Free Access
Math. Model. Nat. Phenom.
Volume 7, Number 3, 2012
Page(s) 227 - 252
Published online 06 June 2012
  1. A. Agresti, Exact inference for categorical data : Recent advances and continuing controversies, Statist. Med. 20 (2001), 2709–2722. [CrossRef] [Google Scholar]
  2. A. Agresti, Categorical data analysis, Wiley, 2002. [Google Scholar]
  3. H. Aurtrup, Genetic polymorphisms in human xenobiotica metabolizing enzymes as susceptibility factors in toxic response, Mutat Res 464 (2000), 65–76. [PubMed] [Google Scholar]
  4. N. Beerenwinkel, L. Pachter, B. Sturmfels, S.F. Elena, R.E. Lenski, Analysis of epistatic interactions and fitness landscapes using a new geometric approach., BMC Evol Biol. 13 (2007), 7 :60. [CrossRef] [Google Scholar]
  5. S.P. Cleary, M. Cotterchio, E. Shi, S. Gallinger, P. Harper, Cigarette smoking, genetic variants in carcinogen-metabolizing enzymes, and colorectal cancer risk, Am. J. Epidemiol. 172 (2010), no. 9, 1000–1014. [CrossRef] [PubMed] [Google Scholar]
  6. H.J. Cordell, Detecting gene-gene interactions that underlie human diseases, Nat Rev Genet, 10 (2009), 392–404. [CrossRef] [PubMed] [Google Scholar]
  7. D. Cox, J. Little, D. O’Shea, Ideals, varieties, and algorithms, Undergraduate Texts in Mathematics, vol. 60, Springer-Verlag, New York, 1992. [Google Scholar]
  8. A.C. Davison, D.V. Hinkley, Bootstrap methods and their applications, Cambridge University Press, Cambridge, 1997. [Google Scholar]
  9. P. Diaconis, B. Sturmfels, Algebraic algorithms for sampling from conditional distributions, Ann. Statist., 26 (1998), 363–397. [CrossRef] [MathSciNet] [Google Scholar]
  10. M. Drton, S. Sullivant, Algebraic statistical model, Statist. Sinica., 17 (2007), 1273–1297. [MathSciNet] [Google Scholar]
  11. F. Dudbridge, A. Gusnanto, B.P.C. Koeleman, Detecting multiple associations in genome-wide studies, Human Genomics, 2 (2006), 310–317. [PubMed] [Google Scholar]
  12. F. Dudbridge, B.P.C. Koeleman, Efficient computation of signifcance levels for multiple associations in large studies of correlated data, including genomewide association studies, Am. J. Hum. Genet, 75 (2004), 424–435. [CrossRef] [PubMed] [Google Scholar]
  13. E.S. Edgington, Randomization tests (3rd ed.), Marcel Dekker, New York, 1995. [Google Scholar]
  14. B. Efron, The jackknife, the bootstrap and other resampling plans, Society of Industrial and Applied Mathematics CBMS-NFS Monographs, vol. 38, Capital City Press, Philadelphia, 1982. [Google Scholar]
  15. L. Fan, J.O. Fuss, Q.J. Cheng, A.S. Arvai, M. Hammel, V.A. Roberts, P.K. Cooper, J.A. Tainer, XPD helicase structures and activities : insights into the cancer and aging phenotypes from xpd mutations., Cell, 133 (2008), 789–800. [CrossRef] [PubMed] [Google Scholar]
  16. C. Fassino, M.L. Torrente, Simple approximate varieties for sets of empirical points, Submitted. Available at [Google Scholar]
  17. I.O. Filiz, X. Guo, J. Morton, B. Sturmfels, Graphical models for correlated defaults, Available at, 2008. [Google Scholar]
  18. R.A. Fisher, The design of experiments, Oliver and Boyd, Edinburgh, 1935. [Google Scholar]
  19. W. Fulton, Introduction to toric varieties, Princeton University Press, 1993. [Google Scholar]
  20. P. Good, Resampling methods : A practical guide to data analysis (3rd edition), Birchäuser, Boston, 2006. [Google Scholar]
  21. H. Gorji, N Shahbazi, P. Habibollahi, S.M. Tavangar, A. Firooz, M.H. Ghahremani, The glutathione-S-transferase P1 polymorphisms correlates with changes in expression of TP53 tumor suppressor in cutaneous basal cell carcinoma, Dermatol Sci 56 (2009), 208–10. [Google Scholar]
