Database mining for selection of SNP markers useful in admixture mapping

  • Tesfaye M Baye1, 2Email author,

    Affiliated with

    • Hemant K Tiwari2,

      Affiliated with

      • David B Allison2, 3, 4 and

        Affiliated with

        • Rodney C Go5

          Affiliated with

          BioData Mining20092:1

          DOI: 10.1186/1756-0381-2-1

          Received: 24 September 2008

          Accepted: 14 February 2009

          Published: 14 February 2009

          Abstract

          Background

          New technologies make it possible for the first time to genotype hundreds of thousands of SNPs simultaneously. A wealth of genomic information in the form of publicly available databases is underutilized as a potential resource for uncovering functionally relevant markers underlying complex human traits. Given the huge amount of SNP data available from the annotation of human genetic variation, data mining is a reasonable approach to investigating the number of SNPs that are informative for ancestry information.

          Methods

          The distribution and density of SNPs across the genome of African and European populations were extensively investigated by using the HapMap, Affymetrix, and Illumina SNP databases. We exploited these resources by mining the data available from each of these databases to prioritize potential candidate SNPs useful for admixture mapping in complex human diseases and traits. Over 4 million SNPs were compared between Africans and Europeans on the basis of a pre-specified recommended allele frequency difference (delta) value of ≥ 0.3.

          Results

          The method identified 15% of HapMap, 11% of Affymetrix, and 14% of Illumina SNP sets as candidate SNPs, termed ancestry informative markers (AIMs). These AIM panels with assigned rs numbers, allele frequencies in each ethnic group, delta value, and map positions are all posted on our website http://​www.​ssg.​uab.​edu/​downloads/​admixture_​mapping/​SNPAIMs.​txt. All marker information in this data set is freely and publicly available without restriction.

          Conclusion

          The selected SNP sets represent valuable resources for admixture mapping studies. The overlap between selected AIMs by this single measure of marker informativeness in the different platforms is discussed.

          Background

          The chromosome of an individual from a recently admixed population such as the African-American population contains large stretches of DNA that resemble mosaics of chromosomal segments [1], each derived from European or African ancestry that have not had sufficient time to break up as a result of recombination. Hence, allelic associations in these populations may extend over distances as large as 20–30 cM [2, 3]. Methods to map genes that rely on admixture may therefore require fewer markers to screen the genome than would other approaches for mapping complex disease genes [4, 5].

          Theoretically, any marker [610] that has an allele frequency difference between ancestral populations, known as ancestry informative markers (AIMs), can be used for admixture mapping. Such markers can also be used to control for population confounding by variations in background ancestry via structural association testing (SAT) [11]. The ideal AIM has one allele that is monomorphic in one population (p = 1.0) and that is not present in another [12]. However, most alleles are shared among populations [1315]. Hence, it is important to identify and choose informative AIMs across populations [16].

          Several single nucleotide polymorphism (SNP) panels have been reported over the past few years [7, 8, 1619] with a focus on identifying markers suitable for admixture studies. Smith et al. [9] screened 744 microsatellite markers for AIMs in 4 different populations and identified a genome spanning set of 315 markers (average spacing 10 cM, frequency difference > 0.3) for mapping in African-Americans and 214 markers (average spacing of 16 cM, frequency difference > 0.25) for mapping in Hispanics. Ninety-seven AIMs were identified for mapping in African-American populations that show limited variation within Africa [10].

          Recently 3011 SNP AIMs were reported for studying African-American populations [19], who have an average of 80% African and 20% European ancestry, after screening 450,000 SNPs for which allele frequencies were available. This panel is considered the gold standard for admixture mapping in this population. However, the SNPs used to develop these AIMs came mostly from African-American (98.6%, over 443,916 SNPs) populations, and the ancestral West African frequencies were inferred or estimated by using the expectation-maximization (EM) algorithm [20] rather than by being directly measured.

          To date, only a limited amount of information characterizing SNPs across the human genome [21, 22] for the majority of ethnic groups is found in the literature [23]. Consequently, mining of SNP frequencies from HapMap and other genomic data sets including Affymetrix 500 K and Illumina 100 K SNPs with an ethnic-dependent background across the genome is an economical, rapid, and practical strategy for developing a more comprehensive and informative panel of AIMs [19, 24]. This may result in a uniform resource that describes nucleotide diversity with sufficient power to infer ancestry for admixed populations [25], beyond the currently available lists of AIMs. The objectives of the present study were to mine databases and develop AIM panels useful in admixture mapping and compare the selected set of AIMs with the widely used AIM panels.

