Abstract
We propose a Bayesian hierarchical mixture model framework that allows us to investigate the genetic and environmental effects, gene by gene interactions and gene by environment interactions in the same model. Our approach incorporates the natural hierarchical structure between the main effects and interaction effects into a mixture model, such that our methods tend to remove the irrelevant interaction effects more effectively, resulting in more robust and parsimonious models. We consider both strong and weak hierarchical models. For a strong hierarchical model, both the main effects between interacting factors must be present for the interactions to be considered in the model development, while for a weak hierarchical model, only one of the two main effects is required to be present for the interaction to be evaluated. Our simulation results show that the proposed strong and weak hierarchical mixture models work well in controlling false-positive rates and provide a powerful approach for identifying the predisposing effects and interactions in gene–environment interaction studies, in comparison with the naive model that does not impose this hierarchical constraint in most of the scenarios simulated. We illustrate our approach using data for lung cancer and cutaneous melanoma.
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Acknowledgments
CIA has been supported by NIH Grant U19CA148127, P50CA093459, and P30CA023108. JM has been supported by NIH Grant R01CA134682. JM also acknowledges the support provided by the Biostatistics/ Epidemiology/ Research Design (BERD) component of the Center for Clinical and Translational Sciences (CCTS) for this project. CCTS is mainly funded by the NIH Centers for Translational Science Award (NIH CTSA) Grant (UL1 RR024148), awarded to University of Texas Health Science Center at Houston in 2006 by the National Center for Research Resources (NCRR) and its renewal (UL1 TR000371) by the National Center for Advancing Translational Sciences (NCATS).
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Liu, C., Ma, J. & Amos, C.I. Bayesian variable selection for hierarchical gene–environment and gene–gene interactions. Hum Genet 134, 23–36 (2015). https://doi.org/10.1007/s00439-014-1478-5
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DOI: https://doi.org/10.1007/s00439-014-1478-5