A Cross-Validated Ensemble Approach to Robust Hypothesis Testing of Continuous Nonlinear Interactions: Application to Nutrition-Environment Studies

References

• Bach, F. (2017), “Breaking the Curse of Dimensionality with Convex Neural Networks,” Journal of Machine Learning Research , 18, 1–53.
   Web of Science ®Google Scholar
• Black, M. M. , Baqui, A. H. , Zaman, K. , Persson, L. A. , El Arifeen, S. , Le, K. , McNary, S. W. , Parveen, M. , Hamadani, J. D. , and Black, R. E. (2004), “Iron and Zinc Supplementation Promote Motor Development and Exploratory Behavior Among Bangladeshi Infants,” The American Journal of Clinical Nutrition , 80, 903–910. DOI: https://doi.org/10.1093/ajcn/80.4.903.
   PubMed Web of Science ®Google Scholar
• Bodenham, D. A. , and Adams, N. M. (2016), “A Comparison of Efficient Approximations for a Weighted Sum of Chi-Squared Random Variables,” Statistics and Computing , 26, 917–928. DOI: https://doi.org/10.1007/s11222-015-9583-4.
   Web of Science ®Google Scholar
• Broadaway, K. A. , Duncan, R. , Conneely, K. N. , Almli, L. M. , Bradley, B. , Ressler, K. J. , and Epstein, M. P. (2015), “Kernel Approach for Modeling Interaction Effects in Genetic Association Studies of Complex Quantitative Traits,” Genetic Epidemiology , 39, 366–375. DOI: https://doi.org/10.1002/gepi.21901.
   PubMed Web of Science ®Google Scholar
• Burges, C. J. C. (1999), Advances in Kernel Methods Cambridge, MA: MIT Press, pp. 89–116.
   Google Scholar
• Buzková, P. , Lumley, T. , and Rice, K. (2011), “Permutation and Parametric Bootstrap Tests for Gene–Gene and Gene–Environment Interactions,” Annals of Human Genetics , 75, 36–45.
   PubMed Web of Science ®Google Scholar
• Cai, T. , Tonini, G. , and Lin, X. (2011), “Kernel Machine Approach to Testing the Significance of Multiple Genetic Markers for Risk Prediction,” Biometrics , 67, 975–986. DOI: https://doi.org/10.1111/j.1541-0420.2010.01544.x.
   PubMed Web of Science ®Google Scholar
• Cornelis, M. C. , Tchetgen, E. J. , Tchetgen, L. L. , Qi, L. , Chatterjee, N. , Hu, F. B. , and Kraft, P. (2012), “Gene–Environment Interactions in Genome-Wide Association Studies: A Comparative Study of Tests Applied to Empirical Studies of Type 2,” American Journal of Epidemiology , 175, 191–202.
   PubMed Web of Science ®Google Scholar
• Cortes, C. , Mohri, M. , and Rostamizadeh, A. (2011), “Ensembles of Kernel Predictors,” in Proceedings of the Twenty-Seventh Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-11) , eds. F. Cozman and A. Pfeffer , Corvallis, Oregon: AUAI Press, pp. 145–152.
   Google Scholar
• Cortes, C. , Mohri, M. , and Rostamizadeh, A. (2012), “Algorithms for Learning Kernels Based on Centered Alignment,” Journal of Machine Learning Research , 13, 795–828.
   Web of Science ®Google Scholar
• Elisseeff, A. , and Pontil, M. (2002), “Leave-One-Out Error and Stability of Learning Algorithms with Applications,” Advances in Learning Theory: Methods, Models, and Applications: Proceedings of the NATO Advanced Study Institute on Learning Theory and Practice , 8–19 July 2002. Leuven, Belgium: IOS Press.
   Google Scholar
• Ge, T. , Nichols, T. E. , Ghosh, D. , Mormino, E. C. , Smoller, Jordan W. , and Sabuncu, M. R. (2015), “A Kernel Machine Method for Detecting Effects of Interaction Between Multidimensional Variable Sets: An Imaging Genetics Application,” NeuroImage , 109, 505–514. DOI: https://doi.org/10.1016/j.neuroimage.2015.01.029.
