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Statistical analysis of genetic interactions

  • NENGJUN YI (a1)

Summary

Many common human diseases and complex traits are highly heritable and influenced by multiple genetic and environmental factors. Although genome-wide association studies (GWAS) have successfully identified many disease-associated variants, these genetic variants explain only a small proportion of the heritability of most complex diseases. Genetic interactions (gene–gene and gene–environment) substantially contribute to complex traits and diseases and could be one of the main sources of the missing heritability. This paper provides an overview of the available statistical methods and related computer software for identifying genetic interactions in animal and plant experimental crosses and human genetic association studies. The main discussion falls under the three broad issues in statistical analysis of genetic interactions: the definition, detection and interpretation of genetic interactions. Recently developed methods based on modern techniques for high-dimensional data are reviewed, including penalized likelihood approaches and hierarchical models; the relationships between these methods are also discussed. I conclude this review by highlighting some areas of future research.

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Corresponding author

*Corresponding author: Department of Biostatistics, The University of Alabama at Birmingham, Birmingham, AL 35294-0022, USA. Tel.: +1 205-934-4924. Fax: +1 205-975-2540. e-mail: TUnyi@ms.soph.uab.eduUT

References

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Ahituv, N., Kavaslar, N., Schackwitz, W., Ustaszewska, A., Martin, J., Hebert, S., Doelle, H., Ersoy, B., Kryukov, G., Schmidt, S., Yosef, N., Ruppin, E., Sharan, R., Vaisse, C., Sunyaev, S., Dent, R., Cohen, J., McPherson, R. & Pennacchio, L. A. (2007). Medical sequencing at the extremes of human body mass. American Journal of Human Genetics 80, 779791.
Akaike, H. (1969). Fitting autoregressive models for prediction. Annals of the Institute of Statistical Mathematics 21, 243247.
Armagan, A. & Zaretzki, R. L. (2010). Model selection via adaptive shrinkage with t priors. Computational Statistics 25, 441461.
Azzopardi, D., Dallosso, A. R., Eliason, K., Hendrickson, B. C., Jones, N., Rawstorne, E., et al. (2008). Multiple rare nonsynonymous variants in the adenomatous polyposis coli gene predispose to colorectal adenomas. Cancer Research 68, 358363.
Bae, K. & Mallick, B. (2004). Gene selection using a two-level hierarchical Bayesian model. Bioinformatics 20, 34233430.
Baierl, A., Bogdan, M., Frommlet, F. & Futschik, A. (2006). On locating multiple interacting quantitative trait loci in intercross designs. Genetics 173, 16931703.
Berrington, A. & Cox, D. R. (2007). Interpretation of interaction: a review. Annals of Applied Statistics 1, 371385.
Bjørnvold, M., Undlien, D. E., Joner, G., Dahl-Jørgensen, K., Njølstad, P. R., Akselsen, H. E., Gervin, K., Rønningen, K. S. & Stene, L. C. (2008). Joint effects of HLA, INS, PTPN22 and CTLA4 genes on the risk of type 1 diabetes. Diabetologia 51, 589596.
Bodmer, W. & Bonilla, C. (2008). Common and rare variants in multifactorial susceptibility to common diseases. Nature Genetics 40, 695701.
Bogdan, M., Ghosh, J. & Doerge, R. (2004). Modifying the Schwarz Bayesian information criterion to locate multiple interacting quantitative trait loci. Genetics 167, 989999.
Box, G. E. P. & Cox, D. R. (1964). An analysis of transformations (with discussion). Journal of Royal Statistical Society B 26, 211252.
Broman, K., Wu, H., Sen, S. & Churchill, G. (2003). R/qtl: QTL mapping in experimental crosses. Bioinformatics 19, 889890.
Broman, K. W. & Speed, T. P. (2002). A model selection approach for the identification of quantitative trait loci in experimental crosses. Journal of the Royal Statistical Society B 64, 641656.
Cantor, R., Lange, K. & Sinsheimer, J. (2010). Prioritizing GWAS results: a review of statistical methods and recommendations for their application. American Journal of Human Genetics 86, 6–22.
Carlborg, O. & Haley, C. (2004). Epistasis: too often neglected in complex trait studies? Nature Reviews Genetics 5, 618625.
