Abstract
When assessing the combined action of genes on the quantitative or qualitative phenotype we encounter a phenomenon that could be named the “paradox of the risk score summation.” It arises when the search of risk allele and assessment of their combined action are performed with the same single dataset. Too often such methodological error occurs when calculating the so called genetic risk score (GRS), which refers to the total number of alleles associated with the disease. Examples from numerous published genetic association studies are considered in which the claimed statistically significant effects can be attributed to the “risk score summation paradox.” In the second section of the review we discuss the current modifications of multiple regression analysis addressed to the so called “n ≪ p problem” (the number of points is much smaller than the number of possible predictors). Various algorithms for the model selection (searching the significant predictor combinations) are considered, beginning from the common marginal screening of the “top” predictors to LASSO and other modern algorithms of compressed sensing.
Similar content being viewed by others
References
Freedman, D.A., A note on screening regression equations, Am. Stat., 1983, vol. 37, no. 2, pp. 152–155.
Lukacs, P.M., Burnham, K.P., and Anderson, D.R., Model selection bias and Freedman’s paradox, Ann. Inst. Stat. Math., 2010, vol. 62, no. 1, pp. 117–125. doi 10.1007/s10463-009-0234-4
Wray, N.R., Yang, J., Hayes, B.J., et al., Pitfalls of predicting complex traits from SNPs, Nat. Rev. Genet., 2013, vol. 14, no. 7, pp. 507–515. doi 10.1038/nrg3457.5
Vral, A., Willems, P., Claes, K., et al., Combined effect of polymorphisms in Rad51 and Xrcc3 on breast cancer risk and chromosomal radiosensitivity, Mol. Med. Rep., 2011, vol. 4, no. 5, pp. 901–912. doi 10.3892/mmr.2011.523
Nagaraja, H.N., Some nondegenerate limit laws for the selection differential, Ann. Stat., 1982, vol. 10, no. 4, pp. 1306–1310.
Yiannakouris, N., Trichopoulou, A., Benetou, V., et al., A direct assessment of genetic contribution to the incidence of coronary infarct in the general population Greek EPIC cohort, Eur. J. Epidemiol., 2006, vol. 21, pp. 859–867. doi 10.1007/s10654-006-9070-5
Joubert, B.R., Reif, D.M., Edwards, S.W., et al., Evaluation of genetic susceptibility to childhood allergy and asthma in an African American urban population, BMC Med. Genet., 2011, vol. 12, no. 25, pp. 1–11. doi 10.1186/1471-2350-12-25
Lluís-Ganella, C., Lucas, G., Subirana, I. et al., Additive effects of multiple genetic variants on the risk of coronary artery disease, Rev. Esp. Cardiol., 2010, vol. 63, no. 8, pp. 925–933. doi 10.1016/S1885-5857(10)70186-9
Hu, P., Muise, A.M., Xing, X.J., et al., Association between a multi-locus genetic risk score and inflammatory bowel disease, Bioinf. Biol. Insights, 2013, vol. 7, pp. 143–152. doi 10.4137/BBI.S11601
Ribeiro, R.J., Monteiro, C.P., Azevedo, A.S., et al., Performance of an adipokine pathway-based multilocus genetic risk score for prostate cancer risk prediction, PLoS One, 2012, vol. 7, no. 6. e39236. doi 10.1371/journalpone.0039236
Smailhodzic, D., Muether, P.S., Chen, J., et al., Cumulative effect of risk alleles in CFH, ARMS2, and VEGFA on the response to ranibizumab treatment in age-related macular degeneration, Ophthalmology, 2012, vol. 119, no. 11, pp. 2304–2311. doi 10.1016/jophtha.2012.05.040
Lång, A., Wegman, P., and Wingren, S., The significance of MDM2 SNP309 and p53 Arg72Pro in young women with breast cancer, Oncol. Rep., 2009, vol. 22, no. 3, pp. 575–579. doi 10.3892/or_00000474
Moumad, K., Lascorz, J., Bevier, M., et al., Genetic polymorphisms in host innate immune sensor genes and the risk of nasopharyngeal narcinoma in North Africa, G3 (Bethesda), 2013, vol. 3, no. 6, pp. 971–977. doi 10.1534/g3.112.005371
Signorello, L.B., Shi, J., Cai, Q., et al., Common variation in vitamin D pathway genes predicts circulating 25-hydroxyvitamin D levels among African Americans, PLoS One, 2011, vol. 6, no. 12, doi 10.1371/journal. pone.0028623
Lu M., Liu, Z., Yu, H., et al., Combined effects of E2F1 and E2F2 polymorphisms on risk and early onset of squamous cell carcinoma of the head and neck, Mol. Carcinog., 2012, vol. 51, suppl. 1, pp. E132–E141. doi 10.1002/mc.2188210.1002/mc.21882
Petukhova, L., Duvic, M., Hordinsky, M., et al., Genome-wide association study in alopecia areata implicates both innate and adaptive immunity, Nature, 2010, vol. 466, pp. 113–117. doi 10.1038/nature09114
Skol, A.D., Scott, L.J., Abecasis, G.R., and Boehnke, M., Joint analysis is more efficient than replication-based analysis for two-stage genome-wide association studies, Nat. Genet., 2006, vol. 38, no. 2, pp. 209–213. doi 10.1038/ng1706
Rubanovich, A.V. and Khromov-Borisov, N.N., Theoretical analysis of the predictability indices of the binary genetic tests, Ekol. Genet., 2013, vol. 11, no. 1, pp. 77–90. doi 10.1134/S2079059714020087
Rencher, A.C. and Pun, F.C., Inflation of R2 in best subset regression, Technometrics, 1980, vol. 22, no. 1, pp. 49–53. doi 10.2307/1268382
Foster, D.P. and Stine, R.A., Honest confidence intervals for the error variance in stepwise regression, J. Econ. Soc. Meas., 2006, vol. 31, nos. 1, 2, pp. 89–102.