          Methods

          Materials

          SNP markers deposited by the HapMap project, 500 K Affymetrix, 100 K Illumina, and the recently published 3011AIM SNP panels for all autosomal and sex chromosomes were used to determine AIMs. The distribution of SNPs in each chromosome and database is shown in Table 1.
          Table 1

          Number of SNPs investigated for data-mining of AIMs for each chromosome for both Yorubans and European populations listed by genotypic platform or source.

          Chr

          HapMap

          500 k Affymetrix

          100 k Illumina

          AIMs

          1

          286584

          39418

          9820

          241

          2

          304922

          40633

          8702

          230

          3

          235256

          33120

          7207

          190

          4

          224433

          31339

          6000

          132

          5

          230257

          31595

          6329

          136

          6

          251838

          31130

          6579

          192

          7

          196235

          25407

          5581

          124

          8

          199358

          26948

          4891

          129

          9

          169079

          22596

          4480

          115

          10

          197292

          28217

          5240

          144

          11

          189407

          28217

          5240

          144

          12

          177798

          25998

          5928

          164

          13

          146641

          24712

          5465

          129

          14

          114909

          18910

          3093

          76

          15

          99603

          15432

          3420

          91

          16

          101959

          14190

          3307

          87

          17

          83339

          15069

          3388

          103

          18

          111158

          11127

          4079

          130

          19

          51689

          14631

          2570

          83

          20

          111869

          6284

          3520

          117

          21

          45994

          12266

          3007

          83

          22

          51037

          7014

          1381

          59

          X

          103517

          6123

          1886

          94

          Y

          54

          -

          -

          -

          Total

          3684228

          492556

          109366

          3011

          Chr = chromosome

          Data mining, processing, and description

          We downloaded the HapMap allele frequency data (http://​www.​hapmap.​org, March 13, 2007 release). The HapMap project contains genotypes from 60 unrelated individuals (parents) from Yorubans in Ibadan, Nigeria [YRI] and 60 unrelated (parents) Caucasians from the United States with northern and western European ancestry [CEU]. There are ~5.8 million SNPs in the combined phase 1 and phase 2 HapMap projects [26, 27].

          The Affymetrix 500 K was downloaded from http://​www.​affymetrix.​com. The Affymetrix 500 K array sets contain "quasi-random" or anonymous SNPs that are spread evenly across the genome and are selected on the basis of information content and could lie between genes. These SNPs were developed for genome-wide association and fine mapping studies. The sample sizes used to generate allele frequency datasets of the 500 K SNP array consist of 48 samples containing 13 trios (5 HapMap CEU trios, 5 HapMap Yoruban trios, and 3 other non-HapMap trios) and 9 unrelated HapMap Asian samples. In total, 39 of the 48 samples are parts of the samples used in the HapMap project. About 365,000 or 73% of the Affymetrix 500 K SNPs have also been typed by the HapMap Project.

          The Illumina 100 K was downloaded from http://​www.​illumina.​com. This panel is a gene-centric collection of SNPs (70% of which are located in exons or within 10 kb of transcripts) developed for genome-wide association studies. The sample sizes used to generate the Illumina 100 K allele frequency data were 32 CEU and 28 Yorubans. Close to 57,000 of the Illumina 100 K SNPs are in the HapMap project. The recently selected panel of 3011 AIM allele frequencies was obtained from http://​www.​cell.​com/​AJHG/​supplemental/​S0002-9297(07)64364-X. A total of 66 European Americans and 64 African Americans genotyped by different platforms were used to generate the 3011 AIMs from the total of 450,000 SNPs screened.

          Each of these data sets, which differ in the way the SNPs were selected [28], has characteristics that make it useful for the current investigation. The HapMap offers an extensive collection of SNPs across ancestral population genomes; the Affymetrix 500 K is a comprehensive widely used chip; the Illumina 100 K has a gene-centric focus; and the AIM panel is the current gold standard SNP panel used in admixture mapping.