Chen, X., Liu, C., Zhang, M. & Zhang, H. (2007). A forest-based approach to identifying gene and gene gene interactions. Proceedings of the National Academy of Sciences of the USA 104, 1919919203.
Chipman, H. (1996). Bayesian variable selection with related predictors. Canadian Journal of Statistics 24, 1736.
Choi, N. H., Li, W. & Zhu, J. (2010). Variable selection with the strong heredity constraint and its oracle property. Journal of the American Statistical Association 105, 354364.
Cirulli, E. T. & Goldstein, D. B. (2010). Uncovering the roles of rare variants in common disease through whole-genome sequencing. Nature Reviews Genetics 11, 415425.
Clark, A. G. (2000). Limits to prediction of phenotype from knowledge of genotypes. In Limits to Knowledge in Evolutionary Genetics (ed, Clegg, M.), pp. 205224. New York: Kluwer Academic/Plenum Publishers.
Clayton, D. (2009). Prediction and interaction in complex disease genetics: experience in type 1 diabetes. PLoS Genetics 5, e1000540.
Cohen, J. C., Boerwinkle, E., Mosley, T. H. Jr & Hobbs, H. H. (2006). Sequence variations in PCSK9, low LDL, and protection against coronary heart disease. New England Journal of Medicine 354, 12641272.
Cohen, J. C., Kiss, R. S., Pertsemlidis, A., Marcel, Y. L., McPherson, R. & Hobbs, H. H. (2004). Multiple rare alleles contribute to low plasma levels of HDL cholesterol. Science 305, 869872.
Cordell, H. (2002). Epistasis: what it means, what it doesn't mean, and statistical methods to detect it in humans. Human Molecular Genetics 11, 24632468.
Cordell, H. (2009). Detecting gene-gene interactions that underlie human diseases. Nature Reviews Genetics 10, 392404.
Cox, D. R. (1984). Interaction. International Statistical Review 52, 131.
de los Campos, G., Naya, H., Gianola, D., Crossa, J., Legarra, A., Manfredi, E., Weigel, K. & Cotes, J. M. (2009). Predicting quantitative traits with regression models for dense molecular markers and pedigree. Genetics 182, 375385.
Dunson, D. B., Herring, A. H. & Engle, S. M. (2008). Bayesian selection and clustering of polymorphisms in functionally related genes. Journal of the American Statistical Association 103, 534546.
Efron, B., Hastie, T., Johnstone, I. & Tibshirani, R. (2004). Least angle regression. Annals of Statistics 32, 407451.
Eichler, E. E., Flint, J., Gibson, G., Kong, A., Leal, S. M., Moore, J. H. & Nadeau, J. H. (2010). Missing heritability and strategies for finding the underlying causes of complex disease. Nature Reviews Genetics 11, 446450.
Figueiredo, M. A. T. (2003). Adaptive sparseness for supervised learning. IEEE Transactions on Pattern Analysis and Machine Intelligence 25, 11501159.
Flint, J. & Mackay, T. (2009). Genetic architecture of quantitative traits in mice, flies, and humans. Genome Research 19, 723733.
Friedman, J., Hastie, T. & Tibshirani, R. (2010). Regularization paths for generalized linear models via coordinate descent. Journal of Statistical Software 33, 122.
Gelman, A., Carlin, J., Stern, H. & Rubin, D. (2003). Bayesian Data Analysis. London: Chapman and Hall.
Gelman, A. & Hill, J. (2007). Data Analysis Using Regression and Multilevel/Hierarchical Models. New York: Cambridge University Press.
Gelman, A., Jakulin, A., Pittau, M. G. & Su, Y. S. (2008). A weakly informative default prior distribution for logistic and other regression models. Annals of Applied Statistics 2, 13601383.
Genkin, A., Lewis, D. D. & Madigan, D. (2007). Large-scale Bayesian logistic regression for text categorization. Technometrics 49, 291304.
Gill, J. (2001). Interpreting interactions and interaction hierarchies in generalized linear models: issues and applications. Presented at the Annual Meeting of the American Political Science Association, San Francisco.
Green, M. J., Medley, G. F. & Browne, W. J. (2009) Use of posterior predictive assessments to evaluate model fit in multilevel logistic regression. Veterinary Research 40, 3040.
