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Bayesian Semiparametric Model for Pathway-Based Analysis with Zero-Inflated Clinical Outcomes

Author

Listed:
  • Lulu Cheng

    (Virginia Polytechnic Institute and State University (Virginia Tech.))

  • Inyoung Kim

    (Virginia Polytechnic Institute and State University (Virginia Tech.))

  • Herbert Pang

    (The University of Hong Kong)

Abstract

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.

Suggested Citation

  • Lulu Cheng & Inyoung Kim & Herbert Pang, 2016. "Bayesian Semiparametric Model for Pathway-Based Analysis with Zero-Inflated Clinical Outcomes," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(4), pages 641-662, December.
    • Handle: RePEc:spr:jagbes:v:21:y:2016:i:4:d:10.1007_s13253-016-0264-3
    DOI: 10.1007/s13253-016-0264-3
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    References listed on IDEAS

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    1. Zaili Fang & Inyoung Kim & Patrick Schaumont, 2016. "Flexible variable selection for recovering sparsity in nonadditive nonparametric models," Biometrics, The International Biometric Society, vol. 72(4), pages 1155-1163, December.
    2. Dawei Liu & Xihong Lin & Debashis Ghosh, 2007. "Semiparametric Regression of Multidimensional Genetic Pathway Data: Least-Squares Kernel Machines and Linear Mixed Models," Biometrics, The International Biometric Society, vol. 63(4), pages 1079-1088, December.
    3. Chib S. & Jeliazkov I., 2001. "Marginal Likelihood From the Metropolis-Hastings Output," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 270-281, March.
    4. Arnab Maity & Xihong Lin, 2011. "Powerful Tests for Detecting a Gene Effect in the Presence of Possible Gene–Gene Interactions Using Garrote Kernel Machines," Biometrics, The International Biometric Society, vol. 67(4), pages 1271-1284, December.
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    Cited by:

    1. Lin Zhang & Inyoung Kim, 2021. "Finite mixtures of semiparametric Bayesian survival kernel machine regressions: Application to breast cancer gene pathway subgroup analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(2), pages 251-269, March.
    2. Zaili Fang & Inyoung Kim & Jeesun Jung, 2018. "Semiparametric Kernel-Based Regression for Evaluating Interaction Between Pathway Effect and Covariate," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 23(1), pages 129-152, March.

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