   PubMed Web of Science ®Google Scholar
• Gleason, K. , Shine, J. P. , Shobnam, N. , Rokoff, L. B. , Suchanda, H. S. , Hasan, M. I. , Mostofa, M. , Amarasiriwardena, C. , Quamruzzaman, Q. , Rahman, M. , Kile, M. , Bellinger, D. , Christiani, D. , Wright, R. O. , and Mazumdar, M. (2014), “Contaminated Turmeric Is a Potential Source of Lead Exposure for Children in Rural Bangladesh,” Journal of Environmental and Public Health , 2014, 730636. DOI: https://doi.org/10.1155/2014/730636.
   PubMedGoogle Scholar
• Gretton, A. , Sejdinovic, D. , Strathmann, H. , Balakrishnan, S. , Pontil, M. , Fukumizu, K. , and Sriperumbudur, B. K. (2012), “Optimal Kernel Choice for Large-Scale Two-Sample Tests,” in Advances in Neural Information Processing Systems (Vol. 25), eds. F. Pereira , C. J. C. Burges , L. Bottou , and K. Q. Weinberger , Red Hook: Curran Associates, Inc., pp. 1205–1213.
   Google Scholar
• Gu, C. (2013), Smoothing Spline ANOVA Models , Springer Science & Business Media. Google-Books-ID: 5VxGAAAAQBAJ.
   Google Scholar
• Gu, C. , and Wahba, G. (1993), “Smoothing Spline ANOVA With Component-Wise Bayesian ‘Confidence Intervals’,” Journal of Computational and Graphical Statistics , 2, 97–117.
   Google Scholar
• Harville, D. A. (1977), “Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems,” Journal of the American Statistical Association , 72, 320–338. DOI: https://doi.org/10.1080/01621459.1977.10480998.
   Web of Science ®Google Scholar
• He, Z. , Zhang, M. , Lee, S. , Smith, J. A. , Kardia, S. L. R. , Diez Roux, A. V. , and Mukherjee, B. (2016), “Set-Based Tests for Gene-Environment Interaction in Longitudinal Studies,” Journal of the American Statistical Association , 112, 966–997. DOI: https://doi.org/10.1080/01621459.2016.1252266.
   PubMed Web of Science ®Google Scholar
• Hornik, K. (1991), “Approximation Capabilities of Multilayer Feedforward Networks,” Neural Networks , 4, 251–257. DOI: https://doi.org/10.1016/0893-6080(91)90009-T.
   Web of Science ®Google Scholar
• Huang, J. Z. (1998), “Functional ANOVA Models for Generalized Regression,” Journal of Multivariate Analysis , 67, 49–71. DOI: https://doi.org/10.1006/jmva.1998.1753.
   Web of Science ®Google Scholar
• Kile, M. L. , Rodrigues, E. G. , Mazumdar, M. , Dobson, C. B. , Diao, N. , Golam, M. , Quamruzzaman, Q. , Rahman, M. , and Christiani, D. C. (2014), “A Prospective Cohort Study of the Association Between Drinking Water Arsenic Exposure and Self-Reported Maternal Health Symptoms During Pregnancy in Bangladesh,” Environmental Health , 13, 29. DOI: https://doi.org/10.1186/1476-069X-13-29.
   PubMed Web of Science ®Google Scholar
• Kimeldorf, G. S. , and Wahba, G. (1970), “A Correspondence Between Bayesian Estimation on Stochastic Processes and Smoothing by Splines,” The Annals of Mathematical Statistics , 41, 495–502. DOI: https://doi.org/10.1214/aoms/1177697089.
   Google Scholar
• Lecué, G. , and Mitchell, C. (2012), “Oracle Inequalities for Cross-Validation Type Procedures,” Electronic Journal of Statistics , 6, 1803–1837. DOI: https://doi.org/10.1214/12-EJS730.
   Web of Science ®Google Scholar
• Li, S. , and Cui, Y. (2012), “Gene-Centric Gene–Gene Interaction: A Model-Based Kernel Machine Method,” The Annals of Applied Statistics , 6, 1134–1161. DOI: https://doi.org/10.1214/12-AOAS545.
