BACKGROUND
genome-wide association studies  using array-based genome-wide individual single nucleotide polymorphism  typing technologies are performed to identify genetic loci associated with complex diseases.
the costs of projects based on individual genotyping using microarrays are still high and increase directly with the number of samples to be analyzed.
gwas using pooled dna samples, the so called allelotyping approach, offers an alternative at significantly lower costs  <cit> .
several earlier studies have described the identification of new or validation of known phenotype-associated genetic loci by allelotyping using older snp genotyping array versions  <cit> .
recently, findings from allelotyping using newer generations of arrays that enable genome-wide snp coverage, such as the affymetrix genome-wide human snp array  <dig> , were also published  <cit> .
in an allelotyping study, the estimated allele frequencies are subject to various quantitative technical errors related to pooling of the dna samples.
these pooling-specific errors result from dna quantification and generation of pools, amplification of target sequence, and frequency estimation with the chosen methodology  <cit> .
while several studies evaluated the pooling-specific error of former array systems  <cit> , error estimated for the affymetrix genome-wide human snp array  <dig>  have not been done so far.
despite the great advantage of cost reduction, allelotyping has also several drawbacks.
most importantly, allelotyping allows only for extraction of the mean allele frequencies of the pooled dna samples instead of determining the individual genotypes.
in addition, adjusting for covariates is almost impossible after dna pooling.
this limitation includes the use of principal components as covariates in the association analysis to adjust for population stratification as commonly done in gwas.
if researchers wish to use the allelotyping approach they need to be certain that little to no stratification exists, or that it will be adequately controlled by e.g.
applying genomic control.
furthermore, the error rate is usually higher in pooled samples compared to individual samples.
notwithstanding these weaknesses, allelotyping represents a well-priced alternative, especially when applied to case–control studies with larger cohort sizes, because in these cases, stronger effects of individual gene variants compared to general-population based cohorts can be expected.
in the present study, we estimated the pooling-related error by comparing the allele frequencies determined from pooled dna samples with those obtained from individually genotyped samples.
in both cases the affymetrix genome-wide human snp array  <dig>  was used as genotyping platform.
furthermore, we compared differences in allele frequencies between several dna pools used for allelotyping.
finally, we evaluated some known and newly developed methods for correcting the pooling-specific error and compared these results to the uncorrected allele frequencies.
our results may help researchers set up an appropriate experimental design for case–control allelotyping studies.
RESULTS
the study population included two groups consisting of  <dig> individuals each.
the dna samples of each group were either pooled and analyzed using one array, or individually genotyped resulting in  <dig> arrays per group.
in each case, the affymetrix genome-wide human snp array  <dig>  was used.
we determined the allele frequencies using relative allele signals   <cit>  .
the original ras value calculations were modified for the affymetrix genome-wide human snp array  <dig> .
two different methods were tested for obtaining the a and b allele intensities used for ras value calculation: the birdseed <dig> genotype calling algorithm  <cit>  and the median probe set intensities from the array-specific cel files .
we estimated the pooling-specific error by comparing the allele frequencies obtained from the allelotyping experiment with the corresponding allele frequencies acquired by individual genotyping.
three different correction methods for the birdseed <dig> based ras values were applied and compared: a) the k-correction method  <cit> , b) a slightly modified ppc correction algorithm according to  <cit>  and c) our newly developed correction method based on tangent-transformation  using three different parameter values n =  <dig> , <dig>  .
comparison of  <dig>  uncorrected ras values calculated from single dna pools of  <dig> samples with those derived from individual genotyping calls and a snp minor allele frequency  >1% resulted in the 90% quantile  of the absolute errors of  <dig>  .
applying the ppc correction method reduced this error to  <dig>  .
our newly developed tan-correction with parameter n =  <dig>  performed second-best with corresponding absolute errors of  <dig>  .
the corresponding error value of the k-correction method amounted to  <dig>  .
