Abstract
The Genotype-Tissue Expression (GTEx) project provides a valuable resource of large-scale gene expressions across multiple tissue types. Under various technical noise and unknown or unmeasured factors, how to robustly estimate the major tissue effect becomes challenging. Moreover, different genes exhibit heterogeneous expressions across different tissue types. Therefore, we need a robust method which adapts to the heterogeneities of gene expressions to improve the estimation for the tissue effect. We followed the approach of the robust estimation based on γ-density-power-weight in the works of Fujisawa, H. and Eguchi, S. (2008). Robust parameter estimation with a small bias against heavy contamination. J. Multivariate Anal. 99: 2053–2081 and Windham, M.P. (1995). Robustifying model fitting. J. Roy. Stat. Soc. B: 599–609, where γ is the exponent of density weight which controls the balance between bias and variance. As far as we know, our work is the first to propose a procedure to tune the parameter γ to balance the bias-variance trade-off under the mixture models. We constructed a robust likelihood criterion based on weighted densities in the mixture model of Gaussian population distribution mixed with unknown outlier distribution, and developed a data-adaptive γ-selection procedure embedded into the robust estimation. We provided a heuristic analysis on the selection criterion and found that our practical selection trend under various γ’s in average performance has similar capability to capture minimizer γ as the inestimable mean squared error (MSE) trend from our simulation studies under a series of settings. Our data-adaptive robustifying procedure in the linear regression problem (AdaReg) showed a significant advantage in both simulation studies and real data application in estimating tissue effect of heart samples from the GTEx project, compared to the fixed γ procedure and other robust methods. At the end, the paper discussed some limitations on this method and future work.
Acknowledgements
The gene expression TPM data used for the analyses described in this manuscript were obtained from GTEx Portal in version 7. We acknowledge the discussions with Hua Tang at Stanford and thank Catalina Vallejos, Associate Editor, and two reviewers for the insightful comments that greatly improved the paper.
Author contribution: MW developed the method. LJ and MPS helped analysing the data. MPS supervised the project. All of the authors wrote the paper and contributed to discussion and revised the paper.
Research funding: The work was supported by the GTEx grant (5U01HL13104203) and the CEGS grant (2RM1HG00773506). The Genotype-Tissue Expression (GTEx) Project was supported by the Common Fund of the Office of the Director of the National Institutes of Health, and by NCI, NHGRI, NHLBI, NIDA, NIMH, and NINDS.
Conflict of interest statement: M.P.S. is a cofounder and is on the scientific advisory board of Personalis, Filtircine, SensOmics, Qbio, January, Mirvie, Oralome, and Proteus. He is also on the scientific advisory board (SAB) of Genapsys and Jupiter. The other authors declare no competing interests.
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Supplementary Material
The online version of this article offers supplementary material (https://doi.org/10.1515/sagmb-2020-0042).
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