          Data analysis

          A computer program using Python http://​www.​python.​org was written to export and pre-process the SNP information from the HapMap databases (the codes are available upon request). A SAS [29] program was used to analyze the data. We used 3 criteria to select the markers to be considered in our analysis: (1) the SNP should be shared between the 2 ancestral populations, (2) a specific marker is retained if it has a delta-value (i.e., the allele frequency difference between 2 parental populations) of 0.3 or higher (a cutoff that has been suggested for AIMs [10], and (3) the physical distance between consecutive selected SNPs must be at least 0.3 cM to avoid the probability of choosing 2 redundant SNPs that are in strong LD [30, 31]. It is expected that markers that are sufficiently spaced throughout the genome will offer independent information about genetic background or ancestry. In each of the 0.3 cM bin, AIMs with the highest delta value were selected to maximize information content of ancestry.

          Several methods for measuring marker informativeness for ancestry have been developed and discussed by Rosenberg et al. [12] and others [19, 32]. However, the absolute allele frequency difference (delta) is the most commonly used measure of informativeness for ancestry between 2 parental populations [12]. Marker informativeness for ancestry can be ascertained through the absolute value of the difference in the frequency of a particular allele observed for 2 ancestral populations. If we let p 11 represent the frequency of a reference allele in the first parental population and p 21 the frequency of the same allele in the second parental population, then the delta value is given by δ = |p 11 - p 12|. A marker with a delta value of 1 provides perfect information regarding its ancestry, whereas a marker with a delta value of 0 carries no information for ancestry.

          Results

          1. SNP allele frequency characterization, racial variation, and databases

          Of the total HapMap SNPs for which both Yoruban and CEU allele frequencies were available, we extracted all the monomorphic SNPs and SNPs with various levels of polymorphism, including 100% informative SNPs between the ancestral populations. Table 2 compares the allele frequency distributions under each scenario of the different databases and shows that there is a slight increase in the proportion of rare variation in the Affymetrix and Illumina groups. From the characterized HapMap, Affymetrix, and Illumina SNP databases, 17.3%, 2.6%, and 1.3%, respectively, were 100% noninformative for ancestry.
          Table 2

          Distribution of allele frequency differences (Yoruba vs. European) across SNP marker databases

          Allele freq difference

          HapMap

          Affymetrix

          Illumina

          AIMs

           

          SNPs

          %

          SNPs

          %

          SNPs

          %

          SNPs

          %

          0

          635890

          17.26

          12813

          2.60

          1392

          1.27

          -

          -

          0.01–0.29

          2477910

          67.257

          385585

          78.28

          91992

          84.11

          -

          -

          0.3–0.50

          440866

          11.966

          73066

          14.83

          15833

          14.62

          993

          33.83

          0.51–0.70

          114055

          3.096

          18910

          3.84

            

          1515

          51.63

          0.71–0.90

          14957

          0.406

          2138

          0.44

          -

          -

          414

          14.11

          0.91–0.99

          520

          0.014

          28

          0.01

          -

          -

          12

          0.40

          1

          30

          0.001

          -

          -

          -

          -

          -

          -

          Chr = chromosome

          A summary of the interpopulation differences using the HapMap databases shows that a total of only 30 of the interpopulation marker comparisons had very large frequency differences or 100% informative for ancestry (delta = 1) between the 2 ancestral groups (Table 2). The few 100% informative SNPs for ancestry in these findings are consistent with prior studies [33, 34], showing that most DNA variation is shared among human populations.

          Using a prespecified recommended allele frequency difference (delta) value of ≥ 0.3, on the average across the databases and genome, 15% of HapMap, 19% of Affymetrix, and 15% of Illumina SNP sets were AIMs (Table 3). However, only 15507 (0.42%) HapMap SNPs had an allele frequency difference of 0.7 and above. Similar to the case with CEU, there were large discrepancies in allele frequencies between SNP data for Yoruban populations from the different databases. For example, the reported allele frequencies of the rs55543 SNP from the HapMap, Affymetrix, and Illumina databases were 0.34, 0.31, and 0.42 generated from sample sizes of 120, 48, and 60 samples, respectively. We suspect that the differences in SNP allele frequency data in the different databases were likely due to small sample sizes and respective large sampling errors of the estimates as suggested by Dvornyk et al. [23]. The SNP AIM characteristics with assigned rs numbers, allele frequencies in each ethnic group, delta value, and map positions are all posted on our website http://​www.​ssg.​uab.​edu/​downloads/​admixture_​mapping/​SNPAIMs.​txt. All marker information in this data set is freely and publicly available without restriction.
          Table 3

          Number of AIMs and percentage with delta ≥ 0.3 (in parentheses) for HapMap, Affymetrix, Illumina and AIM databases.