Griffin, J. E. & Brown, P. J. (2007). Bayesian adaptive lassos with non-convex penalization. Technical Report, IMSAS, University of Kent.
Hamada, M. & Wu, C. (1992). Analysis of designed experiments with complex aliasing. Journal of Quality Technology 24, 130137.
Hans, C. (2009). Bayesian lasso regression. Biometrika 96, 835845.
Hardy, J. & Singleton, A. (2009). Genomewide association studies and human disease. New England Journal of Medicine 360, 17591768.
Hayashi, T. & Iwata, H. (2010). EM algorithm for Bayesian estimation of genomic breeding values. BMC Genetics 11, 3.
Hesterberg, T., Choi, N. H., Meier, L. & Fraley, C. (2008). Least angle and L1 penalized regression: a review. Statistics Surveys 2, 6193.
Hindorff, L., Sethupathy, P., Junkins, H., Ramos, E., Mehta, J., Collins, F. & Manolio, T. A. (2009). Potential etiologic and functional implications of genome-wide association loci for human diseases and traits. Proceedings of the National Academy of Sciences of the USA 106, 93629367.
Hoerl, A. E. & Kennard, R. (1970). Ridge regression: biased estimation for nonorthogonal problems. Technometrics 12, 5567.
Hoggart, C., Whittaker, J., De Iorio, M. & Balding, D. (2008). Simultaneous analysis of all SNPs in genome-wide and re-sequencing association studies. PLoS Genetics 4, e1000130.
Hung, R., Brennan, P., Malaveille, C., Porru, S., Donato, F., Boffetta, P. & Witte, J. S. (2004). Using hierarchical modeling in genetic association studies with multiple markers: application to a case-control study of bladder cancer. Cancer Epidemiology and Biomarkers Prevention 13, 10131021.
Jakobsdottir, J., Gorin, M., Conley, Y., Ferrell, R. & Weeks, D. (2009). Interpretation of genetic association studies: markers with replicated highly significant odds ratios may be poor classifiers. PLoS Genetics 5, e1000337.
Ji, W., Foo, J. N., O'Roak, B. J., Zhao, H., Larson, M. G., Simon, D. B., Newton-Cheh, C., State, M. W., Levy, D. & Lifton, R. P. (2008). Rare independent mutations in renal salt handling genes contribute to blood pressure variation. Nature Genetics 40, 592599.
Kao, C. & Zeng, Z. (2002). Modeling epistasis of quantitative trait loci using Cockerham's model. Genetics 160, 12431261.
Kao, C., Zeng, Z. & Teasdale, R. (1999). Multiple interval mapping for quantitative trait loci. Genetics 152, 12031216.
Kooperberg, C., Leblanc, M., Dai, J. & Rajapakse, I. (2009). Structures and assumptions: strategies to harness gene×gene and gene×environment interactions in GWAS. Statistical Science 24, 472488.
Kraft, P. & Hunter, D. (2009). Genetic risk prediction - are we there yet? New England Journal of Medicine 360, 17011703.
Kraft, P., Wacholder, S., Cornelis, M. C., Hu, F. B., Hayes, R. B., Thomas, G., Hoover, R., Hunter, D. J. & Chanock, S. (2009). Beyond odds ratios - communicating disease risk based on genetic profiles. Nature Reviews Genetics 10, 264269.
Kyung, M., Gill, J., Ghosh, M. & Casella, G. (2010). Penalized regression, standard errors, and Bayesian lassos. Bayesian Analysis 5, 369412.
Lee, S., van der Werf, J., Hayes, B., Goddard, M. & Visscher, P. (2008). Predicting unobserved phenotypes for complex traits from whole-genome SNP data. PLoS Genetics 4, e1000231.
Li, B. & Leal, S. M. (2008). Methods for detecting associations with rare variants for common diseases: application to analysis of sequence data. American Journal of Human Genetics 83, 311321.
Li, J., Reynolds, R., Pomp, D., Allison, D. & Yi, N. (2010). Mapping interacting QTL for count phenotypes using hierarchical Poisson and binomial models: an application to reproductive traits in mice. Genetical Research 92, 1323.