   Web of Science ®Google Scholar
• Pi, I. , Lin, D. , Bromage, S. , Mostofa, M. G. , Allen, J. , Oken, E. , Kile, M. L. , and Christiani, D. C. (2017), “Associations Between Diet and Toenail Arsenic Concentration Among Pregnant Women in Bangladesh: A Prospective Study,” Nutrients , 9, 420. DOI: https://doi.org/10.3390/nu9040420.
   Web of Science ®Google Scholar
• Pi, I. , Lin, D. , Bromage, S. , Mostofa, M. G. , Allen, J. , Oken, E. , Kile, M. L. , and Christiani, D. C. “Validation of a Dish-Based Semiquantitative Food Questionnaire in Rural Bangladesh,” Nutrients , 9, 49.
   Web of Science ®Google Scholar
• Lin, X. (1997), “Variance Component Testing in Generalised Linear Models With Random Effects,” Biometrika , 84, 309–326. DOI: https://doi.org/10.1093/biomet/84.2.309.
   Web of Science ®Google Scholar
• Lin, X. , Lee, S. , Wu, M. C. , Wang, C. , Chen, H. , Li, Z. , and Lin, X. (2016), “Test for Rare Variants by Environment Interactions in Sequencing Association Studies,” Biometrics , 72, 156–164. DOI: https://doi.org/10.1111/biom.12368.
   PubMed Web of Science ®Google Scholar
• Liu, D. , Lin, X. , and Ghosh, D. (2007), “Semiparametric Regression of Multidimensional Genetic Pathway Data: Least-Squares Kernel Machines and Linear Mixed Models,” Biometrics , 63, 1079–1088. DOI: https://doi.org/10.1111/j.1541-0420.2007.00799.x.
   PubMed Web of Science ®Google Scholar
• Maity, A. , and Lin, X. (2011), “Powerful Tests for Detecting a Gene Effect in the Presence of Possible Gene-Gene Interactions Using Garrote Kernel Machines,” Biometrics , 67, 1271–1284. DOI: https://doi.org/10.1111/j.1541-0420.2011.01598.x.
   PubMed Web of Science ®Google Scholar
• Manuck, S. B. , and McCaffery, J. M. (2014), “Gene–Environment Interaction,” Annual Review of Psychology , 65, 41–70. DOI: https://doi.org/10.1146/annurev-psych-010213-115100.
   PubMed Web of Science ®Google Scholar
• Ning, Y. , and Liu, H. (2017), “A General Theory of Hypothesis Tests and Confidence Regions for Sparse High Dimensional Models,” Annals of Statistics , 45, 158–195.
   Web of Science ®Google Scholar
• Raessler, M. (2018), “The Arsenic Contamination of Drinking and Groundwaters in Bangladesh: Featuring Biogeochemical Aspects and Implications on Public Health,” Archives of Environmental Contamination and Toxicology , 75, 1–7. DOI: https://doi.org/10.1007/s00244-018-0511-4.
   PubMed Web of Science ®Google Scholar
• Rasmussen, C. E. , and Williams, C. K. I. (2006, January), Gaussian Processes for Machine Learning , University Press Group Limited, Google-Books-ID: vWtwQgAACAAJ.
   Google Scholar
• Raven, J. , Raven, C. , and Court, J. H. (1998), Manual for Raven’s Progressive Matrices and Vocabulary Scales , Oxford: Oxford Psychologists.
   Google Scholar
• Schölkopf, B. , and Smola, A. J. (2002, January), Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond . Cambridge: MIT Press. Google-Books-ID: y8ORL3DWt4sC.
   Google Scholar
• Seoane, J. , Ian, A. , Day, N. M. , Gaunt, T. R. , and Campbell, C. (2014), “A Pathway-Based Data Integration Framework for Prediction of Disease Progression,” Bioinformatics , 30, 838–845. DOI: https://doi.org/10.1093/bioinformatics/btt610.
