229 Statistical Analysis of Genome-wide Association Studies for Myopia

assuming true effect differs among studies, consider two sources of variances: within-study sampling error and between-study heterogeneity. The commonly used method to test between-study heterogeneity is called Cochran’s Q statistics, for which the large values of Cochran’s Q favor the alternative hypothesis of heterogeneity.56 For datasets i = 1, …,k, T1, …,Tk is the study-specific effect size. The Cochram’s Q statistic is computed by

and wi is the inverse of the estimated variance in dataset i. Q is distributed as a chi-square distribution with k-1 degree of freedom. An alternative form, statistic I2 (inconsistency), derived from Q, 100% × (Q-degree of freedom), is a measure of the percentage of heterogeneity vs total variation across studies. If I2 > 50%, it indicates the presence of heterogeneity. If evidence of heterogeneity is demonstrated, measure to identify its possible cause is needed before any explicit conclusion is drawn. In such a case, additional cohort for replication or fine mapping approaches might be required to further investigate on the true genetic variants of interest.

Visualization Tools

To synthesize hundreds of thousands of p-values for multiple phenotypes from a GWA study, it often relies on good graphical presentation. Manhattan plots and Quantile-Quantil (Q-Q) plots are the most frequently used figures to present p-values of high density markers across the whole genome. Manhattan plot can be easily generated from Haploview program (hapmap.org), and can provide an overall view of the association evidences in the nearby region of the highly significant variants. Here, we show an example of Manhattan plot using the GWA results for SE from right eye from the SCORM GWA studies of Chinese children (Fig. 3). This figure provides snapshots on the chromosomal regions with promising association evidence. For instance, a region in chromosome 13 revealed the best p-value.

Q-Q plots provide a visual summary of the distribution of the observed test statistics (e.g. chi-square test statistic) in the GWA study vs the expected statistic. McCarthy et al. (2008)16 provided a nice illustration of Q-Q plots with interpretation of the pattern (see Box 2 in McCarthy et al.).

230 Y.J. Li and Q. Fan

Figure 3. An overview of GWA results for the SE trait (left eye) from the SCORM and SP datasets, respectively.

For instance, when the Q-Q plot line is close to the diagonal line, it indicates that there is very little association evidence in the study. One the other hand, if the observed line is much off from the diagonal line, there may be concerns for the population stratification. If only the tail part of the Q-Q plot line is much off from the diagonal line, it indicates that there is compelling evidence of the disease association in the dataset.

Both Manhattan and Q-Q plots are tools for summarizing all p-values from GWA studies, not providing additional bioinformation related to the SNP. WGAviewer, another free program, can annotate the SNPs and their associated p-values in relationship to gene structure, SNP function, gene expression, and other GWA studies (http://www.genome.duke.edu/centers/ pg2/downloads/wgaviewer.php).57 This tool can take us beyond p-values by providing biological information for the loci of interest.

Drawing Conclusions

To date, the determination of ‘top-hit’ markers in the GWA setting is mostly p-value driven. The threshold for declaring genome wide significance is widely accepted at 5 × 10–8.1,58,59 However, sample size should be considered even though such a p-value is reached. Regardless what top p-values are observed in the GWA study, it will need to be replicated by other independent datasets. In addition, to judge the p-values from GWA studies, prior genetic research findings can also serve as good references. The genetic research of myopia has a great resource of linkage

231 Statistical Analysis of Genome-wide Association Studies for Myopia

information (e.g. MYP loci) and public expression data, such as EyeSAGE database60 from human retina and retinal pigment epithelium. This information can definitely help investigators to prioritize the GWA results.

Acknowledgments

The grant 06/1/21/19/466 from the Singapore BioMedical Research Council (BMRC) and National Institutes of Health grant 1R21-EY-019086 provided funding for the genome wide association study for SCORM.

References

1.Risch N, Merikangas K. (1996) The future of genetic studies of complex human disorders. Science 273(5281): 1516–1517.

2.Wellcome Trust Case Control Consortium. (2007) Genome-wide association study of 14,000 cases of seven common diseases and 3,000 shared controls. Nature 447(7145): 661–678.

3.Nakanishi H, Yamada R, Gotoh N, et al. (2009) A genome-wide association analysis identified a novel susceptible locus for pathological myopia at 11q24.1. PLoS Genet 5(9): e1000660.

