Allelic imbalances in tumor samples may conveniently be displayed using B allele frequency plots, which illustrate the presence and location of genomic regions of apparently the same allelic proportion (Figure 1a). In contrast to the expected symmetrical behavior of the B allele frequency, SNPs in regions of allelic imbalance appear to have bands of BAF values that are asymmetrically positioned around 0.5 for the analyzed urothelial tumor (Figure 1a). The asymmetry becomes even more apparent when a mirror transformation along the 0.5 axes of BAF to mBAF is performed (Figure 1b). Importantly, the asymmetry also affects genotyping, indicated by the higher number of failed genotype calls for lower BAF values (AA) compared to higher BAF values (BB) for the region 1q32.1 to qter (Figure 1c). In this region there are a total of 6421 SNPs evenly distributed between the upper BAF > 0.5 (3295 SNPs) and the lower BAF < 0.5 (3125 SNPs) parts. Of these 6421 SNPs, 927 SNPs have not been assigned a genotype by BeadStudio. 757 of these 927 failed calls have a BAF value below 0.5, showing that the cause of the observed asymmetry in BAF also affects genotyping. The BAF asymmetry also influences analysis methods for detecting allelic imbalance. Recently, the SOMATICs algorithm was proposed as a solution for detecting allelic imbalances in heterogeneous tumor samples using Infinium II data 20 . The algorithm divides the BAF profile into three bands (red, green, and blue) based on fixed BAF cut-offs. Asymmetry in BAF estimates causes regions of apparent identical allelic imbalance close to the fixed cut-offs to be identified in different bands (see Additional file 1). For copy number estimates asymmetry also exists for regions of CN loss and CN gain (Figure 1d). The asymmetry appears to be caused by an uncorrected curvature between the X and Y intensities for the two alleles (Figure 1e), and an unequal distribution of X and Y values (Figure 1f). We conclude that there seems to be a dye intensity bias between the two channels used in the Infinium II assay and that the bias remains after using the normalization in BeadStudio.

Since the two alleles for each SNP are, with respect to haplotypes, arbitrarily associated with the X and Y intensities, normalized X and Y intensities should, in contrast to figure 1f, be expected to have essentially equal intensity distributions. Quantile normalization can be used to generate identical distributions from a set of distributions 9 . To investigate the effect of within sample QN of X and Y intensities from normal samples, we performed QN on X and Y intensities from HapMap samples used to generate the reference data sets for the Illumina 300 k version 1 (n = 111), 300 k version 2 (n = 120), 370 k (n = 123) and 550 k (n = 120) BeadChips. For each sample and SNP we calculated new normalized theta and R values thereby generating QN reference data sets. QN has been extensively used to normalize one-channel microarray expression data such that identical intensity distributions are generated for a set of arrays (between array normalization) 9 . Here we instead propose to use QN between channels within two-channel SNP arrays.

For each reference data set we computed new BAF and CN estimates and compared these estimates to BeadStudio data. Using QN we obtained CN estimates with significantly lower standard deviations (SD) for three of four reference data sets (Table 1). The mean decrease in SD for CN estimates was 15 – 26% for the 300 k v2, 370 k and 550 k data sets. For the Illumina 300 k v1 set, QN did not show any effect. Intriguingly, the single sample 300 k v1 BeadChips has a significantly lower variation of CN estimates than the Illumina version 2 Duo 300 k BeadChips (Table 1).

QN also showed a positive effect on allelic intensity ratios, generating lower standard deviations and more centralized theta positions for heterozygous SNPs (Table 2). Interestingly, it can be observed in table 2 that the average theta value for heterozygous SNPs differs from the expected 0.5 for all uncorrected and QN reference data sets. QN shows the least deviation from the expected value for all data sets, and also a clearly significant decrease in theta SD for samples across all data sets compared to BeadStudio data (Table 2).

The deviation from theta = 0.5 for heterozygous SNPs in HapMap samples indicates that an imbalance in the X and Y intensity distributions remains after QN (Table 2). The imbalance in theta affects BAF estimates through the calibration of theta into BAF using the HapMap reference genotype clusters. Part of the imbalance can be explained by an uncorrected curvature between X and Y intensities that prior to QN is present for both tumor samples (Figure 1e) and HapMap samples (Figure 2a). To investigate the relationship between allelic intensity ratios and overall intensity we created MR plots where M = log₂(Y/X) and R = log₁₀(X + Y) similar to conventional MA plots 16 . Consequently, in MR plots heterozygote SNPs should have an M value of 0. As expected from figure 2a, curvature is present prior to QN in the MR plot of HapMap sample NA06985 for the AB, BB and AA SNP populations (Figure 2b). The curvature is highlighted by the superimposed lowess curve for each genotype population and the slope of a fitted linear regression line through each population. After QN there is less curvature, although not fully removed (Figure 2c).