           

          HapMap SNPs

          Affymerix SNPs

          Illumina SNPs

          AIM SNPs

          Chr

          Total

          delta (%)

          Total

          delta (%)

          Total

          delta (%)

          Total

          delta (%)

          1

          270009

          36255 (13)

          39418

          4439 (11)

          9820

          1471 (15)

          235

          235 (100)

          2

          293090

          46551 (16)

          40633

          4649 (11)

          8702

          1280(15)

          217

          217(100)

          3

          225937

          35394 (16)

          33120

          3779 (11)

          7207

          1021(14)

          178

          178(100)

          4

          214465

          33242 (16)

          31339

          3449 (11)

          6000

          929(15)

          124

          124(100)

          5

          221858

          31821 (14)

          31595

          3245 (10)

          6329

          879(14)

          129

          129(100)

          6

          244251

          32121 (13)

          31130

          3126 (10)

          6579

          894(14)

          184

          184(100)

          7

          182354

          26745 (15)

          25407

          2785 (11)

          5581

          826(15)

          121

          121(100)

          8

          192846

          32106 (17)

          26948

          3142 (12)

          4891

          751(15)

          122

          122(100)

          9

          162192

          23800 (15)

          22596

          2447 (11)

          4480

          585(13)

          108

          108(100)

          10

          189583

          26671 (14)

          28217

          3005 (11)

          5240

          784(15)

          135

          135(100)

          11

          180434

          23850 (13)

          28217

          2767 (11)

          5240

          863(15)

          154

          154(100)

          12

          169898

          23058 (14)

          25998

          2672 (11)

          5928

          768(14)

          125

          125(100)

          13

          142568

          18327 (13)

          24712

          1909 (10)

          5465

          399(13)

          71

          71(100)

          14

          110229

          16581 (15)

          18910

          1667 (11)

          3093

          499(15)

          88

          88(100)

          15

          95436

          16511 (17)

          15432

          1778 (13)

          3420

          533(16)

          83

          83(100)

          16

          96742

          14331 (15)

          14190

          1741(12)

          3307

          536(16)

          95

          95(100)

          17

          79038

          12212 (16)

          15069

          1342(12)

          3388

          626(15)

          115

          115(100)

          18

          107243

          15605 (15)

          11127

          1613(11)

          4079

          354(14)

          79

          79(100)

          19

          48447

          6970 (14)

          14631

          620(10)

          2570

          439(12)

          102

          102(100)

          20

          108979

          12941 (12)

          6284

          1357(11)

          3520

          431(14)

          80

          80(100)

          21

          43739

          6775 (16)

          12266

          772(11)

          3007

          169(12)

          54

          54(100)

          22

          49009

          6419 (13)

          7014

          620(10)

          1381

          304(16)

          88

          88(100)

          X

          102866

          23368 (23)

          6123

          1867(18)

          1886

          640(18)

          156

          156(100)

          Y

          55

          11 (20)

          -

          -

          -

          -

          -

          -

          Chr = chromosome

          2. Number of overlapping AIMs selected from different platforms

          We compared selected AIM lists from among the different databases. Even though 57,000 Illumina 100 K SNPs are in the HapMap dataset, there were no common SNPs selected as AIMs when we used a 0.3 and above delta threshold of informativeness. Interestingly, the recent 3011 AIM panel [19] developed from databases such as Applied Biosystems, Applera, SeatleSNPs, and dbSNP is well represented in HapMap (total of 1479 SNPs were common with HapMap as AIMs). Affymetrix 500 K and HapMap have about 365,000 common SNPs. However, for AIMs with a delta value of ≥ 0.3, there were only 26,388 sets of SNPs overlapping between the 2 databases. As AIMs, few SNPs appeared in both Affymetrix and the recently developed AIM panel; the same was true for HapMap, Affymetrix, and the recently developed AIM panel.

          However, there was no overlap in the selected AIMs among Affymetrix, Illumina, HapMap, and the recently developed AIM panel (Table 4). This is not surprising because the SNP selection criteria for each platform differed. For example, Affymetrix SNPs are based on proximity to a restriction site and even distribution across the genome, whereas the Illumina platform SNPs are selected in gene-rich regions and thus are not evenly distributed across the genome [28]. Combining nonoverlapping SNPs from different platforms seems a viable approach to increase power and detect signals across the genome.
          Table 4

          Number of overlapping SNP AIMs selected by different platforms (HapMap, Affymetrix, Illumina, and AIMs).