  22. L.W. Hahn, M.D. Ritchie, J.H. Moore, Multifactor dimensionality reduction software for detecting gene-gene and gene-environment interactions, Bioinformatics, 19 (2003), 376–382. [CrossRef] [PubMed] [Google Scholar]
  23. I. Hallgrimsdottir, B Sturmfels, Resultants in genetic linkage analysis, Journal of Symbolic Computation, 41 (2006), 125–137. [CrossRef] [MathSciNet] [Google Scholar]
  24. D.Y. Lin, An efficient monte carlo approach to assessing statistical significance in genomic studies, Bioinformatics, 21 (2005), 781–787. [CrossRef] [PubMed] [Google Scholar]
  25. H.W. Lo, L. Stephenson, X. Cao, M. Milas, R. Pollock, F. Ali-Osman, Identification and functional characterization of the human glutathione S-transferaseP1 gene as a novel transcriptional target of the p53 tumor suppressor gene., Mol Cancer Res, 6 (2008), 843–50. [CrossRef] [PubMed] [Google Scholar]
  26. A.S. Malaspinas, C. Uhler, Detecting epistases via markov bases, Journal of Algebraic Statistics, 2 (2011), no. 1, 36–53. [Google Scholar]
  27. M. Manuguerra, G. Matullo, F. Veglia, H. Autrup, A.M. Dunning, S. Garte, E. Gormally, C. Malaveille, S. Guarrera, S. Polidoro, F. Saletta, M. Peluso, L. Airoldi, K. Overvad, O. Raaschou-Nielsen, F. Clavel-Chapelon, J. Linseisen, H. Boeing, D. Trichopoulos, A. Kalandidi, D. Palli, V. Krogh, R. Tumino, S. Panico, H.B. Bueno-De Mesquita, P.H. Peeters, E. Lund, G. Pera, C. Martinez, P. Amiano, A. Barricarte, M.J. Tormo, J.R. Quiros, G. Berglund, L. Janzon, B. Jarvholm, N.E. Day, N.E. Allen, R. Saracci, R. Kaaks, P. Ferrari, E. Riboli, P. Vineis, Multi-factor dimensionality reduction applied to a large prospective investigation on gene-gene and gene-environment interactions, Carcinogenesis, 28(2) (2007), 414–22. [CrossRef] [PubMed] [Google Scholar]
  28. T. Martone, P. Vineis, C. Malaveille, B. Terracini, Impact of polymorphisms in xeno(endo)biotic metabolism on pattern and frequency of p53 mutations in bladder cancer., Mutat Res, 462 (2000), 303–9. [CrossRef] [PubMed] [Google Scholar]
  29. G. Matullo, A.M. Dunning, S. Guarrera, C. Baynes, S. Polidoro, S. Garte, H. Autrup, C. Malaveille, M. Peluso, L. Airoldi, F. Veglia, E. Gormally, G. Hoek, M. Krzyzanowski, K. Overvad, O. Raaschou-Nielsen, F. Clavel-Chapelon, J. Linseisen, H. Boeing, A. Trichopoulou, D. Palli, V. Krogh, R. Tumino, S. Panico, H.B. Bueno-De Mesquita, P.H. Peeters, E. Lund, G. Pera, C. Martinez, M. Dorronsoro, A. Barricarte, M.J. Tormo, J.R. Quiros, N.E. Day, T.J. Key, R. Saracci, R. Kaaks, E. Riboli, P. Vineis, DNA repair polymorphisms and cancer risk in non-smokers in a cohort study, Carcinogenesis, 27(5) (2006), 997–1007. [CrossRef] [PubMed] [Google Scholar]
  30. Y. Meng, Q. Ma, Y. Yu, J. Farrell, L.A. Farrer, M.A. Wilcox, Multifactor-dimensionality reduction versus family-based association tests in detecting susceptibility loci in discordant sib-pair studies., BMC Genet, 30(6) (2005), S146. [CrossRef] [Google Scholar]
  31. J. Molitor, M. Papathomas, M Jerrett, and S. Richardson, Bayesian profile regression with an application to the national survey of children’s health., Biostatistics, 11 (2010), 484–498. [CrossRef] [PubMed] [Google Scholar]
  32. D.S. Moore, G. McCabe, W. Duckworth, S. Sclove, Chapter 18 :bootstrap methods and permutation tests, The Practice of Business Statistics, W.H. Freeman, New York, 2003. [Google Scholar]
  33. L. Pachter, B. Sturmfels, Parametric inference for biological sequence analysis, Proc Natl Acad Sci U S A, 101 (2004), 16138–43. [CrossRef] [PubMed] [Google Scholar]
  34. L. Pachter, B. Sturmfels, Tropical geometry of statistical models, Proc Natl Acad Sci U S A, 101 (2004), 16132–7. [CrossRef] [PubMed] [Google Scholar]