To address how to improve QN, we investigated how QN transforms the X and Y intensities for HapMap sample NA06985 (Figure 2d and 2e). Low values of X are increased with relatively large factors in intensity, while Y values are generally decreased and scaled with smaller factors. SNPs with a low value of X are predominantly genotyped as BB, and the number of SNPs affected by the increase in X is large as seen by comparing the transformation (Figure 2d) with an X intensity histogram (Figure 2f). The same pattern is not observed for the Y intensity, for which the large majority of SNPs are transformed to a lower intensity (Figures 2e and 2g). Thus, QN introduces a transformation that results in a large increase for low X values, which affects a large number of SNPs.

The transformation imbalance does not appear to affect HapMap CN estimates for which the standard deviation is decreased in three of four reference data sets (Table 1). For CN estimates an increase of a low X value is not critical since the corresponding Y intensity is large and dominate the additive R value. However, an increase of low X values will cause more variation of the allelic ratios for SNPs with high values of Y (predominately genotyped as BB). An increase in the variation of allelic ratios for SNPs with low values of X will have the largest effect on regions with loss of allele A (thus dominated by Y with theta and BAF values close to 1). The impact of the transformation imbalance is further increased if the copy number loss is present in the absolute majority of investigated cells and not dampened by contaminating normal cells. To exemplify the effect of the transformation imbalance, the hemizygous loss of chromosome 9 in the urothelial carcinoma UC456_R is shown for both BeadStudio data (Figure 3a) and QN data (Figure 3b). While QN results in a reduced variation for SNPs with BAF values close to 0 (which have large X values), this improvement is counteracted with a large increase in the variation for SNPs with BAF values close to 1 (which have small X values). Furthermore, the transformation imbalance also appears to affect the correction of BAF asymmetry negatively.

The negative effect of QN on allelic intensity ratios could potentially be circumvented by limiting the factor with which X intensity values are increased. Hence, we introduced a threshold for the QN intensity transformations to limit the increase of X and Y values before calculation of the allelic intensity ratio. In all our analyses, we used a threshold of 1.5 for the factor with which X and Y values could maximally be increased. While the threshold is applied identically to both X and Y transformations, it essentially only influences X values. A value of 1.5 appears reasonable as it incorporates the majority of SNPs with low X values (compare Figures 2d and 2e) without affecting the corresponding Y values, but the threshold may potentially be further improved by tuning. Using this QN modified with a threshold, tQN, we generated new tQN reference data sets. The application of the threshold markedly improved quantile normalized tumor BAF data by removing asymmetry and reducing variation (Figures 3c and 3d). Additionally, the removed asymmetry for allelic intensity ratios may provide a higher probability for SNPs to be genotyped, e.g., as AA for chromosome 9 of urothelial carcinoma UC456_R (Figure 3c compared to 3a) or as AA on 1q32.1 to qter for urothelial carcinoma UC152_I (Figure 3d compared to 1c). Consequently, tQN of Infinium II data could increase the genotype call rate, a variable commonly used to assess sample quality. An increased call rate for tumor specimens may also be beneficial for downstream LOH analysis software relying on genotype calls such as dChipSNP 21 .

To more comprehensively investigate BAF asymmetry before and after tQN, we divided 35 whole-genome tumor BAF profiles into an upper and lower part along the 0.5 axes. BAF values for each part were converted to mBAF, similar to figure 1b. Next, each part was separately segmented to find regions of consistent allelic proportion 22 . If no asymmetry is present for a defined genomic region the difference between segmented mBAF values for the upper and lower part of the BAF profile should be zero. We found that tQN results in significantly lower asymmetry for regions of apparent allelic imbalance in both paired and unpaired tumor samples across different Infinium II platforms (Figure 4). Essentially identical results were obtained irrespectively of which part of the BAF profile that was used to define the investigated regions. As expected from the upward shift of heterozygous theta positions (Table 2), the BeadStudio asymmetry is predominantly the result of higher mBAF values for the upper part of the BAF profile than for the lower part. This asymmetry is consistent with an upward shift of the entire BAF plot, as also observed in figures 1a and 3a. tQN showed the same positive effect on allelic intensity ratios for HapMap samples as shown for QN in table 2. For heterozygous SNPs, standard deviations were essentially identical for tQN and QN, whereas theta positions were marginally more centralized for tQN (data not shown).

Having established that tQN corrects for asymmetry in allelic intensity ratio estimates, we investigated the effects of tQN on CN estimates compared to BeadStudio. To this aim, we applied tQN to Infinium II data sets containing both blood and tumor samples and performed three comparisons. First, we investigated whether tQN increase or decrease the response in log R ratio to CNAs. Second, we investigated if tQN decrease variation in CN estimates. Finally, we applied a CNV calling algorithm to tQN normalized HapMap data to investigate the overlap of identified regions compared to BeadStudio data.