4.Schwartz M, Haim M, Skarsholm D. (1990) X-linked myopia: Bornholm eye disease. Linkage to DNA markers on the distal part of Xq. Clin Genet 38(4): 281–286.

5.Young TL, Ronan SM, Alvear AB, et al. (1998) A second locus for familial high myopia maps to chromosome 12q. Am J Hum Genet 63(5): 1419–1424.

6.Young TL, Ronan SM, Drahozal LA, et al. (1998) Evidence that a locus for familial high myopia maps to chromosome 18p. Am J Hum Genet 63(1): 109–119.

7.Paluru P, Ronan SM, Heon E, et al. (2003) New locus for autosomal dominant high myopia maps to the long arm of chromosome 17. Invest Ophthalmol Vis Sci 44(5): 1830–1836.

8.Paluru PC, Nallasamy S, Devoto M, et al. (2005) Identification of a novel locus on 2q for autosomal dominant high-grade myopia. Invest Ophthalmol Vis Sci 46(7): 2300–2307.

9.Zhang Q, Guo X, Xiao X, et al. (2005) A new locus for autosomal dominant high myopia maps to 4q22-q27 between D4S1578 and D4S1612. Mol Vis 11: 554–560.

10.Zhang Q, Guo X, Xiao X, et al. (2006) Novel locus for X linked recessive high myopia maps to Xq23-q25 but outside MYP1. J Med Genet 43(5): e20.

232Y.J. Li and Q. Fan

11.Nallasamy S, Paluru PC, Devoto M, et al. (2007) Genetic linkage study of high-grade myopia in a Hutterite population from South Dakota. Mol Vis 13: 229–236.

12.Lam CY, Tam PO, Fan DS, et al. (2008) A Genome-wide Scan Maps a Novel High Myopia Locus to 5p15. Invest Ophthalmol Vis Sci 49(9): 3768–3778.

13.Barrett JC, Hansoul S, Nicolae DL, et al. (2008) Genome-wide association defines more than 30 distinct susceptibility loci for Crohn’s disease. Nat Genet 40(8): 955–962.

14.Ciner E, Wojciechowski R, Ibay G, et al. (2008) Genomewide scan of ocular refraction in African-American families shows significant linkage to chromosome 7p15. Genet Epidemiol 32(5): 454–463.

15.Klein AP, Suktitipat B, Duggal P, et al. (2009) Heritability analysis of spherical equivalent, axial length, corneal curvature, and anterior chamber depth in the Beaver Dam Eye Study. Arch Ophthalmol 127(5): 649–655.

16.McCarthy MI, Abecasis GR, Cardon LR, et al. (2008) Genome-wide association studies for complex traits: consensus, uncertainty and challenges. Nat Rev Genet 9(5): 356–369.

17.Devlin B, Roeder K. (1999) Genomic control for association studies. Biometrics 55(4): 997–1004.

18.Pritchard JK, Stephens M, Rosenberg NA, Donnelly P. (2000) Association mapping in structured populations. Am J Hum Genet 67: 170–181.

19.Price AL, Patterson NJ, Plenge RM, et al. (2006) Principal components analysis corrects for stratification in genome-wide association studies. Nat Genet 38(8): 904–909.

20.Skol AD, Scott LJ, Abecasis GR, Boehnke M. (2007) Optimal designs for twostage genome-wide association studies. Genet Epidemiol 31(7): 776–788.

21.Wang H, Thomas DC, Pe’er I, Stram DO. (2006) Optimal two-stage genotyping designs for genome-wide association scans. Genet Epidemiol 30(4): 356–368.

22.Muller HH, Pahl R, Schafer H. (2007) Including sampling and phenotyping costs into the optimization of two stage designs for genomewide association studies. Genet Epidemiol 31(8): 844–852.

23.Barrett JC, Cardon LR (2006) Evaluating coverage of genome-wide association studies. Nat Genet 38(6): 659–662.

24.(2004) Finishing the euchromatic sequence of the human genome. Nature 431(7011): 931–945.

25.Li M, Li C, Guan W. (2008) Evaluation of coverage variation of SNP chips for genome-wide association studies. Eur J Hum Genet 16(5): 635–643.