the comparison of the pooling-specific errors using different correction methods applied on this snp set is shown in figure  <dig>
using  <dig>  ras values with a maf >5% increased the allelotyping accuracy slightly, whereas inclusion of all  <dig>  snps with a genotype call rate of 100% in the analysis strongly increased the overall pooling-specific error.
since the computationally intensive ppc correction algorithm was originally developed for the affymetrix genechip 10 k mapping array representing approximately  <dig>  snps, we could not apply this correction method on the complete set of snps.
for the complete set of snps, the tan-correction method with parameter n =  <dig>  performed best with a 90% quantile  error of  <dig>   compared to  <dig>   using uncorrected ras values obtained from the birdseed <dig> calling algorithm.
the k-correction method slightly increased the accuracy after removing the low-maf snps but did not outperform the accuracy of uncorrected ras values of the complete snp set.
the differences of the error distribution between both single dna-pools varied only marginally.
detailed results are given in table  <dig>
absolute differences  between ras values obtained by allelotyping using dna-pools and expected ras values calculated from calls obtained by individual genotyping of the same dna samples.
q <dig> represents the 90% quantile, sd the standard deviation of the error.
the advantage of the ras correction was diminished when comparing the snp-specific differences of the ras values between the two groups .
however, the k-correction method performed best among all methods giving a 90% quantile  error regarding the ras value differences between both dna pools of  <dig>   after filtering snps with a maf ≤1%.
the second best estimation of the snp-specific differences between both pools was provided by the uncorrected ras values obtained from the birdseed <dig> calling algorithm with a 90% quantile  error of  <dig>  .
the corresponding values of the error distribution of these two methods using the complete snp set were  <dig>   and  <dig>  , respectively, whereas the differences based on the birdseed <dig> ras values were the most accurate among all methods tested.
analyzing the differences of the ras values between both dna-pools, all but the k-corrected methods were less accurate compared to the methods using the uncorrected values, regardless of the maf filter applied.
filtering snps with a maf ≤5% did not result in a better overall accuracy compared to the maf ≤1% filtered snps .
absolute differences  of the ras value differences between both dna pools and the difference of the expected ras values calculated from calls obtained by individual genotyping of the same dna samples.
q <dig> represents the 90% quantile, sd the standard deviation of the error.
discussion
the pooling-specific error of the affymetrix genome-wide human snp array  <dig>  in the context of allelotyping studies and the optimal method for correction strongly depend on the study design.
when comparing allele frequencies determined using pooled dna samples with those obtained by individual genotyping, an appropriate correction for ras values may dramatically increase the overall accuracy.
uncorrected ras values are, however, almost as reliable as  corrected values when comparing the differences in allele frequencies between two pooled dna sample groups.
this finding is of great relevance, since the correction algorithms require prior knowledge of correction values for each snp, which are array specific.
in detail, the k-correction method requires intensity values of heterozygote individuals, the ppc and tan-correction require intensity values from all three genotypes of each snp, which are difficult to obtain, especially for rare snps.
for both the k-correction and the tan-correction algorithms, correction values are calculated only once for each snp as the mean of the ras values obtained from the individually genotyped samples.
in contrast, for the ppc method the ras values of each individually genotyped a and b probe pair have to be included in a regression model, and, in a second step, the median of all corrected probe-specific ras values needs to be calculated per snp.
this results in a large computational effort and increased data handling.
the ppc algorithm was originally developed using approximately  <dig> snps of the former affymetrix genechip 10 k mapping array, which included  <dig> probes per snp distributed over both target dna strands.
this probe-based correction was implemented to compensate for the specific hybridization efficiencies of the probe pairs  <cit> .
since the affymetrix genome-wide human snp array  <dig>  was designed by selecting only 3– <dig> perfect match probe pairs per snp that represent the most reliable  <cit> , we implemented the ppc correction algorithm on a per-snp base using the ras values obtained from the birdseed <dig> calling algorithm.
the accuracy of the  <dig>  snps tested using the adapted ppc correction method was comparable to the accuracy of using the affymetrix genechip 10 k mapping array , but markedly reduced computation time.
