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Convex hierarchical testing of interactions. (English) Zbl 1454.62311

Summary: We consider the testing of all pairwise interactions in a two-class problem with many features. We devise a hierarchical testing framework that considers an interaction only when one or more of its constituent features has a nonzero main effect. The test is based on a convex optimization framework that seamlessly considers main effects and interactions together. We show – both in simulation and on a genomic data set from the SAPPHIRe study – a potential gain in power and interpretability over a standard (nonhierarchical) interaction test.

MSC:

62P10 Applications of statistics to biology and medical sciences; meta analysis

Software:

hierNet; hiertest
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References:

[1] Bien, J., Simon, N. and Tibshirani, R. (2015). Supplement to “Convex hierarchical testing of interactions.” . · Zbl 1454.62311
[2] Bien, J., Taylor, J. and Tibshirani, R. (2013). A lasso for hierarchical interactions. Ann. Statist. 41 1111-1141. · Zbl 1292.62109
[3] Buzkov√°, P., Lumley, T. and Rice, K. (2011). Permutation and parametric bootstrap tests for gene-gene and gene-environment interactions. Ann. Hum. Genet. 1 36-45.
[4] Dudoit, S. and van der Laan, M. J. (2008). Multiple Testing Procedures with Applications to Genomics . Springer, New York. · Zbl 1261.62014
[5] Efron, B. (2010). Large-Scale Inference : Empirical Bayes Methods for Estimation , Testing , and Prediction. Institute of Mathematical Statistics ( IMS ) Monographs 1 . Cambridge Univ. Press, Cambridge. · Zbl 1277.62016
[6] Hsu, L., Jiao, S., Dai, J. Y., Hutter, C., Peters, U. and Kooperberg, C. (2012). Powerful cocktail methods for detecting genome-wide gene-environment interaction. Genet. Epidemiol. 36 183-194.
[7] Huang, J., Lin, A., Narasimhan, B., Quertermous, T., Hsiung, C. A., Ho, L.-T., Grove, J. S., Olivier, M., Ranade, K., Risch, N. J. and Olshen, R. A. (2004). Tree-structured supervised learning and the genetics of hypertension. Proc. Natl. Acad. Sci. USA 101 10529-10534.
[8] Kooperberg, C. and LeBlanc, M. (2008). Increasing the power of identifying gene \times gene interactions in genome-wide association studies. Genet. Epidemiol. 32 255-263.
[9] Park, M. Y. and Hastie, T. (2008). Penalized logistic regression for detecting gene interactions. Biostatistics 9 30-50. · Zbl 1274.62853
[10] Simon, N. and Tibshirani, R. (2012). A permutation approach to testing interactions in many dimensions. Technical report, Stanford Univ., Stanford, CA.
[11] Tusher, V., Tibshirani, R. and Chu, G. (2001). Significance analysis of microarrays applied to transcriptional responses to ionizing radiation. Proc. Natl. Acad. Sci. USA 98 5116-5121. · Zbl 1012.92014
[12] Wu, Z. and Zhao, H. (2009). Statistical power of model selection strategies for genome-wide association studies. PLoS Genet. 5 1-14.
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