segmentation (CBS) algorithm [13] (step 4, Figure Figure5).5). Herein, the segmentation algorithm proposed by Autio et al. was used with the constant for computing the number of changes (c-parameter) set to 10 [14]. Segmented values are used to cluster the K probes into three distinct clusters by means of robust k-means clustering (step 5, Figure Figure5).5). After clustering, there is an option to merge clusters with cluster centers close to each other. Merging is typically useful for samples not displaying three populations, e.g., samples with 1 or 2 copy number populations. When indicated, a merge cluster criterion of 0.2 or 0.3 in M was used. The resulting data consists of 1–3 distinct populations of data that contains information about the genomic mapping, M, and A for each probe. The largest population is selected for lowess normalization [29] generating a population specific correction curve (step 6, Figure Figure5).5). The correction curve is next extrapolated to the entire range of A and used to correct M for all N reporters similar to Lowess (step 7, Figure Figure5).5). The extrapolation is done conservatively in the end points of A by using the first/last data point of the population specific correction curve to level out the global correction curve horizontally in the M-A plot thereby moderating the impact of extreme points or missing values. After lowess correction, one population is selected as the center population and all data is shifted such that this population obtains median M equal to 0. Selection of a center population can be based on different assumptions. Finally, the normalized int1 and int2 intensities are returned (step 8, Figure Figure5).5). By not segmenting the entire set of observations, and by setting the crucial segmentation parameters for detecting breakpoints in the lower scale, speed is gained while still retaining robustness as long as the standard deviation cut off is not set too low. The purpose of segmentation is to refine large regions with identical copy number and not to detect small complex copy number alterations.

For comparisons, the R implemented lowess function was used to create lowess-normalized data. For each identified population (step 1–5, Figure Figure5)5) in every sample in data sets 1–6 and 8, the standard deviations in M of the reporters in the population after Lowess, popLowess, and no normalization (equal to Median) were calculated separately. The number of populations in a data set for which the popLowess strategy rendered a lower standard deviation compared to the competitor was calculated. To evaluate if popLowess resulted in a significant number of populations with lower standard deviations, one sided p-values were calculated using the binomial distribution with p = 0.5. This binomial test corresponds to the null hypothesis that lower standard deviations for popLowess are obtained by chance. This comparison was done both when studying all populations as a whole and for each population individually.

Sample adaptive thresholds for calling gain or loss can be generated by performing steps 1–3 in Figure Figure55 using the same form of data input and standard deviation cut-off criteria. The identified standard deviation cut-off value can be scaled by multiplicative factors to generate sample specific gain/loss thresholds of desired stringency for downstream applications, e.g., calling CNAs after segmentation. Before creating sample adaptive thresholds, data was pre-filtered and normalized using the popLowess strategy. Sample adaptive thresholds for the Ca13928 breast tumor were created before and after a smoothing window of 250 kBp size for 32 K BAC data and 50 kBp for Agilent 244 K data. Thresholds were estimated using a chromosomal moving window of size 1% of the total probe number for each chromosome separately and the standard deviation cut-off value was selected as the median of the standard deviation distribution. The cut-off value was scaled by a factor 2 to create the ± thresholds in M displayed in figure figure99.