Two-Stage Bayesian Approach for GWAS With Known Genealogy

References

• Abecasis, G., Cherny, S., Cookson, W., and Cardon, L. (2002), “Merlin-Rapid Analysis of Dense Genetic Maps Using Sparse Gene Flow Trees,” Nature Genetics, 30, 97–101.
   PubMed Web of Science ®Google Scholar
• Albert, J. (2014), LearnBayes: Functions for Learning Bayesian Inference, R Package Version 2.15, available at https://CRAN.R-project.org/package=LearnBayes.
   Google Scholar
• Balding, D. J. (2006), “A Tutorial on Statistical Methods for Population Association Studies,” Nature, 7, 781–791.
   Web of Science ®Google Scholar
• Barbieri, M. M., and Berger, J. O. (2004), “Optimal Predictive Model Selection,” The Annals of Statistics, 32, 870–897.
   Web of Science ®Google Scholar
• Bayarri, M., Berger, J., Forte, A., and García-Donato, G. (2012), “Criteria for Bayesian Model Choice With Application to Variable Selection,” The Annals of Statistics, 40, 1550–1577.
   Web of Science ®Google Scholar
• Benyamin, B., Visscher, P. M., and McRae, A. F. (2009), “Family-Based Genome-Wide Association Studies,” Pharmacogenomics, 10, 181–190.
   PubMed Web of Science ®Google Scholar
• Berger, J. O., and Pericchi, L. R. (2001), “Objective Bayesian Methods for Model Selection: Introduction and Comparison,” in Model Selection (Vol. 38), ed. P. Lahiri, Beachwood, OH: Institute of Mathematical Statistics, pp. 135–207
   Google Scholar
• Cabras, S., Castellanos, M. E., Biino, G., Persico, I., Sassu, A., Casula, L., del Giacco, S., Bertolino, F., Pirastu, M., and Pirastu, N. (2011), “A Strategy Analysis for Genetic Association Studies With Known Inbreeding,” BMC Genetics, 12, 63–74.
   PubMed Web of Science ®Google Scholar
• Cao, A., Congiu, R., Sollaino, M., Desogus, M., Demartis, F., Loi, D., Cau, M., and Galanello, R. (2008), “Thalassemia and Glucose-6-Phosphate Dehydrogenase Screening in 13- to 14-Year-Old Students of the Sardinian Population: Preliminary Findings,” Community Genetics, 11, 121–128.
   PubMedGoogle Scholar
• Castillo, I., Schmidt-Hieber, J., and van der Vaart, A. (2015), “Bayesian Linear Regression With Sparse Priors,” The Annals of Statistics, 43, 1986–2018.
   Web of Science ®Google Scholar
• Eilers, P. H., and Marx, B. D. (1996), “Flexible Smoothing With b-Splines and Penalties,” Statistical Science, 11, 89–102.
   Web of Science ®Google Scholar
• Frank, L. E., and Friedman, J. H. (1993), “A Statistical View of Some Chemometrics Regression Tools,” Technometrics, 35, 109–135.
   Web of Science ®Google Scholar
• Friedman, J., Hastie, T., and Tibshirani, R. (2010), “Regularization Paths for Generalized Linear Models via Coordinate Descent,” Journal of Statistical Software, 33, 1–22.
   PubMed Web of Science ®Google Scholar
• Fu, W. J. (1998), “Penalized Regressions: The Bridge Versus the Lasso,” Journal of Computational and Graphical Statistics, 7, 397–416.
   Web of Science ®Google Scholar
• Galanello, R., and Origa, R. (2010), “Beta-Thalassemia,” Orphanet Journal of Rare Diseases, 5, 1–11.
   PubMed Web of Science ®Google Scholar
• Garcia-Donato, G., and Forte, A. (2017), BayesVarSel: Bayes Factors, Model Choice and Variable Selection in Linear Models, R Package Version 1.7.1, available at https://CRAN.R-project.org/package=BayesVarSel
   Google Scholar
• García-Donato, G., and Martínez-Beneito, M. (2013), “On Sampling Strategies in Bayesian Variable Selection Problems With Large Model Spaces,” Journal of the American Statistical Association, 108, 340–352.
   Web of Science ®Google Scholar
• George, E. I., and McCulloch, R. E. (1993), “Variable Selection via Gibbs Sampling,” Journal of the American Statistical Association, 88, 881–889.
   Web of Science ®Google Scholar
• ——— (1997), “Approaches for Bayesian Variable Selection,” Statistica Sinica, 7, 339–373.
   Web of Science ®Google Scholar
• Giner, G., and Smyth, G. K. (2016), “statmod: Probability Calculations for the Inverse Gaussian Distribution,” R Journal, 8, 339–351.
   Web of Science ®Google Scholar
• Girosi, F., Jones, M., and Poggio, T. (1993), “Priors Stabilizers and Basis Functions: From Regularization to Radial, Tensor and Additive Splines,” C. B. C. L. Paper No. 75, Artificial Intelligence Laboratory Massachusetts Institute of Technology.