To investigate whether tQN increase or decrease the response in log R ratios to CNAs compared to BeadStudio we applied segmentation to both tQN and BeadStudio tumor data. For each sample we calculated the difference in segmented log R ratios between BeadStudio data and tQN data. For genomic regions with log R ratio > 0 and < 0, respectively, the differences were calculated separately such that a positive difference for both types of regions corresponds to a better log R ratio response to CNAs for BeadStudio normalization compared to tQN. We observed small differences for all four data sets (Figure 5a). For the urothelial tumors, BeadStudio showed a better response for segments with gains, while tQN showed a better response for segments with losses. Such opposing findings indicate that the two methods result in different centering of the data rather than in different response to CNAs. Thus, tQN does not appear to alter the log R ratio response to CNAs compared to BeadStudio.

To investigate the effect on variation in CN estimates by tQN we computed sample adaptive noise thresholds (SATs) for tQN and BeadStudio data as previously described 18 . We obtained significantly lower SATs using tQN for four of six tested data sets, while SATs were essentially unchanged for the remaining two data sets (Figure 5b). The lack of effect by tQN on tumors hybridized on Infinium 300 k v1 BeadChips is in concordance with the reference data set (Table 1). The lack of improvement by tQN for tumors in the breast cancer data set is more difficult to explain. All tumors in this data set are either hyper-diploid or of high aneuploidy resulting in highly unbalanced CN profiles. Unbalanced CN profiles may be problematic for the affine transformation in BeadStudio, which scales the data based on that homozygous SNPs on average should exist in two copies, and therefore may confound normalization and data interpretation for aneuploid tumors 5 . A detailed investigation of this hypothesis is however not within the scope of the current study. The CLL data set is part of a comparison of four different array platforms for detection of CNAs and LOH 23 . In that study, Gunnarsson et al. compared the average copy number ratio and standard deviation for the normal chromosome 1 in all samples between the different platforms. The Illumina platform showed the highest average standard deviation (0.26) of the four platforms. We found that the average standard deviation for chromosome 1 after tQN was 0.21, which is comparable to the results obtained by Gunnarsson et al. for the Agilent platform (0.20). Furthermore, when applying tQN the asymmetry in CN estimates observed in figure 1d was removed (Figure 5c). The effect of tQN on CN and BAF estimates for various tumor and normal samples is further illustrated in Additional file 1. In conclusion, we find that tQN of Infinium II data is beneficial for CN estimates as variation is reduced while the dynamic response in copy number ratios to CNAs remains unchanged. A decreased variation for CN estimates can be beneficial for downstream analysis and detection of CNAs.

To investigate whether the reduced variation in copy number estimates by tQN affected CNV detection compared to BeadStudio we applied the PennCNV algorithm 24 to the HapMap 550 k reference data set. The overlap of identified SNPs between BeadStudio and tQN data was on average 80% across the 120 HapMap samples for CNV regions larger than 8 SNPs. Importantly, the overlap percentage increased for larger CNV regions. Even though we cannot validate the correctness of CNV regions identified in either tQN or BeadStudio data these findings indicate that tQN reduces noise without removing biologically relevant regions.

We used 10 data sets for evaluation of the QN strategy. Data set 1 (HapMap 300 k v2) consists of 120 HapMap 26 samples hybridized on Illumina HumanHap300 version 2 Genotyping BeadChips (Courtesy of Illumina Inc., San Diego, CA). Data set 2 (HapMap 370 k) consists of 123 HapMap samples hybridized on Illumina HumanCNV370 Genotyping BeadChips (Courtesy of Illumina Inc.). Data set 3 (HapMap 550 k) consists of 120 HapMap samples hybridized on Illumina HumanHap550 Genotyping BeadChips (Courtesy of Illumina Inc.). Data set 4 (urothelial tumors 370 k) consists of 17 urothelial carcinomas hybridized on HumanCNV370 Genotyping BeadChips. Data set 5 (normal 370 k) consists of 17 normal samples hybridized on Illumina HumanCNV370 Genotyping BeadChips. Samples in data set 5 displayed call rates between 99.5 to 99.8%. Twelve of the samples in data sets 5 and 6 are paired tumor-normal samples from the same individual. Data set 6 (breast tumors 550 k) consists of six breast tumors hybridized on Illumina HumanHap550 Genotyping BeadChips. Data set 7 (leukemia 300 k v2) consists of ten CLL cases hybridized on Illumina HumanHap300 version 2 Genotyping BeadChips 23 . Data set 8 (breast/colon 300 k v1) consists of six hybridizations on Illumina HumanHap300 version 1 Genotyping BeadChips representing two breast cancers and one colon cancer with matching normal samples (Courtesy of Illumina Inc.). Data set 9 (HapMap 300 k v1) consists of 111 HapMap samples hybridized on Illumina HumanHap300 version 1 Genotyping BeadChips (Courtesy of Illumina Inc.). Data set 10 (normal 550 k) consists of one normal sample hybridized 5 times at different DNA concentrations on Illumina HumanHap550 Genotyping BeadChips (obtained from the PennCNV website 27 ).

