Bayesian Semiparametric Model for Pathway-Based Analysis with Zero-Inflated Clinical Outcomes
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In this paper, we propose a semiparametric regression approach for identifying pathways related to zero-inflated clinical outcomes, where a pathway is a gene set derived from prior biological knowledge. Our approach is developed by using a Bayesian hierarchical framework. We model the pathway effect nonparametrically into a zero-inflated Poisson hierarchical regression model with an unknown link function. Nonparametric pathway effect was estimated via a kernel machine, and the unknown link function was estimated by transforming a mixture of the beta cumulative density function. Our approach provides flexible nonparametric settings to describe the complicated association between gene expressions and zero-inflated clinical outcomes. The Metropolis-within-Gibbs sampling algorithm and Bayes factor were adopted to make statistical inferences. Our simulation results support that our semiparametric approach is more accurate and flexible than zero-inflated Poisson regression with the canonical link function, which is especially true when the number of genes is large. The usefulness of our approach is demonstrated through its applications to the Canine data set from Enerson et al. (Toxicol Pathol 34:27–32, 2006). Our approach can also be applied to other settings where a large number of highly correlated predictors are present.
Supplementary materials accompanying this paper appear on-line.
KeywordsGaussian process Marginal likelihood Mixed model Unknown link Pathway based analysis Zero-inflated poisson
This study was partially supported by grants from the National Science Foundation (CNS-096480 and CNS-1115839).
- Ali, Z.A., Bursill, C.A., Douglas, G., McNeill, E., Papaspyridonos, M., Tatham, A.L., Bendall, J.K., Akhtar, A.M., Alp, N.J., Greaves, D.R., and Channon, K.M. (2008). CCR2-mediated anti-inflammatory effects of endothelial tetrahydrobiopterin inhibit vascular injury-induced accelerated atherosclerosis. Circulation, 118, S71–S77CrossRefGoogle Scholar
- Bai, X., Margariti, A., Hu, Y., Sato, Y., Zeng, L., Ivetic, A., Habi, O., Mason, J.C., Wang, X., and Xu, Q. (2010). Protein kinase Cdelta deficiency accelerates neointimal lesions of mouse injured artery involving delayed reendothelialization and vasohibin-1 accumulation. Arteriosclerosis, Thrombosis, and Vascular Biology, 30, 2467–74.CrossRefGoogle Scholar
- Enerson, B.E., Lin,A., Lu, B., Zhao, H., Lawton, M.P., and Floyd, E. (2006). Acute Drug-Induced Vascular Injury in Beagle Dogs: Pathology and Correlating Genomic Expression. Toxicologic Pathology, 34, 27–32.Google Scholar
- Fang, Z, Kim, I., and Schaumont, P. (2016). Flexible variable selection for recovering sparsity in nonadditive nonparametric model. Biometrics. doi: 10.1111/biom.12518
- Goeman, J.J., van de Geer, S.A., de Kort, F., van Houwelingen, H.C., Mukherjee, S., Ebert,B.L., Gillette, M. A., Paulovich,A., Pomeroy,S.L., Golub,T.R., , and E.S., ,J.P., (2004). A global test for groups of genes: testing association with a clinical outcome. Bioinformatics, 20, 1, 93–99.Google Scholar
- Jeffreys H. (1961). The Theory of Probability, Oxford, New York.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, 4, 1079–1088.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.Google Scholar
- Mootha, V. K., Handschin, C., Arlow, D., Xie, X., Pierre, J. S., Sihag, S., Yang, W., Altshuler, D., Puigserver, P., Patterson, N., Willy, P. J., Schulman, I. G., Heyman, R. A., Lander, E. S., and Spiegelman, B. M. (2004). Err\(\alpha \)-dependent oxidative phosphorylation gene expression that is altered in diabetic muscle. Proceedings of the National Academy of Sciences, 101, 6570–6575.CrossRefGoogle Scholar
- Vecchione, C., Aretini, A., Marino, G., Bettarini, U., Poulet, R., Maffei, A., Sbroggió, M., Pastore, L., Gentile, M.T., Notte, A., Iorio, L., Hirsch, E., Tarone, G., and Lembo, G. (2006) Selective Rac-1 inhibition protects from diabetes-induced vascular injury. Circulation Research, 98, 218–225.CrossRefGoogle Scholar