Segal, M.R., Dahlquist, K.D., and Conklin, B.R., Regression approaches for microarray data analysis, J. Comput. Biol., 2003, vol. 10, no. 6, pp. 961–980. doi 10.1089/106652703322756177
Loh, W., Variable selection for classification and regression in large p, small n problems, Probab. Approximations Beyond, Ser. Lect. Notes Stat., 2011, vol. 205, pp. 135–159. doi 10.1007/978-1-4614-1966-2_10
Hastie, T. and Tibshirani, R., Expression arrays and the problem, 2003. https://webstanfordedu/ ~hastie/Papers/pgtnpdf
Genovese, C.R., Jin, J., and Wasserman, L., Revisiting marginal regression, arXiv:0911.4080v1 [math.ST] 20 Nov 2009. p @ n
Genovese, C.R., Jin, J., Wasserman, L., and Yao, Z., A comparison of the lasso and marginal regression, J. Mach. Learn. Res., 2012, vol. 13, no. 1, pp. 2107–2143.
Whittingham, M.J., Stephens, P.A., Bradbury, R.B., and Freckleton, R.P., Why do we still use stepwise modelling in ecology and behaviour?, J. Anim. Ecol., 2006, vol. 75, no. 5, pp. 1182–1189. doi 10.1111/j.1365-2656.2006.01141x
Fan, J. and Lv, J., Sure independence screening for ultrahigh dimensional feature space, J. R. Stat. Soc., Ser. B Stat. Methodol., 2008, vol. 70, no. 5, pp. 849–911.
Tibshirani, R., Regression shrinkage and selection via the lasso, J. R. Stat. Soc., Ser. B Stat. Methodol., 1996, vol. 58, no. 1, pp. 267–288.
Friedman, J.H., Hastie, T., and Tibshirani, R., Regularization paths for generalized linear models via coordinate descent, J. Statist. Softw., 2009, vol. 33, no. 1. doi 10.18637/jssv033i01
Wainwright, M.J., Information-theoretic limits on sparsity recovery in the high-dimensional and noisy setting, IEEE Trans. Inf. Theory, 2009, vol. 55, no. 12. doi 10.1109/TIT.2009.2032816
Donoho, D. and Stodden, V., Breakdown point of model selection when the number of variables exceeds the number of observations, Proceedings of International Joint Conference on Neural Networks, Vancouver, 2006, pp. 1916–1921. doi 10.1109/IJCNN.2006.246934
Wimmer, V., Lehermeier, C., Albrecht, T., et al., Genetic architecture through efficient variable selection, Genetics, 2013, vol. 195, no. 2, pp. 573–587. doi 10.1534/genetics.113.150078/-/DC1
Goeman, J.J., L1 penalized estimation in the Cox proportional hazards model, Biom. J., 2010, vol. 52, no. 1, pp. 70–84. doi 10.1002/bimj.200900028
Lange, K., Papp, J.C., Sinsheimer, J.S., and Sobel, E.M., Next-generation statistical genetics: modeling, penalization, and optimization in high-dimensional data, Annu. Rev. Stat. Appl., 2014, vol. 1, pp. 279–300. doi 10.1146/annurev-statistics-022513-115638
Buhlmann, P., Kalisch, M., and Meier, L., Highdimensional statistics with a view toward applications in biology, Annu. Rev. Stat. Appl., 2014, vol. 1, pp. 255–278. doi 10.1146/annurev-statistics-022513-115545
Wu, T.T., Chen, Y.F., Hastie, T., et al., Genome-wide association analysis by lasso penalized logistic regression, Bioinformatics, 2009, vol. 25, no. 6, pp. 714–721. doi 10.1093/bioinformatics/btp041
Usai, M.G., Goddard, M.E., and Hayes, B.J., LASSO with cross-validation for genomic selection, Genet. Res. (Camb.), 2009, vol. 91, no. 6, pp. 427–436. doi doi 10.1017/S0016672309990334
Friedman, J.H., Hastie, T., Simon, N., and Tibshirani, R., Package ‘glmnet,’ 2015. https://cranr-projectorg/web/packages/glmnet
Goeman, J., Meijer, R., and Chaturvedi, N., Package ‘penalized’, 2015. https://cranr-projectorg/web/packages/penalized/