at least for comparing differences between allele frequencies of dna pools, the use of uncorrected ras values, obtained from the intensity values of the birdseed <dig> calling algorithm, may represent a reliable and easy-to-implement approach.
there are several limitations of the present study including the lack of a more detailed examination of the snp-specific pooling error and an analysis of the impact of different numbers of pool replicates.
since the number of individual dna samples combined in the pools should not significantly affect the pooling-specific error  <cit> , we decided to use  <dig> dna samples per pool and two true replicates for each of the two dna pools.
this approach has been shown to be more effective with respect to the reduction of the pooling-specific error than just replicating the amplification to hybridization steps of the same dna pool  <cit> .
a limitation of both the ppc and the tan-correction method is that the ras values may be out of the 0– <dig> range.
this affected  <dig> %  and  <dig> %  of the snps with a maf >1% for the tan-correction method, and proportions were similar for the ppc correction.
these values were higher than the number of snps reported in  <cit> , which might be due to the different array design and fewer numbers of technical replicates in our study.
CONCLUSIONS
the comparison of the allele frequency differences between two dna pools were more accurate than the comparison of the allele frequencies of a dna pool with those obtained from individual genotyping.
removing snps with a maf <1% notably increased the accuracy especially in the latter scenario.
compared to the maf <1% filtered snp set, additional removal of all snps with a maf <5% resulted, if at all, in an only marginally increased accuracy.
other studies already estimated the pooling-specific error using earlier affymetrix genotyping array models  <cit> .
here we present the results of an estimation of the pooling-specific error on a genome-wide scale using pools of  <dig> individual dna samples genotyped with the affymetrix genome-wide human snp array  <dig> .
we show that results comparable with those obtained using the earlier affymetrix mapping array systems are achievable, despite the missing mismatch probes and fewer number of probe pairs per snp.
these results demonstrate the theoretical reliability of this array system for analyzing pooled dna samples on a genome-wide scale as a cost saving alternative, especially when searching for moderate or strong genetic effects  <cit> .
nevertheless, due to the pooling-specific error, detection of small genetic effects may be hard, even for common snp variants.
if allelotyping is part of a multi-stage design combined with a screening stage by individual genotyping and a replication stage, the cost savings that can be achieved by the pooling approach depend on several factors like the number of pool replicates, the genetic effect sizes that are present and on the costs per genotype compared to individual genotyping.
depending on the combination of these factors it could, under certain circumstances, be more cost effective to use individual genotyping instead of the pooling approach.
details on the cost estimation are given in  <cit> .
based on the results of this study, we suggest the following approach for analyzing pooled data in the given scenarios.
when comparing pooled dna samples of one group with individual genotypes from another group, and if correction values of all three genotypes per snp are available, we recommend to use the tan-correction with parameter n =  <dig> .
in case an association analysis using dna pools in both groups is to be conducted, the k-correction seems to be a slightly more precise method  than using uncorrected ras values obtained from the birdseed <dig> calling algorithm being the second best option.
in any case, we suggest to focus on snps with a maf >1%.

