Abstract
The International HapMap Project was proposed in order to quantify linkage disequilibrium (LD) relationships among human DNA polymorphisms in an assortment of populations, in order to facilitate the process of selecting a minimal set of markers that could capture most of the signal from the untyped markers in a genome-wide association study. The central dogma can be summarized by the argument that if a marker is in tight LD with a polymorphism that directly impacts disease risk, as measured by the metric r2, then one would be able to detect an association between the marker and disease with sample size that was increased by a factor of 1/r2 over that needed to detect the effect of the functional variant directly. This ‘fundamental theorem’ holds, however, only if one assumes that the LD between loci and the etiological effect of the functional variant are independent of each other, that they are statistically independent of all other etiological factors (in exposure and action), that sampling is prospective, and that the estimates of r2 are accurate. None of these are standard operating assumptions, however. We describe the ramifications of these implicit assumptions, and provide simple examples in which the effects of a functional variant could be unequivocally detected if it were directly genotyped, even as markers in high LD with the functional variant would never show association with disease, even in infinite sample sizes. Both theoretical and empirical refutation of the central dogma of genome-wide association studies is thus presented.
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References
Terwilliger JD, Weiss KM : Linkage disequilibrium mapping of complex disease: fantasy or reality? Curr Opin Biotechnol 1998; 9: 578–594.
Terwilliger JD : On the resolution and feasiblity of genome scanning approaches. Adv Genet 2001; 42: 351–391.
Terwilliger JD, Weiss KM : Confounding, ascertainment bias, and the blind quest for a genetic ‘fountain of youth’. Ann Med 2003; 35: 532–544.
Weiss KM, Terwilliger JD : How many diseases does it take to map a gene with SNPs? Nat Genet 2000; 26: 151–157.
The International HapMap Consortium: The International HapMap Project. Nature 2003; 426: 789–796.
Aquadro CF, DuMont VB, Reed FA : Genome-wide variation in the human and fruitfly: a comparison. Curr Opin Genet Dev 2001; 11: 627–634.
Brookes AJ : Rethinking genetic strategies to study complex diseases. Trends Mol Med 2001; 7: 512–516.
Cardon LR, Bell JI : Association study designs for complex diseases. Nat Rev Genet 2001; 2: 91–99.
Ghosh S, Collins FS : The geneticist's approach to complex disease. Ann Rev Med 1996; 47: 333–353.
Guyer MS, Collins FS : The Human Genome Project and the future of medicine. Am J Dis Children 1993; 147: 1145–1152.
Kruglyak L, Nickerson DA : Variation is the spice of life. Nat Genet 2001; 27: 234–236.
Pritchard JK : Are rare variants responsible for susceptibility to complex diseases? Am J Hum Genet 2001; 69: 124–137.
Pritchard JK, Cox NJ : The allelic architecture of human disease genes: common disease-common variant or not? Hum Mol Genet 2002; 11: 2417–2423.
Risch N, Merikangas K : The future of genetic studies of complex human diseases. Science 1996; 273: 1516–1517.
Zwick ME, Cutler DJ, Chakravarti A : Patterns of genetic variation in Mendelian and complex traits. Annu Rev Genomics Hum Genet 2000; 1: 387–407.
Ardlie KG, Kruglyak L, Seielstad M : Patterns of linkage disequilibrium in the human genome. Nat Rev Genet 2002; 3: 299–309.
Bader JS : The relative power of SNPs and haplotype as genetic markers for association tests. Pharmacogenomics 2001; 2: 11–24.
Barton A, Chapman P, Myerscough A et al: The single-nucleotide polymorphism lottery: How useful are a few common SNPs in identifying disease-associated alleles? Genet Epidemiol 2001; 21: S384–S389.
Black WC, Baer CF, Antolin MF, DuTeau NM : Population genomics: genome-wide sampling of insect populations. Annu Rev Entomol 2001; 46: 441–469.
Clark AG, Weiss KM, Nickerson DA et al: Haplotype structure and population genetic inferences from nucleotide-sequence variation in human lipoprotein lipase. Am J Hum Genet 1998; 63: 595–612.
Collins A, Ennis S, Taillon-Miller P, Kwok PY, Morton NE : Allelic association with SNPs: metrics, populations, and the linkage disequilibrium map. Hum Mutat 2001; 17: 255–262.
Cookson W : The extent and distribution of linkage disequilibrium: problems for SNP mappers. J Med Genet 2001; 38: SP3.