   Google Scholar
• Gradshteyn, I. S., and Ryzhi, I. M. (1965), Table of Integrals, Series and Products, Boston, MA: Academic Press Inc.
   Google Scholar
• Herold, C., Hooli, B. V., Mullin, K., Liu, T., Roehr, J. T., Mattheisen, M., Parrado, A., Bertram, L., Lange, C., and Tanzi, R. E. (2016), “Family-Based Association Analyses of Imputed Genotypes Reveal Genome-Wide Significant Association of Alzheimer’s Disease With Osbpl6, ptprg and pdcl3,” Molecular Psychiatry, 21, 1608–1612.
   PubMed Web of Science ®Google Scholar
• Hoerl, A. E., and Kennard, R. W. (1988), “Ridge Regression,” in Encyclopedia of Statistical Sciences (Vol. 8), eds. N. L. Johnson, S. Kotz, and C. B. Read, New York: Wiley, pp. 129–136.
   Google Scholar
• Ishwaran, H., and Rao, J. S. (2005), “Spike and Slab Variable Selection: Frequentist and Bayesian Strategies,” Annals of Statistics, 33, 730–773.
   Web of Science ®Google Scholar
• Jallow, M., Teo, Y. Y., Small, K. S., Rockett, K. A., Deloukas, P., Clark, T. G., Kivinen, K., Bojang, K. A., Conway, D. J., Pinder, M., Sirugo, G., Sisay-Joof, F., Usen, S., Auburn, S., Bumpstead, S. J., Campino, S., Coffey, A., Dunham, A., Fry, A. E., Green, A., Gwilliam, R., Hunt, S. E., Inouye, M., Jeffreys, A. E., Mendy, A., Palotie, A., Potter, S., Ragoussis, J., Rogers, J., Rowlands, K., Somaskantharajah, E., Whittaker, P., Widden, C., Donnelly, P., Howie, B., Marchini, J., Morris, A., SanJoaquin, M., Achidi, E. A., Agbenyega, T., Allen, A., Amodu, O., Corran, P., Djimde, A., Dolo, A., Doumbo, O. K., Drakeley, C., Dunstan, S., Evans, J., Farrar, J., Fernando, D., Hien, T. T., Horstmann, R. D., Ibrahim, M., Karunaweera, N., Kokwaro, G., Koram, K. A., Lemnge, M., Makani, J., Marsh, K., Michon, P., Modiano, D., Molyneux, M. E., Mueller, I., Parker, M., Peshu, N., Plowe, C. V., Puijalon, O., Reeder, J., Reyburn, H., Riley, E. M., Sakuntabhai, A., Singhasivanon, P., Sirima, S., Tall, A., Taylor, T. E., Thera, M., Troye-Blomberg, M., Williams, T. N., Wilson, M., Kwiatkowski, D. P., Wellcome Trust Case Control Consortium, and Malaria Genomic Epidemiology Network. (2009), “Genome-Wide and Fine-Resolution Association Analysis of Malaria in West Africa,” Nature Genetics, 41, 657–665.
   Google Scholar
• Kass, R., and Raftery, A. (1995), “Bayes Factors,” Journal of the American Statistical Association, 90, 773–795.
   Web of Science ®Google Scholar
• Lee, A., Caron, F., Doucet, A., and Holmes, C. (2012), “Bayesian Sparsity-Path-Analysis of Genetic Association Signal Using Generalized t Priors,” Statistical Applications in Genetics and Molecular Biology, 11, Article 5.
   Google Scholar
• Li, Q., and Lin, N. (2010), “The Bayesian Elastic Net,” Bayesian Analysis, 5, 151–170.
   Web of Science ®Google Scholar
• Malecot, G. (1948), Les Mathematiques de l’Heredire, Paris: Masson et Cie.
   Google Scholar
• Martin, A. D., Quinn, K. M., and Park, J. H. (2011), “MCMCpack: Markov Chain Monte Carlo in R,” Journal of Statistical Software, 42, 22. Available at http://www.jstatsoft.org/v42/i09/
   Web of Science ®Google Scholar
• Nychka, D. W. (2000), “Spatial-Process Estimates as Smoothers,” in Smoothing and Regression: Approaches, Computation, and Application, ed. M. G. Schimek, New York: Wiley, pp. 393–424.
   Google Scholar
• O’Sullivan, F. (1986), “A Statistical Perspective on Ill-Posed Inverse Problems,” Statistical Science, 1, 502–518.
   Google Scholar
• Ott, J., Kamatani, Y., and Lathrop, M. (2011), “Family-Based Designs for Genome-Wide Association Studies,” Nature Reviews Genetics, 12, 465–474.
   PubMed Web of Science ®Google Scholar
• Park, T., and Casella, G. (2008), “The Bayesian Lasso,” Journal of the American Statistical Association, 103, 681–686.
   Web of Science ®Google Scholar
• R Core Team (2017), R: A Language and Environment for Statistical Computing, Vienna, Austria: R Foundation for Statistical Computing.