  35. M. Papathomas, J. Molitor, S. Richardson, E. Riboli, P. Vineis, Examining the joint effect of multiple risk factors using exposure risk profiles : lung cancer in nonsmokers, Environ. Health Perspect, 119 (2011), 84–91. [CrossRef] [PubMed] [Google Scholar]
  36. L. Patchter, B. Sturmfels, Algebraic statistics for computational biology, Cambridge University Press, 2005. [Google Scholar]
  37. M. Peluso, P. Hainaut, L. Airoldi, H. Autrup, A. Dunning, S. Garte, E. Gormally, C. Malaveille, G. Matullo, A. Munnia, E. Riboli, P. Vineis, Methodology of laboratory measurements in prospective studies on gene-environment interactions : the experience of GenAir, Mutat Res, 574 (2005), 92–104. [CrossRef] [PubMed] [Google Scholar]
  38. G. Pistone, E. Riccomagno, and H.P. Wynn, Algebraic statistics, Chapman and Hall/CRC, Boca Raton, 2001. [Google Scholar]
  39. F. Rapallo, Algebraic Markov bases and MCMC for two-way contingency tables, Scandinavian Journal of Statistics, 30 (2003), 385–397. [CrossRef] [MathSciNet] [Google Scholar]
  40. F. Rapallo, Algebraic exact inference for rater agreement models, Statistical Methods & Applications, 14 (2005), 45–66. [CrossRef] [Google Scholar]
  41. E. Riboli, The european prospective investigation into cancer and nutrition (EPIC) : plans and progress., J. Nutr., 131 (2001), no. 1, 170–175. [Google Scholar]
  42. T.K. Rice, N.J. Schork, D.C. Rao, Methods for handling multiple testing, Advances in Genetics, 60 (2008), 293–308. [CrossRef] [PubMed] [Google Scholar]
  43. M.D. Ritchie, L.W. Hahn, N. Roodi, L.R. Bailey, W.D. Dupont, F.F. Parl, J.H. Moore, Multifactor-dimensionality reduction reveals high-order interactions among estrogen-metabolism genes in sporadic breast cancer, Am. J. Hum. Genet., 69 (2001), no. 1, 138–47. [CrossRef] [PubMed] [Google Scholar]
  44. J.L. Simon, Resampling : The new statistics (2nd edition),, 1997. [Google Scholar]
  45. B. Sturmfels, Gröbner bases and convex polytopes, American Mathematical Society, 1996. [Google Scholar]
  46. B. Sturmfels, Solving systems of polynomial equations, American Mathematical Society, 2002. [Google Scholar]
  47. B. Sturmfels, Algebra and geometry of statistical models, Tech. report, John von Neumann Lectures, TU München, 2003. [Google Scholar]
  48. B. Sturmfels, S. Sullivant, Toric ideals of phylogenetic invariants, J Comput Biol, 12 (2005), 204–228. [CrossRef] [PubMed] [Google Scholar]
  49. P. Vineis, L. Airoldi, F. Veglia, L. Olgiati, R. Pastorelli, H. Autrup, A. Dunning, S. Garte, E. Gormally, P. Hainaut, C. Malaveille, G. Matullo, M. Peluso, K. Overvad, A. Tjonneland, F. Clavel-Chapelon, H. Boeing, V. Krogh, D. Palli, S. Panico, R. Tumino, B. Bueno-De Mesquita, P. Peeters, G. Berglund, G. Hallmans, R. Saracci, E. Riboli, Environmental tobacco smoke and risk of respiratory cancer and chronic obstructive pulmonary disease in former smokers and never smokers in the EPIC prospective study., BMJ 330 (2005), 277. [CrossRef] [PubMed] [Google Scholar]
  50. S. Wang, W. Xiong, W. Ma, S. Chanock, W. Jedrychowski, R. Wu, F.P. Perera, Gene-environment interactions on growth trajectories, Genetic Epidemiology (2012), doi : 10.1002/gepi.21613. [Google Scholar]
  51. R.D. Wood, Mammalian nucleotide excision repair proteins and interstrand crosslink repair, Environ Mol Mutagen, 51 (2010), 520–6. [PubMed] [Google Scholar]
  52. Y. Zhang, J.S. Liu, Bayesian inference of epistatic interactions in case-control studies., Nature Genet, 39 (2007), 1167–1173. [CrossRef] [Google Scholar]
  53. Y. Zhang, L.H. Rohde, H. Wu, Involvement of nucleotide excision and mismatch repair mechanisms in double strand break repair, Curr Genomics, 10 (2009), 250–8. [CrossRef] [PubMed] [Google Scholar]

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