26.Fellay J, Shianna KV, Ge D, et al. (2007) A whole-genome association study of major determinants for host control of HIV-1. Science 317(5840): 944–947.

233Statistical Analysis of Genome-wide Association Studies for Myopia

27.Pritchard JK, Donnelly P (2001) Case-control studies of association in structured or admixed populations. Theor Popul Biol 60(3): 227–237.

28.Bacanu SA, Devlin B, Roeder K. (2000) The power of genomic control. Am J Hum Genet 66(6): 1933–1944.

29.Reich M, Liefeld T, Gould J, et al. (2006) GenePattern 2.0. Nat Genet 38(5): 500–501.

30.Patterson N, Price AL, Reich D. (2006) Population Structure and Eigenanalysis. PLoS Genet 2(12): e190.

31.Spielman RS, Ewens WJ. (1996) The TDT and other family-based tests for linkage disequilibrium and association. Am J Hum Genet 59(5): 983–989.

32.Martin ER, Monks SA, Warren LL, Kaplan NL. (2000) A test for linkage and association in general pedigrees: the pedigree disequilibrium test. Am J Hum Genet 67: 146–154.

33.Schaid DJ, Rowland CM, Tines DE, et al. (2002) Score tests for association between traits and haplotypes when linkage phase is ambiguous. Am J Hum Genet 70(2): 425–434.

34.Rabinowitz D, Laird N. (2000) A unified approach to adjusting association tests for population admixture with arbitrary pedigree structure and arbitrary missing marker information. Hum Hered 50: 211–223.

35.Martin ER, Bass MP, Hauser ER, Kaplan NL. (2003) Accounting for linkage in family-based tests of association with missing parental genotypes. Am J Hum Genet 73(5): 1016–1026.

36.Allison DB. (1997) Transmission-disequilibrium tests for quantitative traits.

Am J Hum Genet 60: 676–690.

37.Rabinowitz D. (1997) A transmission disequilibrium test for quantitative trait loci. Hum Hered 47: 342–350.

38.Monks SA, Kaplan NL. (2000) Removing the sampling restrictions from family-based tests of association for a quantitative-trait locus. Am J Hum Genet 66(2): 576–592.

39.Fulker DW, Cherny SS, Sham PC, Hewitt JK. (1999) Combined linkage and association sib-pair analysis for quantitative traits. Am J Hum Genet 64(1): 259–267.

40.Abecasis GR, Cardon LR, Cookson WO. (2000) A general test of association for quantitative traits in nuclear families. Am J Hum Genet 66(1): 279–292.

41.Chung RH, Hauser ER, Martin ER. (2006) The APL test: extension to general nuclear families and haplotypes and examination of its robustness. Hum Hered 61(4): 189–199.

42.Lohmueller KE, Pearce CL, Pike M, et al. (2003) Meta-analysis of genetic association studies supports a contribution of common variants to susceptibility to common disease. Nat Genet 33(2): 177–182.

234Y.J. Li and Q. Fan

43.Lau J, Ioannidis JP, Schmid CH. (1997) Quantitative synthesis in systematic reviews. Ann Intern Med 127(9): 820–826.

44.Munafo MR, Flint J. (2004) Meta-analysis of genetic association studies. Trends Genet. 20(9): 439–444.

45.Zeggini E, Scott LJ, Saxena R, et al. (2008) Meta-analysis of genome-wide association data and large-scale replication identifies additional susceptibility loci for type 2 diabetes. Nat Genet 40(5): 638–645.

46.Bertram L, McQueen MB, Mullin K, et al. (2007) Systematic meta-analyses of Alzheimer disease genetic association studies: the AlzGene database. Nat Genet 39(1): 17–23.

47.Baum AE, Hamshere M, Green E, et al. (2008) Meta-analysis of two genomewide association studies of bipolar disorder reveals important points of agreement. Mol Psychiatry 13(5): 466–467.

48.Guan Y, Stephens M. (2008) Practical issues in imputation-based association mapping. PLoS Genet 4(12): e1000279.

49.Marchini J, Howie B, Myers S, et al. (2007) A new multipoint method for genome-wide association studies by imputation of genotypes. Nat Genet 39(7): 906–913.

50.Li Y, Abecasis GR. (2006) Mach 1.0: Rapid Haplotype Reconstruction and Missing Genotype Inference. Am J Hum Genet S79: 2290.