Lou, X. Y., Chen, G. B., Yan, L., Ma, J. Z., Zhu, J., Elston, R. C. and Li, M. D. (2007). A generalized combinatorial approach for detecting gene-by-gene and gene-by-environment interactions with application to nicotine dependence. American Journal of Human Genetics 80, 11251137.
Lynch, M. & Walsh, B. (1998). Genetics and Analysis of Quantitative Traits. Sunderland, MA: Sinauer Associates Inc.
Mackay, T. (2001). The genetic architecture of quantitative traits. Annual Review of Genetics 35, 303339.
Mackay, T., Stone, E. & Ayroles, J. (2009). The genetics of quantitative traits: challenges and prospects. Nature Reviews Genetics 10, 565577.
Madsen, B. E. & Browning, S. R. (2009). A groupwise association test for rare mutations using a weighted sum statistic. PLoS Genetics 5, e1000384.
Malo, N., Libiger, O. & Schork, N. (2008). Accommodating linkage disequilibrium in genetic-association analyses via ridge regression. American Journal of Human Genetics 82, 375385.
Manichaikul, A., Moon, J., Sen, S., Yandell, B. & Broman, K. (2009). A model selection approach for the identification of quantitative trait loci in experimental crosses, allowing epistasis. Genetics 181, 10771086.
Manolio, T. A., Collins, F. S., Cox, N. J., Goldstein, D. B., Hindorff, L. A., Hunter, D. J., McCarthy, M. I., Ramos, E. M., Cardon, L. R., Chakravarthi, A., Cho, J. H., Guttmacher, A. E., Kong, A., Kruglyak, L., Mardis, E., Rotimi, C. N., Slatkin, M., Valle, D., Whittemore, A. S., Boehnke, M., Clark, A. G., Eichler, E. E., Gibson, G., Haines, J. L., Mackay, T. F., McCarroll, S. A. & Visscher, P. M. (2009). Finding the missing heritability of complex diseases. Nature 461, 747753.
Marchini, J., Donnelly, P. & Cardon, L. (2005). Genome-wide strategies for detecting multiple loci that influence complex diseases. Nature Genetics 37, 413417.
McCullagh, P. & Nelder, J. A. (1989). Generalized Linear Models. London: Chapman and Hall.
Meuwissen, T. H. E., Hayes, B. J. & Goddard, M. E. (2001). Prediction of total genetic value using genome-wide dense marker maps. Genetics 157, 18191829.
Moore, J. (2003). The ubiquitous nature of epistasis in determining susceptibility to common human diseases. Human Heredity 56, 7382.
Moore, J. & Williams, S. (2009). Epistasis and its implications for personal genetics. American Journal of Human Genetics 85, 309320.
Morris, A. P. & Zeggini, E. (2010). An evaluation of statistical approaches to rare variant analysis in genetic association studies. Genetic Epidemiology 34, 188193.
Musani, S. K., Shriner, D., Liu, N., Feng, R., Coffey, C. S., Yi, N., Tiwari, H. K. and Allison, D. B. (2007). Detection of gene×gene interactions in genome-wide association studies of human population data. Human Heredity 63, 6784.
Mutshinda, C. & Sillanpää, M. (2010). Extended Bayesian LASSO for multiple quantitative trait loci mapping and unobserved phenotype prediction. Genetics 186, 10671075.
Nejentsev, S., Walker, N., Riches, D., Egholm, M. & Todd, J. A. (2009). Rare variants of IFIH1, a gene implicated in antiviral responses, protect against type 1 diabetes. Science 324, 387389.
Nelder, J. (1994). The statistics of linear models: back to basics. Statistics and Computing 4, 221234.
Park, M. & Hastie, T. (2008). Penalized logistic regression for detecting gene interactions. Biostatistics 9, 3050.
Park, T. & Casella, G. (2008). The Bayesian Lasso. Journal of the American Statistical Association 103, 681686.
Phillips, P. (2008). Epistasis - the essential role of gene interactions in the structure and evolution of genetic systems. Nature Reviews Genetics 9, 855867.
Price, A. L., Kryukov, G. V., de Bakker, P. I., Purcell, S. M., Staples, J., Wei, L. J. & Sunyaev, S. R. (2010). Pooled association tests for rare variants in exon-resequencing studies. American Journal of Human Genetics 86, 832838.
