Abstract
Chapter 2 discussed both relatedness of study participants and hidden population structure in terms of the correlations induced between the number of copies, n iA and n jA , of a diallelic genetic variant carried by two individuals i and j. In Chap. 3 we discussed the requirement for association studies of unrelated subjects that the outcomes of interest, Y i , be independent between study subjects. In this chapter we will expand on this initial discussion (1) to examine the impact of non-independence on the distribution of statistical tests for the influence of alleles (here a and A) on phenotype or disease risk, and (2) how non-independence between individuals’ outcomes can arise as a direct result of correlation among the genotypes of study subjects due to hidden strata or relatedness or due to other factors (e.g., cultural/behavioral) that act as confounders of genetic associations. The chapter introduces several basic approaches for dealing with population structure in single marker association analyses and shows how all these methods deal, at least in part, with the fundamental problem of the analysis of correlated phenotypes. At the heart of these methods is the empirical estimation of a relationship matrix (more precisely a covariance structure matrix) that describes the relative relatedness of individuals. The statistical methods for dealing with covariances in estimation of single marker effects fall into three categories: fixed effects models utilizing adjustment for eigenvectors (“principal components”) of this matrix; random effects methods dealing explicitly with the relationship matrix as a covariance matrix of random effects in extended generalized linear modeling; and retrospective methods, which invert the usual generalized linear modeling procedures so that the conditional distribution of the genetic markers given the phenotypes (rather than the reverse) is used for inference in genetic association studies. Our discussion of all these approaches is unified around the theme of dealing with false-positive associations that are due to unrecognized inflation of the variance of estimators relied upon in traditional regression methods when correlated data are analyzed. Finally the relative performance of the various methods is described in various settings.
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References
Pike, M. C., Kolonel, L. N., Henderson, B. E., Wilkens, L. R., Hankin, J. H., Feigelson, H. S., et al. (2002). Breast cancer in a multiethnic cohort in Hawaii and Los Angeles: Risk factor-adjusted incidence in Japanese equals and in Hawaiians exceeds that in whites. Cancer Epidemiology, Biomarkers and Prevention, 11, 795–800.
Manolio, T. A., Collins, F. S., Cox, N. J., Goldstein, D. B., Hindorff, L. A., Hunter, D. J., et al. (2009). Finding the missing heritability of complex diseases. Nature, 461, 747–753.
Lango Allen, H., Estrada, K., Lettre, G., Berndt, S. I., Weedon, M. N., Rivadeneira, F., et al. (2010). Hundreds of variants clustered in genomic loci and biological pathways affect human height. Nature, 467, 832–838.
Speliotes, E. K., Willer, C. J., Berndt, S. I., Monda, K. L., Thorleifsson, G., Jackson, A. U., et al. (2010). Association analyses of 249,796 individuals reveal 18 new loci associated with body mass index. Nature Genetics, 42, 937–948.
Chambers, J. C., Zhang, W., Sehmi, J., Li, X., Wass, M. N., Van der Harst, P., et al. (2011). Genome-wide association study identifies loci influencing concentrations of liver enzymes in plasma. Nature Genetics, 43, 1131–1138.
Ehret, G. B., Munroe, P. B., Rice, K. M., Bochud, M., Johnson, A. D., Chasman, D. I., et al. (2011). Genetic variants in novel pathways influence blood pressure and cardiovascular disease risk. Nature, 478, 103–109.
O’Donovan, M. C., Craddock, N., Norton, N., Williams, H., Peirce, T., Moskvina, V., et al. (2008). Identification of loci associated with schizophrenia by genome-wide association and follow-up. Nature Genetics, 40, 1053–1055.
Haiman, C. A., Chen, G. K., Blot, W. J., Strom, S. S., Berndt, S. I., Kittles, R. A., et al. (2011). Genome-wide association study of prostate cancer in men of African ancestry identifies a susceptibility locus at 17q21. Nature Genetics, 43, 570–573.
Knowler, W. C., Williams, R. C., Pettitt, D. J., & Steinberg, A. G. (1988). Gm3;5,13,14 and type 2 diabetes mellitus: An association in American Indians with genetic admixture. American Journal of Human Genetics, 43, 520–526.
Chen, G. K., Millikan, R. C., John, E. M., Ambrosone, C. B., Bernstein, L., Zheng, W., et al. (2010). The potential for enhancing the power of genetic association studies in African Americans through the reuse of existing genotype data. PLoS Genetics, 6, e101096.
Lowe, J. K., Maller, J. B., Pe’er, I., Neale, B. M., Salit, J., Kenny, E. E., et al. (2009). Genome-wide association studies in an isolated founder population from the Pacific Island of Kosrae. PLoS Genetics, 5, e1000365.
Bonnen, P. E., Lowe, J. K., Altshuler, D. M., Breslow, J. L., Stoffel, M., Friedman, J. M., et al. (2010). European admixture on the Micronesian island of Kosrae: Lessons from complete genetic information. European Journal of Human Genetics, 18, 309–316.
Rabinowitz, D., & Laird, N. (2000). A unified approach to adjusting association tests for population admixture with arbitrary pedigree structure and arbitrary missing marker information. Human Heredity, 50, 211–223.
Laird, N. M., Horvath, S., & Xu, X. (2000). Implementing a unified approach to family-based tests of association. Genetic Epidemiology, 19(Suppl 1), S36–S42.