   Google Scholar
• Ročková, V., and George, E. I. (2015), “The Spike-and-Slab Lasso,” Journal of the American Statistical Association, 113, 431–444.
   Google Scholar
• Rosatelli, C., Leoni, G., Tuveri, T., Scalas, M. T., Mosca, A., Galanello, R., Gasperini, D., and Cao, A. (1992), “Heterozygous Beta-Thalassemia: Relationship Between the Hematological Phenotype and the Type of Beta-Thalassemia Mutation,” American Journal of Hematology, 39, 1–4.
   PubMed Web of Science ®Google Scholar
• Rosatelli, M., Dozy, A., Faa, V., Meloni, A., Sardu, R., Saba, L., Kan, Y., and Cao, A. (1992), “Molecular Characterization of Beta-Thalassemia in the Sardinian Population,” American Journal of Human Genetics, 50, 422–426.
   PubMed Web of Science ®Google Scholar
• Rue, H., Martino, S., and Chopin, N. (2009), “Approximate Bayesian Inference for Latent Gaussian Models Using Integrated Nested Laplace Approximations (with discussion),” Journal of the Royal Statistical Society, Series B, 71, 319–392.
   Google Scholar
• Ruppert, D., Wand, M., and Carroll, R. (2003), Semiparametric Regression (Cambridge Series in Statistical and Probabilistic Mathematics), Cambridge: Cambridge University Press.
   Google Scholar
• Scott, J., and Berger, J. (2010), “Bayes and Empirical-Bayes Multiplicity Adjustment in the Variable-Selection Problem,” The Annals of Statistics, 38, 2587–2619.
   Web of Science ®Google Scholar
• Shin, M., Bhattacharya, A., and Johnson, V. E. (2018), “Scalable Bayesian Variable Selection Using Nonlocal Prior Densities in Ultrahigh-Dimensional Settings,” Statistica Sinica, 28, 1053–1078.
   Google Scholar
• Therneau, T. M., and Sinnwell, J. (2015), kinship2: Pedigree Functions, R Package Version 1.6.4, available at https://CRAN.R-project.org/package=kinship2
   Google Scholar
• Tibshirani, R. (1996), “Regression Shrinkage and Selection via the Lasso,” Journal of the Royal Statistical Society, Series B, 58, 267–288.
   Google Scholar
• Trecartin, R., Liebhaber, S., Chang, J., Lee, K., Kan, Y., Fubetta, M., Angius, A., and Cao, A. (1981), “Beta Zero Thalassemia in Sardinia is Caused by a Nonsense Mutation,” Journal of Clinical Investigations, 68, 1012–1017.
   PubMed Web of Science ®Google Scholar
• Uda, M., Galanello, R., Sanna, S., Lettre, G., Sankaran, V. G., Chen, W., Usala, G., Busonero, F., Maschio, A., Albai, G., Piras, MG., Sestu, N., Lai, S., Dei, M., Mulas, A., Crisponi, L., Naitza, S., Asunis, I., Deiana, M., Nagaraja, R., Perseu, L., Satta, S., Cipollina, M. D., Sollainoh, C., Moi, P., Hirschhorn, J. N., Orkin, S. H., Abecasis, G. R., Schlessinger, D., and Cao, A. (2008), “Genome-Wide Association Study Shows Bcl11A Associated With Persistent Fetal Hemoglobin and Amelioration of the Phenotype of β-Thalassemia,” Proceedings of the National Academy of Sciences, 105, 1620–1625.
   PubMed Web of Science ®Google Scholar
• Wagner, M. (2013), “Rare-Variant Genome-Wide Association Studies: A New Frontier in Genetic Analysis of Complex Traits,” Pharmacogenomics, 14, 413–424.
   PubMed Web of Science ®Google Scholar
• Wahba, G. (1990), Spline Models for Observational Data, Philadelphia, PA: SIAM.
   Google Scholar
• Wickham, H. (2011), “The Split-Apply-Combine Strategy for Data Analysis,” Journal of Statistical Software, 40, 1–29. Available at http://had.co.nz/plyr
   Web of Science ®Google Scholar
• Yazdani, A., and Dunson, B. (2015), “A Hybrid Bayesian Approach for Genome-Wide Association Studies on Related Individuals,” Bioinformatics, 31, 3890–3896.
   PubMed Web of Science ®Google Scholar
• Zhou, X., Carbonetto, P., and Stephens, M. (2013), “Polygenic Modelling With Bayesian Sparse Linear Mixed Models,” PLoS Genetics, 9, e1003264.
   PubMed Web of Science ®Google Scholar
• Zhou, X., and Stephens, M. (2012), “Genome-Wide Efficient Mixed-Model Analysis for Association Studies,” Nature Genetics, 44, 821–824.
   PubMed Web of Science ®Google Scholar
• Zou, H., and Hastie, T. (2005), “Regularization and Variable Selection via the Elastic Net,” Journal of the Royal Statistical Society, Series B, 67, 301–320.
   Google Scholar