Rebbeck, T., Spitz, M. & Wu, X. (2004). Assessing the function of genetic variants in candidate gene association studies. Nature Reviews Genetics 5, 589597.
Ritchie, M. D., Hahn, L. W., Roodi, N., Bailey, L. R., Dupont, W. D., Parl, F. F. & Moore, J. H. (2001). Multifactor-dimensionality reduction reveals high-order interactions among estrogen-metabolism genes in sporadic breast cancer. American Journal of Human Genetics 69, 138147.
Romeo, S., Pennacchio, L. A., Fu, Y., Boerwinkle, E., Tybjaerg-Hansen, A., Hobbs, H. H. & Cohen, J. C. (2007). Population-based resequencing of ANGPTL4 uncovers variations that reduce triglycerides and increase HDL. Nature Genetics 39, 513516.
Romeo, S., Yin, W., Kozlitina, J., Pennacchio, L. A., Boerwinkle, E., Hobbs, H. H. & Cohen, J. C. (2009). Rare loss-of-function mutations in ANGPTL family members contribute to plasma triglyceride levels in humans. Journal of Clinical Investigation 119, 7079.
Schork, N. J., Murray, S. S., Frazer, K. A. & Topol, E. J. (2009). Common vs. rare allele hypotheses for complex diseases. Current Opinion in Genetics and Development 19, 212219.
Schwartz, G. (1978). Estimating the dimension of a model. Annals of Statistics 6, 461464.
Spiegelhalter, D. J., Best, N. G., Carlin, B. P., & van der Linde, A. (2002). Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society B 64, 583616.
Sun, W., Ibrahim, J. & Zou, F. (2010). Genomewide multiple-loci mapping in experimental crosses by iterative adaptive penalized regression. Genetics 185, 349359.
Tanck, M., Jukema, J. & Zwinderman, A. (2006). Simultaneous estimation of gene-gene and gene-environment interactions for numerous loci using double penalized log-likelihood. Genetic Epidemiology 30, 645651.
Thomas, D. (2004). Statistical Methods in Genetic Epidemiology. Oxford: Oxford University Press.
Thomas, D. (2010). Gene-environment-wide association studies: emerging approaches. Nature Reviews Genetics 11, 259272.
Thomas, D. C., Conti, D. V., Baurley, J., Nijhout, F., Reed, M. & Ulrich, C. M. (2009). Use of pathway information in molecular epidemiology. Human Genomics 4, 2142.
Tibshirani, R. (1996). Regression shrinkage and selection via the Lasso. Journal of the Royal Statistical Society B 58, 267288.
VanderWeele, T. (2010). Epistatic interactions. Statistical Applications in Genetics and Molecular Biology 9, Article 1. DOI: 10.2202/1544-6115.1517.
Vanderweele, T. & Laird, N. (2010). Tests for compositional epistasis under single interaction-parameter models. Annals of Human Genetics doi:10.1111/j.1469-1809.2010.00600.x.
Wang, T. & Zeng, Z. (2006). Models and partition of variance for quantitative trait loci with epistasis and linkage disequilibrium. BMC Genetics 7, 9.
Wang, T. & Zeng, Z. (2009). Contribution of genetic effects to genetic variance components with epistasis and linkage disequilibrium. BMC Genetics 10, 52.
Wei, Z., Wang, K., Qu, H. Q., Zhang, H., Bradfield, J., Kim, C., Frackleton, E., Hou, C., Glessner, J. T., Chiavacci, R., Stanley, C., Monos, D., Grant, S. F., Polychronakos, C. & Hakonarson, H. (2009). From disease association to risk assessment: an optimistic view from genome-wide association studies on type 1 diabetes. PLoS Genetics 5, e1000678.
Wray, N., Goddard, M. & Visscher, P. (2008). Prediction of individual genetic risk of complex disease. Current Opinion in Genetics and Development 18, 257263.
WTCCC (2007). Genome-wide association study of 14,000 cases of seven common diseases and 3,000 shared controls. Nature 447, 661678.
Wu, T., Chen, Y., Hastie, T., Sobel, E. & Lange, K. (2009). Genome-wide association analysis by lasso penalized logistic regression. Bioinformatics 25, 714721.
Wu, T. T. & Lange, K. (2008). Coordinate descent algorithms for lasso penalized regression. Annals of Applied Statistics 2, 224244.
