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VARIABLE SELECTION FOR BAYESIAN SURVIVAL MODELS USING BREGMAN DIVERGENCE MEASURE

Published online by Cambridge University Press:  22 June 2018

Daoyuan Shi  and
Lynn Kuo Open the ORCID record for Lynn Kuo [Opens in a new window]
Daoyuan Shi
Affiliation:
Department of Statistics, University of Connecticut, Storrs, Connecticut, USA E-mail: [email protected]
Lynn Kuo
Affiliation:
Department of Statistics, University of Connecticut, Storrs, Connecticut, USA E-mail: [email protected]
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Abstract

The variable selection has been an important topic in regression and Bayesian survival analysis. In the era of rapid development of genomics and precision medicine, the topic is becoming more important and challenging. In addition to the challenges of handling censored data in survival analysis, we are facing increasing demand of handling big data with too many predictors where most of them may not be relevant to the prediction of the survival outcome. With the desire of improving upon the accuracy of prediction, we explore the Bregman divergence criterion in selecting predictive models. We develop sparse Bayesian formulation for parametric regression and semiparametric regression models and demonstrate how variable selection is done using the predictive approach. Model selections for a simulated data set, and two real-data sets (one for a kidney transplant study, and the other for a breast cancer microarray study at the Memorial Sloan-Kettering Cancer Center) are carried out to illustrate our methods.

Keywords

reliability theorystochastic modeling
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 34 , Special Issue 3: Analytic Methods in Health Care and in Clinical Trials In Honor and Memory of Lycourgos (Lee) Papayanopoulos , July 2020 , pp. 364 - 380
Copyright
Copyright © Cambridge University Press 2018