51.Browning SR, Browning BL. (2007) Rapid and accurate haplotype phasing and missing-data inference for whole-genome association studies by use of localized haplotype clustering. Am J Hum Genet 81(5): 1084–1097.

52.Servin B, Stephens M. (2007) Imputation-based analysis of association studies: candidate regions and quantitative traits. PLoS Genet 3(7): e114.

53.Ellinghaus D, Schreiber S, Franke A, Nothnagel M. (2009) Current software for genotype imputation. Hum Genomics 3(4): 371–380.

54.Mantel N, Haenszel W. (1959) Statistical aspects of the analysis of data from retrospective studies of disease. J Natl Cancer Inst 22(4): 719–748.

55.de Bakker PI, Ferreira MA, Jia X, et al. (2008) Practical aspects of imputationdriven meta-analysis of genome-wide association studies. Hum Mol Genet 17(R2): R122–R128.

56.Cochran WG. (1954) The combination of estimates from different experiments. Biometrics 10: 101–129.

57.Ge D, Zhang K, Need AC, et al. (2008) WGAViewer: software for genomic annotation of whole genome association studies. Genome Res 18(4): 640–643.

58.International HapMap Consortium. (2005) A haplotype map of the human genome. Nature 437(7063): 1299–1320.

59.Hoggart CJ, Clark TG, De IM, et al. (2008) Genome-wide significance for dense SNP and resequencing data. Genet Epidemiol 32(2): 179–185.

235Statistical Analysis of Genome-wide Association Studies for Myopia

60.Bowes Rickman C, Ebright JN, Zavodni ZJ, et al. (2006) Defining the human macula transcriptome and candidate retinal disease genes using EyeSAGE.

Invest Ophthalmol Vis Sci 47(6): 2305–2316.

61.Young TL. (2009) Molecular genetics of human myopia: an update. Optom Vis Sci 86(1): E8–E22.

62.Klein R, Klein BE, Tomany SC, Cruickshanks KJ. (2003) The association of cardiovascular disease with the long-term incidence of age-related maculopathy: the Beaver Dam Eye Study. Ophthalmology 110(6): 1273–1280.

63.Metlapally R, Li YJ, Tran-Viet KN, et al. (2009) COL1A1, COL2A1 Genes and Myopia Susceptibility: evidence of Association and Suggestive Linkage to the COL2A1 Locus. Invest Ophthalmol Vis Sci.

64.Pertile KK, Schache M, Islam FM, et al. (2008) Assessment of TGIF as a candidate gene for myopia. Invest Ophthalmol Vis Sci 49(1): 49–54.

65.Mutti DO, Hayes JR, Mitchell GL, et al. (2007) Refractive error, axial length, and relative peripheral refractive error before and after the onset of myopia.

Invest Ophthalmol Vis Sci 48(6): 2510–2519.

66.Stambolian D, Ibay G, Reider L, et al. (2004) Genomewide linkage scan for myopia susceptibility loci among Ashkenazi Jewish families shows evidence of linkage on chromosome 22q12. Am J Hum Genet 75(3): 448–459.

67.Ibay G, Doan B, Reider L, et al. (2004) Candidate high myopia loci on chromosomes 18p and 12q do not play a major role in susceptibility to common myopia. BMC Med Genet 5: 20.

68.Heath S, Robledo R, Beggs W, et al. (2001) A novel approach to search for identity by descent in small samples of patients and controls from the same mendelian breeding unit: a pilot study on myopia. Hum Hered 52(4): 183–190.

69.Yanovitch T, Li YJ, Metlapally R, et al.(2009) Hepatocyte growth factor and myopia: genetic association analyses in a Caucasian population. Mol Vis 15: 1028–1035.

70.Han W, Leung KH, Fung WY, et al. (2009) Association of PAX6 polymorphisms with high myopia in Han Chinese nuclear families. Invest Ophthalmol Vis Sci 50(1): 47–56.

71.Liang CL, Hung KS, Tsai YY, et al. (2007) Systematic assessment of the tagging polymorphisms of the COL1A1 gene for high myopia. J Hum Genet 52(4): 374–377.

This page intentionally left blank

Section 4

Animal Models and

the Biological Basis of Myopia

This page intentionally left blank