 Proceedings
 Open Access
 Published:
Genomewide association analysis of rheumatoid arthritis data via haplotype sharing
BMC Proceedings volume 3, Article number: S30 (2009)
Abstract
We present computationally simple association tests based on haplotype sharing that can be easily applied to genomewide association studies, while allowing use of fast (but not likelihoodbased) haplotyping algorithms, and properly accounting for the uncertainty introduced by using inferred haplotypes. We also give haplotype sharing analyses that adjust for population stratification. We apply our methods to a genomewide association study of rheumatoid arthritis available as Problem 1 of Genetic Analysis Workshop 16. In addition to the HLA region on chromosome 6, we find genomewide significant signals at 7q33 and 13q31.3. These regions contain genes with interesting potential connections with rheumatoid arthritis and are not identified using single singlenucleotide polymorphism methods.
Background
The large number of markers tested in a genomewide association study (GWAS) has forced a simplification of analytic approaches. While sophisticated methodology may be used to adjust for multiple comparisons and population stratification, the sheer number of tests in a GWAS requires that each test be fairly simple; currently, most studies are analyzed by computing a simple test such as the CochranArmitage trend test at each locus. Methods that account for the special features of genetic association studies, yet remain computationally feasible for genomewide analysis, are desirable because they may lead to increased power to detect associations. Haplotype sharing is a simple concept that attempts to translate between population genetics and genetic epidemiology. In brief, for recent mutations that cause disease, we would expect that haplotypes of case participants would be more similar to each other in the immediate region of a mutation than they would be to the haplotypes of control participants, suggesting a comparison of sharing in a region between cases and controls. We have recently proposed a class of computationally simple association tests based on haplotype sharing that can be easily applied to casecontrol studies on the genomewide scale. The computational simplicity allows for quick assessment of genomewide significance while adjusting for population stratification via a stratified analysis employing the twostep method of Epstein et al. [1]. We apply this methodology to the rheumatoid arthritis (RA) wholegenome association data available as Problem 1 of Genetic Analysis Workshop 16.
Methods
We begin by giving an overview of the class of test statistics we consider. A more detailed presentation of our approach can be found in Allen and Satten [2]. Let d_{ i }and z_{ i }indicate disease status and stratum membership, respectively, for the i^{th} individual. We consider haplotypes of fixed length L so that there are = 2^{L}possible haplotypes to consider. Let , , and be dimensional vectors having j^{th} components given by the frequency of haplotypes, in stratum z, among the cases, controls, and the entire sample, respectively. Define the × matrix whose (j, j') element is the sharing between the j^{th} and j'^{th} haplotypes about a fixed locus k. Here we measure sharing by the maximum information length contrast [3] metric which counts the number of singlenucleotide polymorphisms (SNPs) that the j^{th} and j'^{th} haplotypes share identically by state in a window centered at locus k. To simplify notation we drop the index k, though it should be understood that all quantities are computed relative to a given locus k. For each locus, we consider statistics of the form
where γ is a dimensional vector that defines the member of the class and w_{ z }is a scalar weight function. Implicit in these definitions is a "working" model φ (hg) the probability of diplotype h given multilocus genotype g. This model is used when we compute , and , the distribution of haplotypes consistent with the i^{th} individual's observed genotype data, under phase ambiguity. It is not hard to show that (1) can be derived as the efficient score of a model within the class of models previously studied by Allen and Satten [4]. As a consequence, they remain valid even if the "working" model φ (hg) is misspecified. Further, it is not necessary to adjust the variance of our test statistic to account for uncertainty in haplotype frequencies. We exploit these facts by choosing computationally fast, though perhaps inconsistent, estimates of φ (hg) secure in the fact that such a choice will not affect the validity of our testing procedure. Here we consider two members of the class given by Eq. (1): first, the "p" statistic in which γ_{ z }= , and the "cross" statistic in which γ_{ z }= ().
We can interpret the "p" and "cross" statistics as testing for differences in sharing between cases and controls in the direction of and , respectively. The "p" statistic has the simple variance estimator,
For the "cross" statistic the situation is a bit more complex. We can show that is distributed as a mixture of independent χ^{2} variates with weights given by the eigenvalues of . We approximate this distribution using the threemoment approximation of Imhoff [5], which has the computational advantage of only depending on the trace of ()^{m}for m = 1, 2, 3.
We applied our proposed haplotype sharing methodology to the RA data provided in Genetic Analysis Workshop 16 Problem 1. This data set has been described elsewhere but, in brief, contains genotypes that include over 545,000 unique SNPs for 868 patients with RA and 1194 controls.
Genotypes, haplotypes, and quality control