          Chr

          H<->A

          H<->I

          H<->S

          A <->I

          A<->S

          I<->S

          H<->A<->I

          H<-> A<>S

          H<->I <->S

          A<->I <->S

          All

          1

          1923

          0

          107

          0

          5

          0

          0

          1

          0

          0

          0

          2

          2180

          0

          114

          0

          7

          0

          0

          5

          0

          0

          0

          3

          1983

          0

          88

          0

          1

          0

          0

          1

          0

          0

          0

          4

          1433

          0

          58

          0

          6

          0

          0

          3

          0

          0

          0

          5

          1590

          0

          71

          0

          7

          0

          0

          4

          0

          0

          0

          6

          1836

          0

          105

          0

          8

          0

          0

          7

          0

          0

          0

          7

          1240

          0

          55

          0

          2

          0

          0

          2

          0

          0

          0

          8

          1546

          0

          61

          0

          5

          0

          0

          4

          0

          0

          0

          9

          1073

          0

          63

          0

          2

          0

          0

          2

          0

          0

          0

          10

          1275

          0

          69

          0

          5

          0

          0

          2

          0

          0

          0

          11

          1167

          0

          67

          0

          2

          0

          0

          1

          0

          0

          0

          12

          1071

          0

          67

          0

          6

          0

          0

          5

          0

          0

          0

          13

          1073

          0

          38

          0

          1

          0

          0

          1

          0

          0

          0

          14

          760

          0

          46

          0

          2

          0

          0

          2

          0

          0

          0

          15

          863

          0

          45

          0

          2

          0

          0

          2

          0

          0

          0

          16

          824

          0

          52

          0

          4

          0

          0

          3

          0

          0

          0

          17

          694

          0

          56

          0

          2

          0

          0

          2

          0

          0

          0

          18

          883

          0

          55

          0

          5

          0

          0

          3

          0

          0

          0

          19

          244

          0

          48

          0

          1

          0

          0

          1

          0

          0

          0

          20

          863

          0

          47

          0

          3

          0

          0

          3

          0

          0

          0

          21

          431

          0

          31

          0

          6

          0

          0

          5

          0

          0

          0

          22

          361

          0

          41

          0

          5

          0

          0

          1

          0

          0

          0

          X

          1075

          0

          95

          0

          7

          0

          0

          5

          0

          0

          0

          Chr = chromosome, H = HapMap, A = Affymerix, I = Illumina, and S = AIMs identified by Smith et al. (2004)

          However, most SNPs are not fixed among ancestral populations and so we cannot rule out the chance that the delta measures of informativeness pick different markers in the different platforms. Moreover, the average sample size (number of individuals) or DNA samples in each of the 2 populations used to estimate allele frequencies and the laboratory procedures used vary between platforms. For instance HapMap data were based on 120 samples, Affymetrix was based on 48 samples, and Illumina used 60 samples. Hence, we believe that the selected SNPs that are present in at least 2 platforms could be considered to be the best candidates for admixture mapping.

          3. Private SNP data set

          We observed significant differences in allele frequencies of few SNPs in the present study. These SNPs with significant variation in allele frequencies in populations of different ethnicity may be appropriate for studying the genetic basis of between-ethnic differences in the rates of complex diseases. Although the small sample sizes in this study preclude any definite conclusion regarding the complete absence of a particular allele in any given population, we observed 30 HapMap SNPs (0.001%) that were segregating in only one population sample ("private SNPs"). Most of these private SNPs (77%) were segregating in the African sample, although private SNPs were also observed for European populations. This may owe to the fact that African populations harbor more unique polymorphic alleles than non-African populations [35]. Follow-up studies of the highly differentiated regions might provide significant insight into phenotypic diversity, selection and local adaptation between populations. No private SNPs were observed in the Affymetrix and Illumina data sets.

          Discussion

          The SNP databases are important resources for performing genetic linkage, association, and admixture studies. Both academic and commercial groups are developing large numbers of genome-wide SNP datasets. These databases now contain over 12.6 million SNPs. However, only a small fraction of these SNPs are well characterized and validated [21]. Users of these data sets have several common questions regarding the existing databases, including the following: What is the frequency spectrum of the SNPs in these databases? What is the distribution picture of these SNPs across different ethnic and geographic populations? What fraction of the total number of SNPs is already captured by these databases?

