691
Views
10
CrossRef citations to date
0
Altmetric
Original Articles

Variable selection with group LASSO approach: Application to Cox regression with frailty model

ORCID Icon, ORCID Icon & ORCID Icon
Pages 881-901 | Received 28 Feb 2018, Accepted 08 Jan 2019, Published online: 11 Mar 2019

References

  • Akaike, H. 1973. Information theory and an extension of the maximum likelihood principle. In Proceedings of the second international symposium on information theory, ed. B. N. Petrov and F. Caski, 267–81. Budapest: Akademiai Kiado.
  • Andersen, P. K., and R. D. Gill. 1982. Cox’s regression model for counting processes: a large sample study. The Annals of Statistics 10 (4):1100–20. doi:10.1214/aos/1176345976.
  • Antoniadis, A., and J. Fan. 2001. Regularization of wavelet approximations (with discussion). Journal of the American Statistical Association 96 (455):939–67. doi:10.1198/016214501753208942.
  • Bakin, S. 1999. Adaptive regression and model selection in data mining problems. PhD diss., Australian National University, Canberra.
  • Breiman, L. 1995. Better subset regression using the nonnegative garrote. Technometrics 37 (4):373–85. doi:10.1080/00401706.1995.10484371.
  • Cai, T. T. 2001. Regularization of wavelet approximations: Discussion. Journal of the American Statistical Association 96 (455):960–2.
  • Cox, D. R. 1972. Regression models and life-tables. Journal of the Royal Statistical Society Series B 34 :187–220.
  • Cox, D. R., and D. Oakes. 1984. Analysis of survival data. London: Chapman and Hall
  • Craven, P., and G. Wahba. 1978. Smoothing noisy data with spline functions. Numerische Mathematik 31 (4):377–403. doi:10.1007/BF01404567.
  • Fan, J., and R. Li. 2002. Variable selection for Cox's proportional hazards model and frailty model. The Annals of Statistics 30 :74–99. doi:10.1214/aos/1015362185.
  • Fan, J., and R. Li. 2001. Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association 96 (456):1348–60. doi:10.1198/016214501753382273.
  • Friedberg, J. W. 2011. Relapsed/refractory diffuse large B-cell lymphoma. Hematology American Society of Hematology Education Program 2011 (1):498–505. doi:10.1182/asheducation-2011.1.498.
  • Friedman, J., T. Hastie, and R. Tibshirani. 2010. A note on the group lasso and a sparse group lasso. arXiv preprint arXiv:1001.0736
  • Fu, Z., S. Ma, H. Lin, C. R. Parikh, and B. Zhou. 2017. Penalized variable selection for multi-center competing risks data. Statistics in Biosciences 9 (2):379–405. doi:10.1007/s12561-016-9181-9.
  • Genkin, A., D. D. Lewis, and D. Madigan. 2007. Large-scale Bayesian logistic regression for text categorization. Technometrics 49 (3):291–304. doi:10.1198/004017007000000245.
  • Gilhodes, J., C. Zemmour, S. Ajana, A. Martinez, J.-P. Delord, E. Leconte, J.-M. Boher, and T. Filleron. 2017. Comparison of variable selection methods for high-dimensional survival data with competing events. Computers in Biology and Medicine 91 :159–67. doi:10.1016/j.compbiomed.2017.10.021.
  • Greenland, S. 2008. Invited commentary: variable selection versus shrinkage in the control of multiple confounders. American Journal of Epidemiology 167 (5):523–9. doi:10.1093/aje/kwm355.
  • Hastie, T., R. Tibshirani, and J. Friedman. 2009. Unsupervised Learning. In The Elements of Statistical Learning, (pp. 485–585). New York, NY: Springer.
  • Hoerl, A. E., and R. W. Kennard. 1970. Ridge regression: biased estimation for nonorthogonal problems. Technometrics 12 (1):55–67. doi:10.1080/00401706.1970.10488634.
  • Hou, J., A. Paravati, J. Hou, R. Xu, and J. Murphy. 2018. High-dimensional variable selection and prediction under competing risks with application to SEER-Medicare linked data. Statistics in Medicine 37 (24):3486–502. doi:10.1002/sim.7822.
  • Hougaard, P. 1986. A class of multivanate failure time distributions. Biometrika 73 (3):671–8. doi:10.1093/biomet/73.3.671.
  • Kim, J., I. Sohn, S.-H. Jung, S. Kim, C. Park. 2012. Analysis of survival data with group lasso. Communications in Statistics-Simulation and Computation 41 (9):1593–605. doi:10.1080/03610918.2011.611311.
  • Le Cessie, S., and J. C. Van Houwelingen. 1992. Ridge estimators in logistic regression. Applied Statistics 41 (1):191–201. doi:10.2307/2347628.