Following Fellay et al. [6], we excluded data from SNPs that had extensive missingness (missingness >10), deviations from HardyWeinberg equilibrium (pvalue < 0.001 in controls), and low minor allele frequency (<0.2%). After this quality control (QC) filtering, 530,817 SNPs remained. Using the software package PLINK [7], we confirmed that all pairs of individuals shared less than 12.5% of SNP alleles (the threshold used by Fellay et al.) identically by descent. Thus, no individuals were excluded for cryptic relatedness. No individuals were excluded for missingness.
We used a computationally efficient estimator of the distribution of haplotypes given the observed genotype data φ (hg). The phasing program ent [8] was used to impute a single diplotype for each chromosome of each study participant. For a given window, the empirical distribution of the imputed haplotypes composed of SNPs in the window was used as a simple haplotype frequency estimator. Haplotype frequency estimates computed in this way were then used in specifying the "working" model for φ (hg), assuming HardyWeinberg equilibrium. We note that although we imputed individual haplotypes as a simple way to estimate φ (hg), that when computing , , and , we summed individual contributions over φ (hg), and therefore, explicitly accounted for phase ambiguity. As discussed above, misspecification of φ (hg) will not affect the validity of the haplotypesharing tests.
Adjustment for confounding due to population stratification
We used the stratification score of Epstein et al. [1] to adjust our analyses for confounding due to population stratification. In Epstein et al. [1], partial least squares (PLS) were used to estimate the stratification score. Here we used a modified principalcomponent (PC) approach [6] in place of PLS. This modified PC approach captures the largescale genetic variation in the data by minimizing the influence of a few high linkage disequilibrium (LD) regions from dominating the first few PCs. This is accomplished by excluding SNPs that reside in regions of known high LD from the PC analysis and then further pruning the PC SNP set to minimize the LD between the remaining SNPs [6]. Using the first few PCs, four individuals (D0009459, D0011466, D0012257, and D0012446) were found to be significant outliers, suggesting appreciable nonwhite ancestry. These individuals were excluded from subsequent analyses and when the PC analysis was repeated, no further outliers were identified. The first ten PCs were then used in a logistic model of disease to estimate each individual's stratification scoretheir predicted probability of being a case given the genomic information contained in the PCs. Four strata were then formed based on the quantiles of the stratification scores, for use in a stratified haplotypesharing analysis. For each locus k, we used the sample size in the z^{th} stratum as the weight function w_{ z }in Eq. (1).
Genomewide haplotype sharing analysis
The final analysis data set consisted of 517,843 autosomal SNP genotypes that passed QC from 868 case participants with RA and 1190 control participants. To this data set we applied two stratified haplotypesharing tests: the cross test and the p test. Each test was calculated using a sliding window of seven SNPs. We measured inflation of test statistics due to residual population stratification by the variance inflation factor (VIF), defined as ratio of the median of the observed and expected chisquare statistics across the genome. Permutation tests were conducted by randomly permuting case/control labels within each strata and then capturing the minimum pvalue of each statistic across the genome for each permutation. We estimated genomewide significance by comparing the observed pvalues to this permutation distribution.
Results
We first confirmed the stratification score controlled for inflation due to population stratification. An unadjusted single locus analysis [9] showed a VIF of 1.44, suggesting that significant stratification exist in these data. The stratified p and cross tests had VIFs of 1.03 and 1.04, respectively, suggesting minimal residual inflation. The results of these stratified haplotype sharing analyses across autosomal SNPs are given in Figure 1.
Outside the HLA region on chromosome 6, the p test shows no further regions associated with RA. However, the cross test implicated two genomic regions having log_{10}(pvalue)s that exceed the permutationbased genomewide threshold. These regions are: 7q33 (windows centered at rs6467709, rs6964837, rs834092, rs834082, rs834067, rs1646366, rs834063, and rs864434), and 13q31.3 (window centered at rs9584093). Each of these regions contain genes with interesting potential connections with RA. The region on chromosome 7 is adjacent to the pleiotrophin gene (PTN), which has been found to be upregulated in synovial tissues from patients with RA [10]. The region on chromosome 7 contains glypican 6 (GPC 6). Glypicans have been shown to be expressed differentially in chronically inflamed synovium [11].
Conclusion
Apart from the HLA region on chromosome 6, none of the regions implicated in our analysis were found by a singlelocus GWA analysis that was appropriately corrected for population stratification [9]. This suggests that haplotypebased methods should have a role in the analysis of GWAS. The current approach of singlelocus tests, possibly followed by a smallscale application of haplotype methods in candidate regions or regions where the singleSNP results are significant or almost significant may miss regions where a haplotypebased approach would find a signal. More generally, the strategy of evaluating haplotype methods by evaluating their performance in regions implicated by singleSNP methods may result in the false impression that singleSNP methods outperform haplotypebased methods.
Abbreviations
 GPC 6:

