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.


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


hierNet; hiertest
Full Text: DOI arXiv Euclid


[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.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.