 genome-wide association studies using array-based genome-wide individual single nucleotide polymorphism typing technologies are performed to identify genetic loci associated with complex diseases. the costs of projects based on individual genotyping using microarrays are still high and increase directly with the number of samples to be analyzed. gwas using pooled dna samples, the so called allelotyping approach, offers an alternative at significantly lower costs. several earlier studies have described the identification of new or validation of known phenotype-associated genetic loci by allelotyping using older snp genotyping array versions. recently, findings from allelotyping using newer generations of arrays that enable genome-wide snp coverage, such as the affymetrix genome-wide human snp array, were also published. in an allelotyping study, the estimated allele frequencies are subject to various quantitative technical errors related to pooling of the dna samples. these pooling-specific errors result from dna quantification and generation of pools, amplification of target sequence, and frequency estimation with the chosen methodology. while several studies evaluated the pooling-specific error of former array systems, error estimated for the affymetrix genome-wide human snp array have not been done so far. despite the great advantage of cost reduction, allelotyping has also several drawbacks. most importantly, allelotyping allows only for extraction of the mean allele frequencies of the pooled dna samples instead of determining the individual genotypes. in addition, adjusting for covariates is almost impossible after dna pooling. this limitation includes the use of principal components as covariates in the association analysis to adjust for population stratification as commonly done in gwas. if researchers wish to use the allelotyping approach they need to be certain that little to no stratification exists, or that it will be adequately controlled by e.g. applying genomic control. furthermore, the error rate is usually higher in pooled samples compared to individual samples. notwithstanding these weaknesses, allelotyping represents a well-priced alternative, especially when applied to case–control studies with larger cohort sizes, because in these cases, stronger effects of individual gene variants compared to general-population based cohorts can be expected. in the present study, we estimated the pooling-related error by comparing the allele frequencies determined from pooled dna samples with those obtained from individually genotyped samples. in both cases the affymetrix genome-wide human snp array was used as genotyping platform. furthermore, we compared differences in allele frequencies between several dna pools used for allelotyping. finally, we evaluated some known and newly developed methods for correcting the pooling-specific error and compared these results to the uncorrected allele frequencies. our results may help researchers set up an appropriate experimental design for case–control allelotyping studies.  the study population included two groups consisting of individuals each. the dna samples of each group were either pooled and analyzed using one array, or individually genotyped resulting in arrays per group. in each case, the affymetrix genome-wide human snp array was used. we determined the allele frequencies using relative allele signals. the original ras value calculations were modified for the affymetrix genome-wide human snp array. two different methods were tested for obtaining the a and b allele intensities used for ras value calculation: the birdseed genotype calling algorithm and the median probe set intensities from the array-specific cel files. we estimated the pooling-specific error by comparing the allele frequencies obtained from the allelotyping experiment with the corresponding allele frequencies acquired by individual genotyping. three different correction methods for the birdseed based ras values were applied and compared: a) the k-correction method, b) a slightly modified ppc correction algorithm according to and c) our newly developed correction method based on tangent-transformation using three different parameter values n = ,. comparison of uncorrected ras values calculated from single dna pools of samples with those derived from individual genotyping calls and a snp minor allele frequency >1% resulted in the 90% quantile of the absolute errors of. applying the ppc correction method reduced this error to. our newly developed tan-correction with parameter n =  performed second-best with corresponding absolute errors of. the corresponding error value of the k-correction method amounted to. the comparison of the pooling-specific errors using different correction methods applied on this snp set is shown in figure  using ras values with a maf >5% increased the allelotyping accuracy slightly, whereas inclusion of all snps with a genotype call rate of 100% in the analysis strongly increased the overall pooling-specific error. since the computationally intensive ppc correction algorithm was originally developed for the affymetrix genechip 10 k mapping array representing approximately snps, we could not apply this correction method on the complete set of snps. for the complete set of snps, the tan-correction method with parameter n =  performed best with a 90% quantile error of compared to using uncorrected ras values obtained from the birdseed calling algorithm. the k-correction method slightly increased the accuracy after removing the low-maf snps but did not outperform the accuracy of uncorrected ras values of the complete snp set. the differences of the error distribution between both single dna-pools varied only marginally. detailed results are given in table  absolute differences between ras values obtained by allelotyping using dna-pools and expected ras values calculated from calls obtained by individual genotyping of the same dna samples. q represents the 90% quantile, sd the standard deviation of the error. the advantage of the ras correction was diminished when comparing the snp-specific differences of the ras values between the two groups. however, the k-correction method performed best among all methods giving a 90% quantile error regarding the ras value differences between both dna pools of after filtering snps with a maf ≤1%. the second best estimation of the snp-specific differences between both pools was provided by the uncorrected ras values obtained from the birdseed calling algorithm with a 90% quantile error of. the corresponding values of the error distribution of these two methods using the complete snp set were and, respectively, whereas the differences based