Abstract
The aim of the paper is to discuss the association between SNP genotype data and a disease. For genetic association studies, the statistical analyses with multiple markers have been shown to be more powerful, efficient, and biologically meaningful than single marker association tests. As the number of genetic markers considered is typically large, here we cluster them and then study the association between groups of markers and disease. We propose a two-step procedure: first a Bayesian nonparametric cluster estimate under normalized generalized gamma process mixture models is introduced, so that we are able to incorporate the information from a large-scale SNP data with a much smaller number of explanatory variables. Then, thanks to the introduction of a genetic score, we study the association between the relevant disease response and groups of markers using a logit model. Inference is obtained via an MCMC truncation method recently introduced in the literature. We also provide a review of the state of art of Bayesian nonparametric cluster models and algorithms for the class of mixtures adopted here. Finally, the model is applied to genome-wide association study of Crohn’s disease in a case-control setting.
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References
Argiento, R., Guglielmi, A., and Pievatolo, A. (2010). Bayesian density estimation and model selection using nonparametric hierarchical mixtures. Comput. Stat. Data Anal., 54, 816–832.
Argiento, R., Cremaschi, A., and Guglielmi, A. (2014). A density-based algorithm for cluster analysis using species sampling Gaussian mixture models. J. Comput. Graph. Stat., 23, 1126–1142.
Argiento, R., Bianchini, I., and Guglielmi, A. (2015). A blocked Gibbs sampler for NGG-mixture models via a priori truncation. Statist. Comp., Online First.
Asimit, J. and Zeggini, E. (2010). Rare variant association analysis methods for complex traits. Annu. Rev. Genet., 44, 293–308.
Bansal, V., Libiger, O., Torkamani, A., and Schork, N. J. (2010). Statistical analysis strategies for association studies involving rare variants. Nat. Rev. Genet., 11, 773–785.
Barrios, E., Lijoi, A., Nieto-Barajas, L. E., Prünster, I., et al. (2013). Modeling with normalized random measure mixture models. Stat. Sci., 28, 313–334.
Caron, F. (2012). Bayesian nonparametric models for bipartite graphs. In Advances in Neural Information Processing Systems, pages 2051–2059.
Caron, F. and Fox, E. B. (2014). Bayesian nonparametric models of sparse and exchangeable random graphs. ar**v preprint ar**v:1401.1137.
Chen, C., Ding, N., and Buntine, W. (2012). Dependent hierarchical normalized random measures for dynamic topic modeling. International conference on machine learning (ICML), Edimburg, UK.
Chen, L. S., Hutter, C. M., Potter, J. D., Liu, Y., Prentice, R. L., Peters, U., and Hsu, L. (2010). Insights into colon cancer etiology via a regularized approach to gene set analysis of GWAS data. Am. J. Hum. Genet., 86, 860–871.
Cho, J. H. (2008). The genetics and immunopathogenesis of inflammatory bowel disease. Nat. Rev. Immunol., 8, 458–466.
Chung, Y. and Dunson, D. (2009). Nonparametric Bayes conditional distribution modeling with variable selection. J. Am. Stat. Assoc., 104, 1646–1660.
Dahl, D. B. (2006). Model-based clustering for expression data via a Dirichlet process mixture model. In V. M. Do K.-A., Müller P., editor, Bayesian inference for gene expression and proteomics, pages 201–218. Cambridge: Cambridge University Press.
De Blasi, P., Favaro, S., Lijoi, A., Mena, R., Prünster, I., and Ruggiero, M. (2014). Are Gibbs-type priors the most natural generalization of the Dirichlet process? IEEE Trans. Pattern Anal. Mach. Intell., 37, 212–229.
de Paus, R. A., Geilenkirchen, M. A., van Riet, S., van Dissel, J. T., and van de Vosse, E. (2013). Differential expression and function of human il-12rβ2 polymorphic variants. Molecular immunology, 56(4), 380–389.