Glypican 6
 GWAS:

Genomewide association study
 LD:

Linkage disequilibrium
 PC:

Principal component
 PLS:

Partial least squares
 QC:

Quality control
 RA:

Rheumatoid arthritis
 SNP:

Singlenucleotide polymorphism
 VIF:

Variance inflation factor
References
 1.
Epstein MP, Allen AS, Satten GA: A simple and improved correction for population stratification in casecontrol studies. Am J Hum Genet. 2007, 80: 921930. 10.1086/516842.
 2.
Allen AS, Satten GA: A novel haplotype sharing approach for genomewide casecontrol association studies implicates the calpastatin gene in Parkinson's disease. Genet Epidemiol in press.
 3.
Bourgain C, Genin E, Quesneville H, ClergetDarpoux F: Search for multifactorial disease susceptibility genes in founder populations. Ann Hum Genet. 2000, 64: 255265. 10.1046/j.14691809.2000.6430255.x.
 4.
Allen AS, Satten GA: Robust estimation and testing of haplotype effects in casecontrol studies. Genet Epidemiol. 2008, 32: 2940. 10.1002/gepi.20259.
 5.
Imhoff JP: Computing the distribution of quadratic forms in normal variables. Biometrika. 1961, 48: 419426.
 6.
Fellay J, Shianna KV, Ge D, Colombo S, Ledergerber B, Weale M, Zhang K, Gumbs C, Castagna A, Cossarizza A, CozziLepri A, De Luca A, Easterbrook P, Francioli P, Mallal S, MartinezPicado J, Miro JM, Obel N, Smith JP, Wyniger J, Descombes P, Antonarakis SE, Letvin NL, McMichael AJ, Haynes BF, Telenti A, Goldstein DB: A wholegenome association study of major determinants for host control of HIV1. Science. 2007, 317: 944947. 10.1126/science.1143767.
 7.
Purcell S, Neale B, ToddBrown K, Thomas L, Ferreira MA, Bender D, Maller J, Sklar P, de Bakker PI, Daly MJ, Sham PC: PLINK: a toolset for wholegenome association and populationbased linkage analysis. Am J Hum Genet. 2007, 81: 559575. 10.1086/519795.
 8.
Gusev A, Mãndoiu II, Paşaniuc B: Highly scalable genotype phasing by entropy minimization. IEEE/ACM Trans Comput Biol Bioinform. 2008, 5: 252261. 10.1109/TCBB.2007.70223.
 9.
Sarasua SM, Collins JS, Williamson DM, Satten GA, Allen AS: Effect of population stratification on the identification of significant singlenucleotide polymorphisms in genomewide association studies. BMC Proceedings. 2009, 3 (Suppl 7): S1310.1186/175365613s7s13.
 10.
Pufe T, Bartscher M, Petersen W, Tillman B, Mentlein R: Expression of pleiotrophin, an embryonic growth and differentiation factor, in rheumatoid arthritis. Arthritis Rheum. 2003, 48: 660667. 10.1002/art.10839.
 11.
Patterson AM, Cartwright A, David G, Fitzgerald O, Bresnihan B, Ashton BA: Differential expression of syndecans and glypicans in chronically inflamed synovium. Ann Rheum Dis. 2008, 67: 592601. 10.1136/ard.2006.063875.
Acknowledgements
The Genetic Analysis Workshops are supported by NIH grant R01 GM031575 from the National Institute of General Medical Sciences.
ASA acknowledges support from grants R01 MH084680 and K25 HL077663 from the National Institutes of Health.
This article has been published as part of BMC Proceedings Volume 3 Supplement 7, 2009: Genetic Analysis Workshop 16. The full contents of the supplement are available online at http://www.biomedcentral.com/17536561/3?issue=S7.
Author information
Affiliations
Corresponding author
Additional information
Competing interests
The authors declare that they have no competing interests.
Authors' contributions
ASA and GAS conceived the study and planned the analyses. ASA analyzed the data. ASA and GAS wrote the manuscript.
Rights and permissions
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.
About this article
Cite this article
Allen, A.S., Satten, G.A. Genomewide association analysis of rheumatoid arthritis data via haplotype sharing. BMC Proc 3, S30 (2009). https://doi.org/10.1186/175365613S7S30
Published:
Keywords
 Rheumatoid Arthritis
 Partial Little Square
 Population Stratification
 Haplotype Sharing
 Genetic Analysis Workshop