Chromosomes 1 to 22 were used in all comparisons. Data sets 4 and 5 were generated at the SCIBLU Genomics Centre at Lund University, Sweden 28 and data sets 6 and 7 at the SNP technology platform in Uppsala, Sweden 29 according to manufacturers instructions.

Fluorescent signals were imported into the BeadStudio software version 3.1 (Illumina Inc) and normalized. For each sample, the normalized fluorescence signal intensities were compared with the signal intensities of a set of reference genotypes, and the log₂-ratios between sample and reference signals were calculated on a SNP per SNP basis. In addition, the frequency of the B-allele was for each sample estimated based on the reference genotype clusters 5 . Normalized X and Y intensities were exported for further analysis. Manifest used for 300 k version 2 BeadChips was HumanHap300v2_A. Manifest used for 300 k version 1 BeadChips was BDCHP-1x10-HUMANHAP300v1-1_11219278_C. Manifest used for 370 k BeadChips was HumanCNV370v1_C. Manifest used for 550 k BeadChips was HumanHap550v3_A. Mirrored B allele frequencies (mBAF) were calculated as mBAF = abs(BAF - 0.5) + 0.5 22 .

tQN was performed individually for each sample using affine normalized intensities (X, Y) from BeadStudio and the R 30 package limma 31 . The combined SNP intensity, R, was calculated from tQN intensities. A threshold of 1.5 for the intensity transformations X_QN/X and Y_QN/Y was applied prior to calculation of theta: X_QN intensities larger than 1.5 * X were set to 1.5 * X; Y_QN intensities larger than 1.5 * Y were set to 1.5 * Y. Theta, B allele frequencies and copy number estimates were calculated from tQN normalized intensities and reference data sets as previously described 5 . CNV probes in analyzed samples were excluded from normalization due to lack of genotype information. Instead, for these probes the BeadStudio BAF and log R ratio values were used.

Quantile normalized reference data sets were created from HapMap data sets using intensities (X, Y) normalized in BeadStudio as the starting point. For each sample and SNP, quantile normalized R and theta values were calculated as previously described 5 . Cluster positions in theta and R were calculated for each SNP and genotype based on genotype information (AA, AB and BB) using the mean of all samples for the specific SNP and genotype. SNPs with no cluster positions (no genotype assignment across all HapMap samples) were excluded from the analysis. BAF and copy number estimates for SNPs with only one genotype across all HapMap samples were calculated using the value of the single cluster position. Theta values for SNPs with one heterozygous and only one homozygous cluster position (e.g. AB and AA) were imputed for the missing homozygous cluster position (e.g. BB) by the median of all theta values for the missing genotype. Corresponding R estimates for the missing genotype were set as missing values. For CNV probes the original BeadStudio cluster positions were kept.

For matched tumor-normal samples, SNPs homozygous in both the tumor and its matched normal sample were first removed from the tumor BAF profile. Next, each tumor sample was split into an upper and lower data set, based on BAF values > 0.5 or < 0.5. Both data sets were mirrored from BAF to mBAF (compare figure 1b) and segmented by CBS 32 using default settings as recently described 22 . Segments from the lower and upper part of the BAF profile were cross-mapped and the difference in the average segmented mBAF values between the upper and lower part for each genomic segment was calculated. If no asymmetry is present, the difference between the upper and lower part of the BAF profile should be zero. Only segments larger than 30 SNPs in size and with a segmented mBAF value > 0.6 in the upper and/or lower part was used for evaluation of asymmetry. For tumor samples without a matched normal, SNPs with BAF > 0.97 or < 0.03 were removed prior to splitting BAF profiles into an upper and lower part.

Segmentation was performed on normalized Log R ratios for each sample, platform and method using CBS 32 . The significance level for accepting change-points, α, was set to 0.001 for all analyzed data sets and normalization methods. For comparisons between methods only segmented regions > 20 SNPs were used.

Sample adaptive thresholds for CN estimates were calculated as previously described 18 , using a smoothing window of 21 SNPs, the median of the SD distribution as cut-off, and a scaling factor of 2 for all analyzed data sets and normalization methods.