Duerr, R. H., Taylor, K. D., Brant, S. R., Rioux, J. D., Silverberg, M. S., Daly, M. J., Steinhart, A. H., Abraham, C., Regueiro, M., Griffiths, A., et al. (2006). A genome-wide association study identifies IL23R as an inflammatory bowel disease gene. Science, 314, 1461–1463.
Favaro, S. and Teh, Y. W. (2013). MCMC for normalized random measure mixture models. Stat. Sci., 28, 335–359.
Ferguson, T. S. (1973). A Bayesian analysis of some nonparametric problems. Ann. Statist., 1, 209–230.
Fritsch, A. and Ickstadt, K. (2009). Improved criteria for clustering based on the posterior similarity matrix. Bayesian Anal., 4, 367–392.
Glas, J., Seiderer, J., Wetzke, M., Konrad, A., Török, H.-P., Schmechel, S., Tonenchi, L., Grassl, C., Dambacher, J., Pfennig, S., et al. (2007). rs1004819 is the main disease-associated il23r variant in German Crohn’s disease patients: combined analysis of IL23R, CARD15, and OCTN1/2 variants. PloS One, 2, e819.
Griffin, J. E. (2014). An adaptive truncation method for inference in Bayesian nonparametric models. Statist. Comp., Online First, 1–19.
Griffin, J. E. and Walker, S. G. (2011). Posterior simulation of normalized random measure mixtures. J. Comput. Graph. Stat., 20, 241–259.
Hu, J. and Tzeng, J.-Y. (2014). Integrative gene set analysis of multi-platform data with sample heterogeneity. Bioinformatics, 30, 1501–1507.
Huang, H., Chanda, P., Alonso, A., Bader, J. S., and Arking, D. E. (2011). Gene-based tests of association. PLoS Genetics, 7, e1002177.
Ishwaran, H. and James, L. F. (2001). Gibbs sampling methods for stick-breaking priors. J. Amer. Statist. Assoc., 96, 161–173.
Jasra, A., Holmes, C., and Stephens, D. (2005). Markov chain Monte Carlo methods and the label switching problem in Bayesian mixture modeling. Stat. Sci., 20, 50–67.
Johnstone, I. M. and Silverman, B. W. (2004). Needles and straw in haystacks: Empirical Bayes estimates of possibly sparse sequences. Ann. Statist., 32, 1594–1649.
Jostins, L., Ripke, S., Weersma, R. K., Duerr, R. H., McGovern, D. P., Hui, K. Y., Lee, J. C., Schumm, L. P., Sharma, Y., Anderson, C. A., et al. (2012). Host-microbe interactions have shaped the genetic architecture of inflammatory bowel disease. Nature, 491, 119–124.
Lau, J. W. and Green, P. J. (2007). Bayesian model based clustering procedures. J. Comput. Graph. Stat, 16, 526–558.
Lee, I., Blom, U. M., Wang, P. I., Shim, J. E., and Marcotte, E. M. (2011). Prioritizing candidate disease genes by network-based boosting of genome-wide association data. Genome Res., 21, 1109–1121.
Lijoi, A., Mena, R. H., and Prünster, I. (2007). Controlling the reinforcement in Bayesian nonparametric mixture models. J. R. Stat. Soc., B, 69, 715–740.
Liverani, S., Hastie, D. I., Azizi, L., Papathomas, M., and Richardson, S. (2015). PReMiuM: An R package for profile regression mixture models using Dirichlet processes. J. Stat. Softw., forthcoming.
Medvedovic, M., Yeung, K. Y., and Bumgarner, R. E. (2004). Bayesian mixture model based clustering of replicated microarray data. Bioinformatics, 20, 1222–1232.
Molitor, J., Papathomas, M., Jerrett, M., and Richardson, S. (2010). Bayesian profile regression with an application to the national survey of children’s health. Biostatistics, 11, 484–498.
Mooney, S. (2005). Bioinformatics approaches and resources for single nucleotide polymorphism functional analysis. Brief Bioinform., 6, 44–56.