Efron, B., Hastie, T., Johnstone, I., and Tibshirani, R., Least angle regression, Ann. Stat., 2004, vol. 32, no. 2, pp. 407–499. doi 10.1214/009053604000000067
Lockhart, R., Taylor, J., Tibshirani, R.J., and Tibshirani, R., A significance test for the lasso, Ann. Statist., 2014, vol. 42, no. 2, pp. 413–468. doi 10.1214/13-AOS1175
Foucart, S. and Rauhut, H., A Mathematical Introduction to Compressive Sensing, Basel: Birkhäuser, 2013. doi 10.1007/978-0-8176-4948-7
Candes, E. and Tao, T., The Dantzig selector: statistical estimation when p is much larger than n, Ann. Stat., 2007, vol. 35, no. 6, pp. 2313–2351. doi 10.1214/009053606000001523
Ho, C.M. and Hsua, S.D., Determination of nonlinear genetic architecture using compressed sensing. arXiv:1408.6583v1 [q-bio.GN]. 19 Jul 2015.
Vattikuti, S., Lee, J.J., Chang, C.C., et al., Applying compressed sensing to genome-wide association studies. GigaScience, 2014, vol. 3, no. 10, paper 3.
Boulesteix, A.L. and Strimmer, K. Partial least squares: a versatile tool for the analysis of high-dimensional genomic data, Brief Bioinf., 2007, vol. 8, no. 1, pp. 32–44. doi 10.1093/bib/bbl016
Huang, C.C., Tu, S.H., Huang, C.S., et al., Multiclass prediction with partial least square regression for gene expression data: applications in breast cancer intrinsic taxonomy, Biomed. Res. Int., 2013. Article ID248648. doi 10.1155/2013/248648
Feng, Z.Z., Yang, X., Subedi, S., and McNicholas, P.D., The LASSO and sparse least square regression methods for SNP selection in predicting quantitative traits, IEEE/ACM Trans Comput. Biol. Bioinf., 2012, vol. 9, no. 2, pp. 629–636. doi 10.1109/TCBB.2011.139
Yang, J., Benyamin, B., McEvoy, B.P., et al., Common SNPs explain a large proportion of the heritability for human height, Nat. Genet., 2010, vol. 42, no. 7, pp. 565–569. doi 10.1038/ng.608
Yang, J., Lee, S.H., Goddard, M.E., and Visscher, P.M., GCTA: a tool for genome-wide complex trait analysis, Am. J. Hum. Genet., 2011, vol. 88, no. 1, pp. 76–82. doi 10.1016/jajhg.2010.11.011
Lee, S.H., Wray, N.R., Goddard, M.E., and Visscher, P.M., Estimating missing heritability for disease from genome-wide association studies, Am. J. Hum. Genet., 2011, vol. 88, no. 3, pp. 294–305. doi 10.1016/jajhg.2011.02.002
Yang, J., Zaitlen, N.A., Goddard, M.E., et al., Mixed model association methods: advantages and pitfalls, Nat. Genet., 2014, vol. 46, no. 2, pp. 100–106. doi 10.1038/ng.2876
Charney, E., Still chasing hosts: a new genetic methodology will not find the “missing heritability,” Indep. Sci. News, 2013, 19 September.
Kumar, K.S., Feldman, M.W., Rehkopf, D.H., and Tuljapurkar, S., Limitations of GCTA as a solution to the missing heritability problem, Proc. Natl. Acad. Sci. U.S.A., 2016, vol. 113, no. 1, pp. E61–E70. doi 10.1073/pnas.1520109113
Yang, J., Lee, S.H., Wray, N.R., et al., Commentary on “Limitations of GCTA as a solution to the missing heritability problem,” bioRxiv 036574. Jan 20 2016. http://dxdoiorg/10.1101/036574
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.V. Rubanovich, N.N. Khromov-Borisov, 2016, published in Genetika, 2016, Vol. 52, No. 7, pp. 865–878.
Rights and permissions
About this article
Cite this article
Rubanovich, A.V., Khromov-Borisov, N.N. Genetic risk assessment of the joint effect of several genes: Critical appraisal. Russ J Genet 52, 757–769 (2016). https://doi.org/10.1134/S1022795416070073
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1022795416070073