×

zbMATH — the first resource for mathematics

Using the theory of added-variable plot for linear mixed models to decompose genetic effects in family data. (English) Zbl 1296.92028
Summary: Effective analytical tools are highly desirable for data analysis and for making the biological link between genotypic and phenotypic measures. In family data it is important to reconcile the methods that explain the phenotypic variability through fixed genetic effects and ones that estimate variance components using classical heritability methods. Thus, in this paper, we propose a method based on added-variable plot for polygenic linear mixed models applied to genome wide association studies in family-based designs. Our goal is to be able to discriminate genetic predictor variables in effects due to random polygenic and residual components. We also propose an index to detect influential families for each predictor variable identified with genetic effect. We assess the performance of our proposed method using our own family simulated data and the Genetic Analysis Workshop 17 family simulated data.
MSC:
92B15 General biostatistics
Software:
Plotly; pyuvdata; SimPed
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Almasy, L. and J. Blangero (1998): “Multipoint quantitative-trait linkage analysis in general pedigrees,” Am. J. Hum. Genet., 62, 1198-1211.
[2] Almasy, L., T. D. Dyer, J. M. Peralta, J. W. Kent, J. C. Charlesworth, J. E. Curran and J. Blangero (2011): “Genetic analysis workshop 17 mini-exome simulation,” BMC Proc., 5 (Suppl 9), S2.
[3] Amin, N., C. M. Van Duijn and Y. S. Aulchenko (2007): “A genomic bacground based method for association analysis in related individuals,” PLoS One, 2 (12), e1274.
[4] Amos, C. I. (1994): “Robust variance-components approach for assessing genetic linkage in pedigrees,” Am. J. Hum. Genet., 54 (3), 535-543.
[5] Atkinson, A. C. (1985): Plots, transformations, and regression, Clarendon Press, Oxford. · Zbl 0582.62065
[6] Aulchenko, Y. S., D. J. de Koning and C. Haley (2007): “Genome-wide rapid association using mixed model and regression: a fast and simple method for genome-wide pedigree-based quantitative trait loci association analysis,” Genetics, 177, 577-585.
[7] Chien, L. C. (2011): “A robust diagnostic plot for explanatory variables under model misspecification,” J. Appl. Stat., 38 (1), 113-126.
[8] Comuzzie, A. G., J. E. Hixson, B. D. Mitchell, M. C. Mahaney, T. D. Dyer and M. P. Stern (1997): “A major quantitative trait locus determining serum leptin levels and fat mass is located on human chromosome 2,” Nat. Genet., 15, 273-275.
[9] Cook, R. D. and S. Weisberg (1982): Residuals and influence in regression, Chapman and Hall, New York. · Zbl 0564.62054
[10] Cook, R. D. and S. Weisberg (1994): An introduction to regression graphics, Wiley, New York, NY. · Zbl 0925.62287
[11] de Andrade, M., C. I. Amos and T. J. Thiel (1999): “Methods to estimate genetic components of variance for quantitative traits in family studies,” Genet. Epidemiol., 17, 64-76.
[12] de Andrade, M., B. Fridley, E. Boerwinkle and S. Turner (2003): “Diagnostic tools in linkage analysis for quantitative traits,” Genet. Epidemiol., 39, 1-38.
[13] Duggal, P., E. Gilanders, T. N. Holmes and J. E. Biley-Wilson (2008): “Establishing an adjusted p-value threshold to control the family-wide type 1 error in genome-wide association studies,” BMC Genomics, 9, 516.
[14] Harville, D. A. (1976): “Extension of the Gauss-Markov theorem to include the estimation of random effects,” Ann. Stat., 4 (2), 384-395. · Zbl 0323.62043
[15] Hazelton, M. L. and L. C. Gurrin (2003): “A note on genetic variance components in mixed models,” Genet. Epidemiol., 24, 297-301.
[16] Hilden-Minton, J. A. (1995): Multilevel diagnostics for mixed and hierarchical linear models, PhD Thesis, University of California, Los Angeles, Ed Moderna.
[17] Hodges, J. (1994): Some algebra and geometry for hierarchical models, applied to diagnostics, Research Report 94-0009, University of Minessota, Minneapolis, Minessota.
[18] Hodges, J. (1998): “Some algebra and geometry for hierarchical models, applied to diagnostics,” J. Roy. Stat. Soc. B., 60, 497-536. · Zbl 0909.62072
[19] Hopper, J. L. and J. D. Mathews (1982): “Extensions to multivariate normal models for pedigree analysis,” Ann. Hum. Genet., 46, 373-383. · Zbl 0493.62091
[20] Huggins, R. M. (1993): “On the robust analysis of variance components models for pedigree data,” Aust. J. Stat., 35, 43-57. · Zbl 0772.62062
[21] Ionita-Laza, I., M. B. McQueen, N. M. Laird and C. Lange (2007): “Genome-wide weighted hypothesis testing in family-based association studies, with an application to a 100K scan,” Am. J. Hum. Genet., 81, 607-614.
[22] Ionita-Laza, I., S. Lee, V. Makarov, J. D. Buxbaum and X. Lin (2013): “Sequence Kernel association tests for the combined effect of rare and common variants,” Am. J. Hum. Genet., 92, 1-13.
[23] Johnson, B. W. and R. E. McCulloch (1987): “Added-variable plots in linear regression,” Technometrics, 29, 427-433.
[24] Kraft, P. and M. de Andrade (2003): “Group 6: pleiotropy and multivariate analysis,” Genet. Epidemiol., 25 (Suppl 1), S50-S56.
[25] Leal, S. M., K. Yang and B. Muller-Myhsok (2005): “SimPed: a simulation program to generate haplotype and genotype data for pedigree structures,” Hum. Hered., 60 (2), 119-122.
[26] Mosteller, F. and J. W. Tukey (1977): Data analysis and regression, Addison-Wesley Reading, MA.
[27] Nobre, J. S. and J. M. Singer (2007): “Residuals analysis for linear mixed models,” Biometrical. J., 49, 863-875.
[28] Nobre, J. S. and J. M. Singer (2011): “Leverage analysis for linear mixed models,” J. Appl. Stat., 38 (5), 1063-1072.
[29] Olswold, C. and M. de Andrade (2003): “Localization of genes involved in the metabolic syndrome using multivariate linkage analysis,” BMC Genet., 4 (Suppl) 1, S57.
[30] Rao, C. R. (1973): Linear statistical inference and its applications, Jonh Wiley and Sons, New York. · Zbl 0256.62002
[31] Royall, R. M. and T. S. Sou (2003): “Interpreting statistical evidence by using imperfect models: Robust adjusted likelihood functions,” J. Roy. Stat. Soc. B., 65, 391-404. · Zbl 1065.62047
[32] Searle, S. R., G. Cassela and C. E. McCullogh (1992): Variance components, Jonh Wiley and Sons, New York.
[33] Schork, N. J. (1993): “Extended multipoint identity-by-descent analysis of human quantitative traits: efficiency, power and modeling considerations,” Am. J. Hum. Genet., 53 (6), 1306-1319.
[34] Verbeke, G. and G. Molenberghs (1997): Linear mixed models in practique: A SAS oriented approach, Springer-Verlag, New York. · Zbl 0882.62064
[35] Wang, P. C. (1985): “Adding a variable in generalized linear models,” Technometrics, 27, 273-276.
[36] Yang, J., S. H. Lee, M. E. Goddard and P. M. Visscherl (2011): “GCTA: a tool for genome-wide complex trait analysis,” Am. J. Hum. Genet., 88, 76-82.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.