  • Leng, C., Y. Lin, and G. Wahba. 2006. A note on the lasso and related procedures in model selection. Statistica Sinica 16 :1273–84.
  • Lenz, G., G. Wright, S. S. Dave, W. Xiao, J. Powell, H. Zhao, W. Xu, B. Tan, N. Goldschmidt, J. Iqbal, et al. 2008. Stromal gene signatures in large-B-cell lymphomas. The New England Journal of Medicine 359 (22):2313–23. doi:10.1056/NEJMoa0802885.
  • Lokhorst, J. 1999. The lasso and generalised linear models. Honors project. Australia: The University of Adelaide.
  • Ma, L., J. Teruya-Feldstein, and R. A. Weinberg. 2007. Tumour invasion and metastasis initiated by microRNA-10b in breast cancer. Nature 449 (7163):682–8. doi:10.1038/nature06174.
  • Martinussen, T., and T. H. Scheike. 2006. Dynamic regression models for survival data. Statistics for biology and health. New York: Springer.
  • Meier, L., S. Van De Geer, and P. Bühlmann. 2008. The group lasso for logistic regression. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 70(1):53–71. doi:10.1111/j.1467-9868.2007.00627.x.
  • National Research Council of the National Academies 2009. Science and decisions: Advancing risk assessment. Washington, D.C.: National Academies Press.
  • Nielsen, G. G., R. D. Gimll, P. K. Andersen, and T. I. Sorensen. 1992. A counting process approach to maximum likelihood estimation in frailty models. Scandinavian Journal of Statistics 19 :25–43.
  • Rosenwald, A., G. Wright, W. C. Chan, J. M. Connors, E. Campo, R. I. Fisher, R. D. Gascoyne, H. K. Muller-Hermelink, E. B. Smeland, J. M. Giltnane, et al. 2002. The use of molecular profiling to predict survival after chemotherapy for diffuse large-B-cell lymphoma. New England Journal of Medicine 346 (25):1937–47. doi:10.1056/NEJMoa012914.
  • Roth, V. 2004. The generalized LASSO. IEEE Transactions on Neural Networks 15 (1):16–28. doi:10.1109/TNN.2003.809398.
  • Saadati, M., J. Beyersmann, A. Kopp-Schneider, and A. Benner. 2018. Prediction accuracy and variable selection for penalized cause-specific hazards models. Biometrical Journal 60 (2):288–306. doi:10.1002/bimj.201600242.
  • Schwarz, G. 1978. Estimating the dimension of a model. The Annals of Statistics 6 (2):461–4. doi:10.1214/aos/1176344136.
  • Tibshirani, R. J. 1996. Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society: Series B (Methodological) 58 :267–88. doi:10.1111/j.2517-6161.1996.tb02080.x.
  • Tibshirani, R. J. 1997. The lasso method for variable selection in the cox model. Statistics in Medicine 16 (4):385–95. doi:10.1002/(SICI)1097-0258(19970228)16:4<385::AID-SIM380>3.0.CO;2-3.
  • Tweedie, M. C. K. 1984. An index which distinguishes between some important exponential families. In Statistics: Applications and new directions: Proc. Indian statistical institute golden Jubilee International conference (579), 579–604.
  • Van der Vaat, A. W. 1998. Asymptotic statistics. Cambridge: Cambridge University Press.
  • Vaupel, J. W., K. G. Manton, and E. Stallard. 1979. The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography 16 (3):439–54. doi:10.2307/2061224.
  • Verweij, P. J., and H. C. Van Houwelingen. 1994. Penalized likelihood in cox regression. Statistics in Medicine 13 (23–24):2427–36. doi:10.1002/sim.4780132307.
  • Wang, H., and C. Leng. 2008. A note on adaptive group lasso. Computational Statistics & Data Analysis 52 (12):5277–86. doi:10.1016/j.csda.2008.05.006.
  • Wei, F., J. Huang, and H. Li. 2011. Variable selection and estimation in high-dimensional varying-coefficient models. Statistica Sinica 21 (4):1515–40.
  • Yuan, M., and Y. Lin. 2006. Model selection and estimation in regression with grouped variables. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 68 (1):49–67. doi:10.1111/j.1467-9868.2005.00532.x.
  • Yuan, M., and Y. Lin. 2007. On the non-negative Garrotte estimator. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 69 (2):143–61. doi:10.1111/j.1467-9868.2007.00581.x.
  • Yun, S., P. Tseng, and K. C. Toh. 2011. A block coordinate gradient descent method for regularized convex separable optimization and covariance selection. Mathematical Programming 129(2):331–55. doi:10.1007/s10107-011-0471-1.
  • Zou, H. 2006. The adaptive lasso and its oracle properties. Journal of the American Statistical Association 101 (476):1418–29. doi:10.1198/016214506000000735.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.