          We mined and compared the HapMap SNP database against Affymetrix 500 K and the gene centric Illumina 100 K SNP chips. This comparison suggests that a relatively large fraction (> 80%) of SNPs in these databases do not meet the cutoff for acceptable markers as AIMs [10], which means that they are either of very low frequency or not ancestry informative between the 2 ancestral populations. As a result, we developed and preset the AIM panels for each database individually. Our analyses showed that the SNP databases in their current status might have some limitation for studies of complex disorders, especially in different ethnic groups, as a result of incomplete or uneven representation of SNPs along the genome [23]. As indicated above, the different databases have different sets of SNPs. Because the SNP allele frequencies were determined by different genotyping labs that used different sample sizes and genotyping methods (see Methods), it would be difficult to perform several tests to assess data quality and identify sources of experimental variation. In critically evaluating our results, it is important to note that our analyses, and hence interpretations, are subject to several limitations. First, many of our analyses relied on data derived from available databases with contents that are, and will continue to be for some time, in a state of change. Moreover, the allele frequencies across the platforms were based on different sets of DNA samples. Therefore, our results represent a snapshot based on currently available data, and ultimately, when the human genome annotation becomes more stable, it will be important to verify these results. Second, the SNP allele frequencies were determined by using relatively small sample sizes (see Methods), and stochastic variation could affect the robustness of our conclusions.

          Several studies discussed the similarities between human populations in terms of genetic constituents, and hence a large sample size may enable the detection of small differences in rare outcomes. Although we observed a strong correlation in allele frequencies between SNPs from different platforms (data not shown), confirming these allele frequency estimates in a larger sample size will be important. The analytical caveats associated with each database, such as how surrogates are Yorubans or CEU to each ancestral population and how much of the data (for example, in HapMap) is transferable to the diverse populations in Africa where there is extreme adaptive variation along the various countries is also debatable.

          Most studies consider Europe as a relatively homogeneous population. Consequently, it has been argued that European population stratification does not represent a substantial source of bias in epidemiologic studies [36]. However, recent autosomal SNP studies have highlighted significant patterns of structure within Europe along a north-south axis [37] and also the presence of several significant axes of stratification within Europe, most prominently in a northern-southeastern trend, but also along an east-west axis. The study emphasized the importance of considering population stratification in studies using European and European-American individuals, and the need to develop EuroAIMs (European ancestry informative markers) for ancestry estimation and correction [38]. Moreover, the fundamental theorem underpinning HapMap is the common disease common variance (CD/CV) hypothesis [39]. How much information we can capture from rare variants is not clear [40].

          Conclusion

          We presented AIM databases for all SNPs that show promise in distinguishing ancestral populations and thus that will be useful in admixture mapping for finding loci influencing complex phenotypes. These databases will also be useful for controlling stratification (or confounding factors) when the variation in admixture levels among individuals causes false-positive associations in genetic association studies. This investment will result in a unique genetic resource of high quality and global importance for genetic studies in admixed populations. Its size and complexity will allow systematic research into the genetics of many complex disorders in admixed populations and thus, by serving a wide variety of disciplines, will feed research in this promising area for many years to come.

          Declarations

          Acknowledgements

          This work was supported by the National Institutes of Health grants, R01NS045934, R01MH066181, P30DK056336, R01GM077490, R01DK52431 and R21LM008791. The opinions expressed are those of the authors and not necessarily those of the NIH or any other organization which with the authors are affiliated.

          Electronic Database Information

          URL for lists of AIM panels extracted from HapMap, Affymetrix, and Illumina are given: http://​www.​ssg.​uab.​edu/​downloads/​admixture_​mapping/​SNPAIMs.​txt

          Authors’ Affiliations

          (1)
          Current address: Human and Molecular Genetics Center, Medical College of Wisconsin
          (2)
          Section on Statistical Genetics, Department of Biostatistics, University of Alabama at Birmingham
          (3)
          Clinical Nutrition Research Center, University of Alabama at Birmingham
          (4)
          Department of Nutrition Sciences, University of Alabama at Birmingham
          (5)
          Department of Epidemiology, University of Alabama at Birmingham

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          Copyright

          © Baye et al. 2009

          This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://​creativecommons.​org/​licenses/​by/​2.​0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.