Muliere, P. and Tardella, L. (1998). Approximating distributions of random functionals of Ferguson-Dirichlet priors. Can. J. Stat., 26, 283–297.
Müller, P., Quintana, F. A., and Rosner, G. A. (2011). A product partition model with regression on covariates. J. Comput. Graph. Stat, 20, 260–278.
Nguyen, L. B., Diskin, S. J., Capasso, M., Wang, K., Diamond, M. A., Glessner, J., Kim, C., Attiyeh, E. F., Mosse, Y. P., Cole, K., et al. (2011). Phenotype restricted genome-wide association study using a gene-centric approach identifies three low-risk neuroblastoma susceptibility loci. PLoS Genetics, 7, e1002026.
Onogi, A., Nurimoto, M., and Morita, M. (2011). Characterization of a Bayesian genetic clustering algorithm based on a Dirichlet process prior and comparison among Bayesian clustering methods. BMC Bioinformatics, 12, 263–278.
Papathomas, M., Molitor, J., Hoggart, C., Hastie, D., and Richardson, S. (2012). Exploring data from genetic association studies using Bayesian variable selection and the Dirichlet process: application to searching for gene × gene patterns. Genet. Epidemiol., 36, 663–674.
Pitman, J. (1996). Some developments of the Blackwell-MacQueen urn scheme. In B. M. Ferguson TS, Shapley LS, editor, Statistics, Probability and Game Theory: Papers in Honor of David Blackwell, pages 245–267. Hayward: Institute of Mathematical Statistics.
Quintana, F. A. and Iglesias, P. L. (2003). Bayesian clustering and product partition models. J. R. Stat. Soc., B, 65, 557–574.
Ramanan, V. K., Shen, L., Moore, J. H., and Saykin, A. J. (2012). Pathway analysis of genomic data: concepts, methods, and prospects for future development. Trends Genet., 28, 323–332.
Reece, J. B., Urry, L. A., Cain, M. L., Wasserman, S. A., Minorsky, P. V., and Jackson, R. (2014). Campbell Biology. Boston: Pearson.
Regazzini, E., Lijoi, A., and Prünster, I. (2003). Distributional results for means of normalized random measures with independent increments. Ann. Statist., 31, 560–585.
Rodriguez, A., Dunson, D. B., and Gelfand, A. E. (2008). The nested Dirichlet process. J. Am. Stat. Assoc., 103, 1131–1154.
Tadesse, M. G., Sha, N., and Vannucci, M. (2005). Bayesian variable selection in clustering high-dimensional data. J. Am. Stat. Assoc., 100, 602–617.
The 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, 661–678.
Wakefield, J. (2007). A Bayesian measure of the probability of false discovery in genetic epidemiology studies. Am. J. Hum. Genet., 81, 208–227.
Wakefield, J. (2009). Bayes factors for genome-wide association studies: comparison with p-values. Genet. Epidemiol., 33, 79–86.
Wang, C., Ruggeri, F., Hsiao, C., and Argiento, R. (2014). Bayesian nonparametric clustering and association studies for large-scale SNP observations. Submitted.
Wei, Y. C., Wen, S. H., Chen, P. C., Wang, C. H., and Hsiao, C. K. (2010). A simple Bayesian mixture model with a hybrid procedure for genome-wide association studies. Eur. J. Hum. Genet., 18.8, 942–947.
Yau, C. and Holmes, C. (2011). Hierarchical Bayesian nonparametric mixture models for clustering with variable relevance determination. Bayesian Anal., 6, 329–351.
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Argiento, R., Guglielmi, A., Hsiao, C.K., Ruggeri, F., Wang, C. (2015). Modeling the Association Between Clusters of SNPs and Disease Responses. In: Mitra, R., MĂĽller, P. (eds) Nonparametric Bayesian Inference in Biostatistics. Frontiers in Probability and the Statistical Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-19518-6_6
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DOI: https://doi.org/10.1007/978-3-319-19518-6_6
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