Devlin, B., & Roeder, K. (1999). Genomic control for association studies. Biometrics, 55, 997–1004.
Devlin, B., Roeder, K., & Wasserman, L. (2001). Genomic control, a new approach to genetic-based association studies. Theoretical Population Biology, 60, 155–166.
Price, A. L., Patterson, N. J., Plenge, R. M., Weinblatt, M. E., Shadick, N. A., & Reich, D. (2006). Principal components analysis corrects for stratification in genome-wide association studies. Nature Genetics, 38, 904–909.
Kirkpatrick, M. (2010). How and why chromosome inversions evolve. PLoS Biology, 8. doi: 10.1371/journal.pbio.1000501.
Zou, F., Lee, S., Knowles, M. R., & Wright, F. A. (2010). Quantification of population structure using correlated SNPs by shrinkage principal components. Human Heredity, 70, 9–22.
Hoggart, C. J., O’Reilly, P. F., Kaakinen, M., Zhang, W., Chambers, J. C., Kooner, J. S., et al. (2012). Fine-scale estimation of location of birth from genome-wide single-nucleotide polymorphism data. Genetics, 190, 669–677.
Patterson, N., Price, A. L., & Reich, D. (2006). Population structure and eigenanalysis. PLoS Genetics, 2, e190.
Tracy, C., & Widom, H. (1994). Level-spacing distributions and the Airy kernel. Communications in Mathematical Physics, 159, 151–174.
Price, A. L., Zaitlen, N. A., Reich, D., & Patterson, N. (2010). New approaches to population stratification in genome-wide association studies. Nature Reviews Genetics, 11, 459–463.
Anderson, T. W. (1973). Asympotically efficient estimation of covariance matrices with linear structure. The Annals of Statistics, 1, 135–141.
Goldstein, H. (1986). Multilevel mixed linear model analysis using iterative generalized least squares. Biometrika, 73, 43–56.
Yang, J., Benyamin, B., McEvoy, B. P., Gordon, S., Henders, A. K., Nyholt, D. R., et al. (2010). Common SNPs explain a large proportion of the heritability for human height. Nature Genetics, 42, 565–569.
Fisher, R. A. (1918). The correlation between relatives on the supposition of Mendelian inheritance. Transactions of the Royal Society of Edinburgh, 52, 399–433.
Pilia, G., Chen, W. M., Scuteri, A., Orru, M., Albai, G., Dei, M., et al. (2006). Heritability of cardiovascular and personality traits in 6,148 Sardinians. PLoS Genetics, 2, e132.
Falconer, D. S., & Mcackay, T. F. C. (1996). Introduction to quantitative genetics. Harlow: Longman.
Kang, H. M., Sul, J. H., Service, S. K., Zaitlen, N. A., Kong, S. Y., Freimer, N. B., et al. (2010). Variance component model to account for sample structure in genome-wide association studies. Nature Genetics, 42, 348–354.
Jennrich, R. I., & Schluchter, M. D. (1986). Unbalanced repeated-measures models with structured covariance matrices. Biometrics, 42, 805–820.
Almasy, L., & Warren, D. M. (2005). Software for quantitative trait analysis. Human Genomics, 2, 191–195.
Wu, M. C., Kraft, P., Epstein, M. P., Taylor, D. M., Chanock, S. J., Hunter, D. J., et al. (2010). Powerful SNP-set analysis for case–control genome-wide association studies. American Journal of Human Genetics, 86, 929–942.
Prentice, R., & Pyke, R. (1979). Logistic disease incidence models and case–control studies. Biometrika, 66, 403–411.
Bourgain, C., Hoffjan, S., Nicolae, R., Newman, D., Steiner, L., Walker, K., et al. (2003). Novel case–control test in a founder population identifies P-selectin as an atopy-susceptibility locus. American Journal of Human Genetics, 73, 612–626.
Rakovski, C., & Stram, D. O. (2009). A kinship-based modification of the Armitage trend test to address population structure and small differential genotyping errors. PloS One, 4, e5825.
Thornton, T., & McPeek, M. S. (2010). ROADTRIPS: Case–control association testing with partially or completely unknown population and pedigree structure. American Journal of Human Genetics, 86, 172–184.
Gauderman, W. J., Witte, J. S., & Thomas, D. C. (1999). Family-based association studies. Journal of the National Cancer Institute Monographs, 31–37.
Astle, W., & Balding, D. J. (2009). Population structure and cryptic relatedness in genetic association studies. Statistical Science, 24, 451–471.
Spielman, R. S., McGinnis, R. E., & Ewens, W. J. (1993). Transmission test for linkage disequilibrium: The insulin gene region and insulin-dependent diabetes mellitus (IDDM). American Journal of Human Genetics, 52, 506–516.
Cornelis, M. C., Tchetgen, E. J., Liang, L., Qi, L., Chatterjee, N., Hu, F. B., et al. (2012). Gene-environment interactions in genome-wide association studies: A comparative study of tests applied to empirical studies of type 2 diabetes. American Journal of Epidemiology, 175, 191–202.
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Stram, D.O. (2014). Correcting for Hidden Population Structure in Single Marker Association Testing and Estimation. In: Design, Analysis, and Interpretation of Genome-Wide Association Scans. Statistics for Biology and Health. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9443-0_4
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