on the birdseed ras values were the most accurate among all methods tested. analyzing the differences of the ras values between both dna-pools, all but the k-corrected methods were less accurate compared to the methods using the uncorrected values, regardless of the maf filter applied. filtering snps with a maf ≤5% did not result in a better overall accuracy compared to the maf ≤1% filtered snps. absolute differences of the ras value differences between both dna pools and the difference of the expected ras values calculated from calls obtained by individual genotyping of the same dna samples. q represents the 90% quantile, sd the standard deviation of the error. discussion the pooling-specific error of the affymetrix genome-wide human snp array in the context of allelotyping studies and the optimal method for correction strongly depend on the study design. when comparing allele frequencies determined using pooled dna samples with those obtained by individual genotyping, an appropriate correction for ras values may dramatically increase the overall accuracy. uncorrected ras values are, however, almost as reliable as corrected values when comparing the differences in allele frequencies between two pooled dna sample groups. this finding is of great relevance, since the correction algorithms require prior knowledge of correction values for each snp, which are array specific. in detail, the k-correction method requires intensity values of heterozygote individuals, the ppc and tan-correction require intensity values from all three genotypes of each snp, which are difficult to obtain, especially for rare snps. for both the k-correction and the tan-correction algorithms, correction values are calculated only once for each snp as the mean of the ras values obtained from the individually genotyped samples. in contrast, for the ppc method the ras values of each individually genotyped a and b probe pair have to be included in a regression model, and, in a second step, the median of all corrected probe-specific ras values needs to be calculated per snp. this results in a large computational effort and increased data handling. the ppc algorithm was originally developed using approximately snps of the former affymetrix genechip 10 k mapping array, which included probes per snp distributed over both target dna strands. this probe-based correction was implemented to compensate for the specific hybridization efficiencies of the probe pairs. since the affymetrix genome-wide human snp array was designed by selecting only 3– perfect match probe pairs per snp that represent the most reliable, we implemented the ppc correction algorithm on a per-snp base using the ras values obtained from the birdseed calling algorithm. the accuracy of the snps tested using the adapted ppc correction method was comparable to the accuracy of using the affymetrix genechip 10 k mapping array, but markedly reduced computation time. at least for comparing differences between allele frequencies of dna pools, the use of uncorrected ras values, obtained from the intensity values of the birdseed calling algorithm, may represent a reliable and easy-to-implement approach. there are several limitations of the present study including the lack of a more detailed examination of the snp-specific pooling error and an analysis of the impact of different numbers of pool replicates. since the number of individual dna samples combined in the pools should not significantly affect the pooling-specific error, we decided to use dna samples per pool and two true replicates for each of the two dna pools. this approach has been shown to be more effective with respect to the reduction of the pooling-specific error than just replicating the amplification to hybridization steps of the same dna pool. a limitation of both the ppc and the tan-correction method is that the ras values may be out of the 0– range. this affected % and % of the snps with a maf >1% for the tan-correction method, and proportions were similar for the ppc correction. these values were higher than the number of snps reported in, which might be due to the different array design and fewer numbers of technical replicates in our study.  the comparison of the allele frequency differences between two dna pools were more accurate than the comparison of the allele frequencies of a dna pool with those obtained from individual genotyping. removing snps with a maf <1% notably increased the accuracy especially in the latter scenario. compared to the maf <1% filtered snp set, additional removal of all snps with a maf <5% resulted, if at all, in an only marginally increased accuracy. other studies already estimated the pooling-specific error using earlier affymetrix genotyping array models. here we present the results of an estimation of the pooling-specific error on a genome-wide scale using pools of individual dna samples genotyped with the affymetrix genome-wide human snp array. we show that results comparable with those obtained using the earlier affymetrix mapping array systems are achievable, despite the missing mismatch probes and fewer number of probe pairs per snp. these results demonstrate the theoretical reliability of this array system for analyzing pooled dna samples on a genome-wide scale as a cost saving alternative, especially when searching for moderate or strong genetic effects. nevertheless, due to the pooling-specific error, detection of small genetic effects may be hard, even for common snp variants. if allelotyping is part of a multi-stage design combined with a screening stage by individual genotyping and a replication stage, the cost savings that can be achieved by the pooling approach depend on several factors like the number of pool replicates, the genetic effect sizes that are present and on the costs per genotype compared to individual genotyping. depending on the combination of these factors it could, under certain circumstances, be more cost effective to use individual genotyping instead of the pooling approach. details on the cost estimation are given in. based on the results of this study, we suggest the following approach for analyzing pooled data in the given scenarios. when comparing pooled dna samples of one group with individual genotypes from another group, and if correction values of all three genotypes per snp are available, we recommend to use the tan-correction with parameter n = . in case an association analysis using dna pools in both groups is to be conducted, the k-correction seems to be a slightly more precise method than using uncorrected ras values obtained from the birdseed calling algorithm being the second best option. in any case, we suggest to focus on snps with a maf >1%. 