Xu, S. (2003). Estimating polygenic effects using markers of the entire genome. Genetics 163, 789801.
Xu, S. (2007). An empirical Bayes method for estimating epistatic effects of quantitative trait loci. Biometrics 63, 513521.
Xu, S. (2010). An expectation-maximization algorithm for the Lasso estimation of quantitative trait locus effects. Heredity 105, 483494. doi:10.1038/hdy.2009.180.
Yandell, B. S., Mehta, T., Banerjee, S., Shriner, D., Venkataraman, R., Moon, J. Y., Neely, W. W., Wu, H., von Smith, R. & Yi, N. (2007). R/qtlbim: QTL with Bayesian Interval Mapping in experimental crosses. Bioinformatics 23, 641643.
Yang, J., Benyamin, B., McEvoy, B., Gordon, S., Henders, A., Nyholt, D., Madden, P., Heath, A., Martin, N., Montgomery, G., Goddard, M., & Visscher, P. (2010). Common SNPs explain a large proportion of the heritability for human height. Nature Genetics 42, 565569.
Yi, N. (2004). A unified Markov chain Monte Carlo framework for mapping multiple quantitative trait loci. Genetics 167, 967975.
Yi, N. & Banerjee, S. (2009). Hierarchical generalized linear models for multiple quantitative trait locus mapping. Genetics 181, 11011113.
Yi, N., Banerjee, S., Pomp, D. & Yandell, B. (2007 a). Bayesian mapping of genomewide interacting quantitative trait loci for ordinal traits. Genetics 176, 18551864.
Yi, N., Kaklamani, V. G. & Pasche, B. (2010). Bayesian analysis of genetic interactions in case-control studies, with application to adiponectin genes and colorectal cancer risk. Annals of Human Genetics doi:10.1111/j.1469-1809.
Yi, N. & Shriner, D. (2008). Advances in Bayesian multiple quantitative trait loci mapping in experimental crosses. Heredity 100, 240252.
Yi, N., Shriner, D., Banerjee, S., Mehta, T., Pomp, D. & Yandell, B. (2007 b). An efficient Bayesian model selection approach for interacting quantitative trait loci models with many effects. Genetics 176, 18651877.
Yi, N. & Xu, S. (2008). Bayesian LASSO for quantitative trait loci mapping. Genetics 179, 10451055.
Yi, N., Yandell, B., Churchill, G., Allison, D., Eisen, E. & Pomp, D. (2005). Bayesian model selection for genome-wide epistatic quantitative trait loci analysis. Genetics 170, 13331344.
Yi, N. & Zhi, D. (2010). Bayesian analysis of rare variants in genetic association studies. Genetic Epidemiology 32, 113.
Yuan, M., Joseph, V. & Lin, Y. (2007). An efficient variable selection approach for analyzing designed experiments. Technometrics 49, 430439.
Zeng, Z., Kao, C. & Basten, C. (1999). Estimating the genetic architecture of quantitative traits. Genetic Research 74, 279289.
Zeng, Z., Wang, T. & Zou, W. (2005). Modeling quantitative trait Loci and interpretation of models. Genetics 169, 17111725.
Zhang, Y. & Liu, J. (2007). Bayesian inference of epistatic interactions in case-control studies. Nature Genetics 39, 11671173.
Zhang, Y. & Xu, S. (2005). A penalized maximum likelihood method for estimating epistatic effects of QTL. Heredity 95, 96–104.
Zhao, P., Rocha, G. & Yu, B. (2009). The composite absolute penalties family for grouped and hierarchical variable selection. Annals of Statistics 37, 34683497.
Zhou, H., Sehl, M., Sinsheimer, J. & Lange, K. (2010). Association screening of common and rare genetic variants by penalized regression. Bioinformatics 26, 23752382.
Zou, F., Huang, H., Lee, S. & Hoeschele, I. (2010). Nonparametric Bayesian variable selection with applications to multiple quantitative trait loci mapping with epistasis and gene–environment interaction. Genetics 186, 385394.
Zou, H. & Hastie, T. (2005). Regularization and variable selection via the elastic net. Journal of Royal Statistical Society B 67, 301320.

Statistical analysis of genetic interactions

  • NENGJUN YI (a1)

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