Daly MJ, Rioux JD, Schaffner SE, Hudson TJ, Lander ES : High-resolution haplotype structure in the human genome. Nat Genet 2001; 29: 229–232.
Dunning AM, Durocher F, Healey CS et al: The extent of linkage disequilibrium in four populations with distinct demographic histories. Am J Hum Genet 2000; 67: 1544–1554.
Goldstein DB, Weale ME : Population genomics: linkage disequilibrium holds the key. Curr Biol 2001; 11: R576–R579.
Johnson GCL, Esposito L, Barratt BJ et al: Haplotype tagging for the identification of common disease genes. Nat Genet 2001; 29: 233–237.
Jorde LB, Watkins WS, Bamshad MJ : Population genomics: a bridge from evolutionary history to genetic medicine. Hum Mol Genet 2001; 10: 2199–2207.
Judson R, Salisbury B, Schneider J, Windemuth A, Stephens JC : How many SNPs does a genome-wide haplotype map require? Pharmacogenomics 2002; 3: 379–391.
Maniatis N, Collins A, Xu CF et al: The first linkage disequilibrium (LD) maps: Delineation of hot and cold blocks by diplotype analysis. Proc Natl Acad Sci USA 2002; 99: 2228–2233.
Morris RW, Kaplan NL : When is haplotype analysis advantageous for linkage- disequilibrium mapping? Am J Hum Genet 2001; 69: 30.
Morton NE, Zhang W, Taillon-Miller P, Ennis S, Kwok PY, Collins A : The optimal measure of allelic association. Proc Natl Acad Sci USA 2001; 98: 5217–5221.
Pritchard JK, Przeworski M : Linkage disequilibrium in humans: models and data. Am J Hum Genet 2001; 69: 1–14.
Remington DL, Thornsberry JM, Matsuoka Y et al: Structure of linkage disequilibrium and phenotypic associations in the maize genome. Proc Natl Acad Sci USA 2001; 98: 11479–11484.
Service SK, Ophoff RA, Freimer NB : The genome-wide distribution of background linkage disequilibrium in a population isolate. Hum Mol Genet 2001; 10: 545–551.
Sham PC, Zhao JH, Curtis D : The effect of marker characteristics on the power to detect linkage disequilibrium due to single or multiple ancestral mutations. Ann Hum Genet 2000; 64: 161–169.
Stephens JC, Schneider JA, Tanguay DA et al: Haplotype variation and linkage disequilibrium in 313 human genes. Science 2001; 293: 489–493.
Terwilliger JD, Haghighi F, Hiekkalinna TS, Goring HH : A bias-ed assessment of the use of SNPs in human complex traits. Curr Opin Genet Dev 2002; 12: 726–734.
Varilo T, Laan M, Hovatta I, Wiebe V, Terwilliger JD, Peltonen L : Linkage disequilibrium in isolated populations: Finland and a young sub-population of Kuusamo. Eur J Hum Genet 2000; 8: 604–612.
Varilo T, Paunio T, Parker A et al: The interval of linkage disequilibrium (LD) detected with multiallelic and biallelic markers in chromosomes of early and late settlement regions of Finland, 2002.
Weiss KM, Clark AG : Linkage disequilibrium and the mapping of complex human traits. Trends Genet 2002; 18: 19–24.
Culverhouse R, Lin J, Liu KY, Suarez BK : Exploiting linkage disequilibrium in population isolates. Genet Epidemiol 2001; 21: S429–S434.
Kere J : Human population genetics: Lessons from Finland. Annu Rev Genomics Hum Genet 2001; 2: 103–128.
Peltonen L, Palotie A, Lange K : Use of population isolates for mapping complex traits. Nat Rev Genet 2000; 1: 182–190.
Pritchard JK, Donnelly P : Case–control studies of association in structured or admixed populations. Theor Popul Biol 2001; 60: 227–237.
Pritchard JK, Stephens M, Rosenberg NA, Donnelly P : Association mapping in structured populations. Am J Hum Genet 2000; 67: 170–181.
Scriver CR : Human genetics: Lessons from Quebec populations. Annu Rev Genomics Hum Genet 2001; 2: 69–101.
Terwilliger JD, Lee JH : Natural experiments in human gene mapping. In: Craford MH (ed): Anthropol Genet. Cambridge: Cambridge University Press, 2005.