   PubMed Web of Science ®Google Scholar
• Staudenmayer, J. , Lake, E. E. , and Wand, M. P. (2009), “Robustness for General Design Mixed Models Using the t-Distribution,” Statistical Modelling , October. DOI: https://doi.org/10.1177/1471082X0800900304.
   Web of Science ®Google Scholar
• Stone, C. J. (1994), “The Use of Polynomial Splines and Their Tensor Products in Multivariate Function Estimation,” Annals of Statistics , 22, 118–171.
   Web of Science ®Google Scholar
• Tchetgen Tchetgen, E. J. , and Kraft, P. (2011), “On the Robustness of Tests of Genetic Associations Incorporating Gene-Environment Interaction When the Environmental Exposure is Misspecified,” Epidemiology (Cambridge, Mass.) , 22, 257–261. DOI: https://doi.org/10.1097/EDE.0b013e31820877c5.
   PubMed Web of Science ®Google Scholar
• Tsybakov, A. B. (2003),“Optimal Rates of Aggregation,” In Learning Theory and Kernel Machines, Lecture Notes in Computer Science, Berlin: Springer, pp. 303–313.
   Google Scholar
• UNICEF . (2016). Global Nutrition Report. Technical report, June 2016.
   Google Scholar
• Valeri, L. , Mazumdar, J. F. B. , Henn, B. C. , Rodrigues, E. , Sharif, O. I. A. , Kile, M. L. , Quamruzzaman, Q. , Afroz, S. , Golam, M. , Amarasiriwardena, C. , Bellinger, D. C. , Christiani, D. C. , Coull, B. A. , and Wright, R. O. (2017), “The Joint Effect of Prenatal Exposure to Metal Mixtures on Neurodevelopmental Outcomes at 20-40 Months of Age: Evidence from Rural Bangladesh,” Environmental Health Perspectives , 125, 067015. DOI: https://doi.org/10.1289/EHP614.
   PubMed Web of Science ®Google Scholar
• van der Laan, M. , and Dudoit, S. (2003), “Unified Cross-Validation Methodology For Selection Among Estimators and a General Cross-Validated Adaptive Epsilon-Net Estimator: Finite Sample Oracle Inequalities and Examples,” U.C. Berkeley Division of Biostatistics Working Paper Series, November.
   Google Scholar
• Wahba, G. (1990), Spline Models for Observational Data . Philadelphia: Society for Industrial and Applied Mathematics (SIAM). Google-Books-ID: ScRQJEETs0EC.
   Google Scholar
• Wu, M. C. , Lee, S. , Cai, T. , Li, Y. , Boehnke, M. , and Lin, X. (2011), “Rare-Variant Association Testing for Sequencing Data with the Sequence Kernel Association Test,” American Journal of Human Genetics , 89, 82–93. DOI: https://doi.org/10.1016/j.ajhg.2011.05.029.
   PubMed Web of Science ®Google Scholar
• Wu, M. C. , Maity, A. , Lee, S. , Simmons, E. M. , Harmon, Q. E. , Lin, X. , Engel, S. M. , Molldrem, J. J. , and Armistead, P. M. (2013), “Kernel Machine SNP-set Testing under Multiple Candidate Kernels,” Genetic Epidemiology , 37, 267–275. DOI: https://doi.org/10.1002/gepi.21715.
   PubMed Web of Science ®Google Scholar
• Zhang, D. , and Lin, X. (2003), “Hypothesis Testing in Semiparametric Additive Mixed Models,” Biostatistics (Oxford, England) , 4, 57–74. DOI: https://doi.org/10.1093/biostatistics/4.1.57.
   PubMed Web of Science ®Google Scholar
• Zhao, N. , Chen, J. , Carroll, I. M. , Ringel-Kulka, T. , Epstein, M. P. , Zhou, H. , Zhou, J. J. , Ringel, Y. , Li, H. , and Wu, M. C. (2015), “Testing in Microbiome-Profiling Studies with MiRKAT, the Microbiome Regression-Based Kernel Association Test,” American Journal of Human Genetics , 96, 797–807. DOI: https://doi.org/10.1016/j.ajhg.2015.04.003.
   PubMed Web of Science ®Google Scholar