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References

1.Banerjee, A., Merugu, S., Dhillon, I.S. & Ghosh, J. (2005). Clustering with Bregman divergences. Journal of Machine Learning Research 6: 1705–1749.Google Scholar
2.Berger, J.O. & Pericchi, L.R. (1996). The intrinsic Bayes factor for model selection and prediction. Journal of the American Statistical Association 91(433): 109–122.CrossRefGoogle Scholar
3.Bernardo, J.M. & Smith, A.F. (2000). Bayesian Theory. Somerset, NJ: John Wiley & Sons.Google Scholar
4.Bregman, L.M. (1967). The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming. USSR Computational Mathematics and Mathematical Physics 7(3): 200–217.CrossRefGoogle Scholar
5.Cox, D.R. (1972). Regression models and life-tables. Journal of the Royal Statistical Society. Series B (Methodological) 34(2): 187–220.CrossRefGoogle Scholar
6.Cox, D.R. (1980). Local ancillarity. Biometrika 67(2): 279–286.CrossRefGoogle Scholar
7.Dawid, A.P. (1984). Present position and potential developments: some personal views: statistical theory: the prequential approach. Journal of the Royal Statistical Society. Series A (General) 147(2): 278–292.CrossRefGoogle Scholar
8.Geisser, S. & Eddy, W.F. (1979). A predictive approach to model selection. Journal of the American Statistical Association 74(365): 153–160.CrossRefGoogle Scholar
9.Gelfand, A.E. & Dey, D.K. (1994). Bayesian model choice: asymptotics and exact calculations. Journal of the Royal Statistical Society. Series B 56(3): 501–514.Google Scholar
10.Gelman, A., Hwang, J. & Vehtari, A. (2014). Understanding predictive information criteria for Bayesian models. Statistics And Computing 24(6): 997–1016.CrossRefGoogle Scholar
11.Goh, G. (2015). Applications of Bregman divergence measures in Bayesian modeling. Doctoral Dissertations, 785, University of Connecticut, Storrs, CT, USA. http://digitalcommons.uconn.edu/dissertations/785.Google Scholar
12.Goh, G. & Dey, K.D. (2017) Bayesian model assessment and selection using Bregman divergence. Preprint. Bayesian Analysis, under review.Google Scholar
13.Guerrier, S. & Victoria-Feser, M. (2015) A prediction divergence criterion for model selection. arXiv: 1511.04485v1.Google Scholar
14.Gui, J. & Li, H. (2005). Penalized Cox regression analysis in the high-dimensional and low-sample size settings, with applications to microarray gene expression data. Bioinformatics 21(13): 3001–3008.CrossRefGoogle ScholarPubMed
15.Higgins, M.E., Claremont, M., Major, J.E., Sander, C. & Lash, A.E. (2007). CancerGenes: a gene selection resource for cancer genome projects. Nucleic Acids Research 35(suppl 1): D721–D726.CrossRefGoogle ScholarPubMed
16.Ibrahim, J.G., Chen, M.H., Zhang, D. & Sinha, D. (2013). Bayesian analysis of the Cox model. Handbook of Survival Analysis 27–48.Google Scholar
17.Itakura, F. & Saito, S. (1970). A statistical method for estimation of speech spectral density and formant frequencies. Electronics and Comunications in Japan 53: 36–43.Google Scholar
18.Kalbfleisch, J.D. (1978). Nonparametric Bayesian analysis of survival time data. Journal of the Royal Statistical Society. Series B (Methodological) 40(2): 214–221.CrossRefGoogle Scholar
19.Klein, J.P. & Moeschberger, M.L. (2003). Survival Analysis: Techniques for Censored and Truncated Data. New York, NY: Springer Science & Business Media.CrossRefGoogle Scholar
20.Kyung, M., Gill, J., Ghosh, M. & Casella, G. (2010). Penalized regression, standard errors, and Bayesian LASSOs. Bayesian Analysis 5(2): 369–411.CrossRefGoogle Scholar
21.Lee, K.H., Chakraborty, S. & Sun, J. (2011). Bayesian variable selection in semiparametric proportional hazards model for high dimensional survival data. The International Journal of Biostatistics 7(1): 1–32.CrossRefGoogle Scholar
22.Lee, K.H., Chakraborty, S. & Sun, J. (2015). Survival prediction and variable selection with simultaneous shrinkage and grouping priors. Statistical Analysis and Data Mining: The ASA Data Science Journal 8(2): 114–127.CrossRefGoogle Scholar
23.Lee, K.H., Chakraborty, S. & Sun, J. (2017). Penalized Parametric and Semiparametric Bayesian Survival Models with Shrinkage and Grouping Priors. R-Package https://cran.r-project.org/web/packages/psbcGroup/psbcGroup.pdf.Google Scholar
24.Lewis, P.O., Xie, W., Chen, M.H., Fan, Y. & Kuo, L. (2014). Posterior predictive Bayesian phylogenetic model selectoion. Systematic Biology 63(3): 309–321.CrossRefGoogle Scholar
25.Li, Q. & Lin, N. (2010). The Bayesian elastic net. Bayesian Analysis 5(1): 151–170.CrossRefGoogle Scholar
26.Park, T. & Casella, G. (2008). The Bayesian LASSO. Journal of the American Statistical Association 103(482): 681–686.CrossRefGoogle Scholar
27.Spiegelhalter, D., Best, N.G., Carlin, B.P. & van der Linde, A. (2002). Bayesian measures of model complexity and fit (with discussion). Journal of the Royal Statistical Society. Series B (Methodological) 64(4): 583–639.CrossRefGoogle Scholar
28.Stone, M. (1974). Cross-validatory choice and assessment of statistical predictions. Journal of the Royal Statistical Society. Series B (Methodological) 36(2): 111–147.CrossRefGoogle Scholar
29.Tibshirani, R. (1997). The lasso method for variable selection in the Cox model. Statistics in Medicine 16(4): 385–395.3.0.CO;2-3>CrossRefGoogle ScholarPubMed
30.Watanabe, S. (2010). Asymptotic equivalence of Bayes cross validation and widely applicable information criterion in singular learning theory. Journal of Machine Learning Research 11: 3571–3594.Google Scholar
31.Zhang, W., Ota, T., Shridhar, V., Chien, J., Wu, B. & Kuang, R. (2013). Network-based survival analysis reveals subnetwork signatures for predicting outcomes of ovarian cancer treatment. PLoS Computational Biology 9(3): e1002975.CrossRefGoogle ScholarPubMed
32.Zou, H. & Hastie, T. (2005). Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 67(2): 301–320.CrossRefGoogle Scholar