Terwilliger JD, Göring HHH, Magnusson PKE, Lee JH : Study design for genetic epidemiology and gene mapping: The Korean diaspora project. Shengming Kexue Yanjiu (Life Science Research) 2002; 6: 95–115.
Terwilliger JD, Zollner S, Laan M, Paabo S : Mapping genes through the use of linkage disequilibrium generated by genetic drift: ‘drift mapping’ in small populations with no demographic expansion. Hum Heredity 1998; 48: 138–154.
Wright AF, Carothers AD, Pirastu M : Population choice in mapping genes for complex diseases. Nat Genet 1999; 23: 397–404.
Ott J : Analysis of Human Genetic Linkage. Baltimore: Johns Hopkins University Press, 1985.
Lewontin RC : On Measures of Gametic Disequilibrium. Genetics 1988; 120: 849–852.
Gabriel SB, Schaffner SF, Nguyen H et al: The structure of haplotype blocks in the human genome. Science 2002; 296: 2225–2229.
Pritchard JK, Przeworski M : Linkage disequilibrium in humans: models and data. Am J Hum Genet 2001; 69: 1–14.
Ahlstrom S, Bloomfield K, Knibbe R : Gender differences in drinking patterns in nine european countries: descriptive findings. Subst Abus 2001; 22: 69–85.
Cargill M, Altshuler D, Ireland J et al: Characterization of single-nucleotide polymorphisms in coding regions of human genes. Nat Genet 1999; 22: 231–238.
Altshuler D, Clark AG : Genetics harvesting medical information from the human family tree. Science 2005; 307: 1052–1053.
Chakravarti A : The nature and distribution of human genetic disease. Am Naturalist 2001; 158: 12.
Chakravarti A : Single nucleotide polymorphisms to a future of genetic medicine. Nature 2001; 409: 822–823.
Day INM, Gu DF, Ganderton RH, Spanakis E, Ye S : Epidemiology and the genetic basis of disease. Int J Epidemiol 2001; 30: 661–667.
Goring HHH, Terwilliger JD : Linkage analysis in the presence of errors I: complex-valued recombination fractions and complex phenotypes. Am J Hum Genet 2000; 66: 1095–1106.
Goring HHH, Terwilliger JD : Linkage analysis in the presence of errors II: marker-locus genotyping errors modeled with hypercomplex recombination fractions. Am J Hum Genet 2000; 66: 1107–1118.
Goring HHH, Terwilliger JD : Linkage analysis in the presence of errors III: marker loci and their map as nuisance parameters. Am J Hum Genet 2000; 66: 1298–1309.
Goring HHH, Terwilliger JD : Linkage analysis in the presence of errors IV: joint pseudomarker analysis of linkage and/or linkage disequilibrium on a mixture of pedigrees and singletons when the mode of inheritance cannot be accurately specified. Am J Hum Genet 2000; 66: 1310–1327.
Terwilliger JD : A likelihood-based extended admixture model of oligogenic inheritance in ‘model-based’ and ‘model-free’ analysis. Eur J Hum Genet 2000; 8: 399–406.
Terwilliger JD, Goring HHH : Gene mapping in the 20th and 21st centuries: statistical methods, data analysis, and experimental design. Hum Biol 2000; 72: 63–132.
Acknowledgements
Grant MH63749 from the National Institutes of Mental Health, along with funding from the Sigrid Juselius Foundation, the Academy of Finland, The Finnish Cultural Foundation, and the Burroughs-Wellcome Fund is gratefully acknowledged. r2 estimates for pairs of SNPs on all Chromosomes from CEU, CHB, JPT and YRI datasets, release date June 16th 2005, from the International HapMap Consortium were used for Figure 2, and as such the consortium is acknowledged. Thanks to Harald H.H. Göring for critical comments on the manuscript.
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Appendix
Appendix
Demonstration that multiplicativity of correlation coefficients implies conditional independence.
Since
then ρAC=ρAB ρBC if and only if
Expanding the right side of this equation leads to the following:
However, if we expand the left side of the equation,
and according to the Chain rule from elementary probability, this implies that
but this only equals the right side of Eq. (1) above, if we assume that we have conditional independence of A and C when B is true, such that, for example, P(A∣BC)=P(A∣B).
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Terwilliger, J., Hiekkalinna, T. An utter refutation of the ‘Fundamental Theorem of the HapMap’. Eur J Hum Genet 14, 426–437 (2006). https://doi.org/10.1038/sj.ejhg.5201583
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DOI: https://doi.org/10.1038/sj.ejhg.5201583
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