using pooled samples and analyzing snps with a minor allele frequency of >1% and applying the best correction method for the corresponding type of comparison, the 90% quantile of the pooling-specific absolute error of the ras values for single sub-pools and the snp-specific difference in allele frequency comparing two pools was and, respectively. in the present study, data from dna samples individually genotyped with the affymetrix genome-wide human snp array were used to estimate the error of the pooling approach by comparing the results with those obtained using the same array type but dna pools each composed of of the same samples. regardless of the intensity correction method applied, the pooling-specific error of the pool intensity values was larger for single pools than for the comparison of the intensity values of two pools, which reflects the scenario of a case–control study. we developed a new correction method with high accuracy but low computational costs. our findings allow for improving the estimation of the pooling-specific error and may help in designing allelotyping studies using the affymetrix genome-wide human snp array. similarly, differences in ras values between pools were determined and compared. correction of the ras values reduced the error of the ras values when analyzing single pool intensities. genome-wide association studies using array-based genotyping technology are widely used to identify genetic loci associated with complex diseases or other phenotypes. genotyping using pooled dna samples, as also being referred as to allelotyping approach, offers an alternative at affordable costs. furthermore, the relative allele intensity signals obtained by allelotyping were compared to the corresponding values derived from individual genotyping.
 genome-wide association studies using array-based genotyping technology are widely used to identify genetic loci associated with complex diseases or other phenotypes. the costs of gwas projects based on individual genotyping are still comparatively high and increase with the size of study populations. genotyping using pooled dna samples, as also being referred as to allelotyping approach, offers an alternative at affordable costs. in the present study, data from dna samples individually genotyped with the affymetrix genome-wide human snp array were used to estimate the error of the pooling approach by comparing the results with those obtained using the same array type but dna pools each composed of of the same samples. newly developed and established methods for signal intensity correction were applied. furthermore, the relative allele intensity signals obtained by allelotyping were compared to the corresponding values derived from individual genotyping. similarly, differences in ras values between pools were determined and compared.  regardless of the intensity correction method applied, the pooling-specific error of the pool intensity values was larger for single pools than for the comparison of the intensity values of two pools, which reflects the scenario of a case–control study. using pooled samples and analyzing snps with a minor allele frequency of >1% and applying the best correction method for the corresponding type of comparison, the 90% quantile of the pooling-specific absolute error of the ras values for single sub-pools and the snp-specific difference in allele frequency comparing two pools was and, respectively.  correction of the ras values reduced the error of the ras values when analyzing single pool intensities. we developed a new correction method with high accuracy but low computational costs. correction of ras, however, only marginally reduced the error of true differences between two sample groups and those obtained by allelotyping. exclusion of snps with a minor allele frequency of ≤1% notably reduced the pooling-specific error. our findings allow for improving the estimation of the pooling-specific error and may help in designing allelotyping studies using the affymetrix genome-wide human snp array. 