Journal of the Korean Data and Information Science Society

한국데이터정보과학회 (The Korean Data and Information Science Society)
권호 표지
DOI QR코드

DOI QR Code

H-likelihood approach for variable selection in gamma frailty models

  • 투고 : 2011.11.11
  • 심사 : 2011.12.14
  • 발행 : 2012.01.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

Recently, variable selection methods using penalized likelihood with a shrink penalty function have been widely studied in various statistical models including generalized linear models and survival models. In particular, they select important variables and estimate coefficients of covariates simultaneously. In this paper, we develop a penalize h-likelihood method for variable selection in gamma frailty models. For this we use the smoothly clipped absolute deviation (SCAD) penalty function, which satisfies a good property in variable selection. The proposed method is illustrated using simulation study and a practical data set.

키워드

참고문헌

  1. Andersen, P. K., Klein, J. P. and Zhang M.-J. (1999). Testing for centre e ects in multi-centre survival studies: A monte carlo comparison of xed and random e ects tests. Statistics in Medicine, 18, 1489-1500. https://doi.org/10.1002/(SICI)1097-0258(19990630)18:12<1489::AID-SIM140>3.0.CO;2-#
  2. Breslow, N. E.(1972). Discussion of professor Cox's paper. Journal of the Royal Statistical Society B, 34, 216-7.
  3. Cho, D., Shim, J and Seok, K. H. (2010). Doubly penalized kernel method for heteroscedastic autoregressive data. Journal of Korean Data & Information Science Society, 21, 155-162.
  4. Craven, P. and Wahba, G. (1979). Smoothing noisy data with spline functions: Estimating the correct degree of smoothing by the method of generalized cross-validation. Numerische Mathematik, 31, 377-403.
  5. Duchateau, L. and Janssen, P. (2008). The frailty model, Springer-Verlag, New York.
  6. Fan, J. and Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association, 96, 1348-1360. https://doi.org/10.1198/016214501753382273
  7. Fan, J. and Li, R. (2002). Variable selection for Cox's proportional hazards model and frailty model. The Annals of Statistics, 30, 74-99. https://doi.org/10.1214/aos/1015362185
  8. Fleming, T. R. and Harrington, D. P. (1991). Counting processes and survival analysis, Wiley, New York.
  9. Ha, I. D. (2008). A HGLM framework for meta-analysis of clinical trials with binary outcomes. Journal of Korean Data & Information Science Society, 19, 1429-1440.
  10. Ha, I. D. (2009). A correction of SE from penalized partial likelihood in frailty models. Journal of Korean Data & Information Science Society, 20, 895-903.
  11. Ha, I. D. (2011). Inference for heterogeneity of treatment e ect in multi-center clinical trial. Journal of Korean Data & Information Science Society, 22, 605-612.
  12. Ha, I. D. and Lee, Y. (2003). Estimating frailty models via Poisson hierarchical generalized linear models. Journal of Computational Graphical Statistics, 12, 663-681. https://doi.org/10.1198/1061860032256
  13. Ha, I. D., Lee, Y. and Song, J.-K. (2001). Hierarchical likelihood approach for frailty models. Biometrika,88, 233-243. https://doi.org/10.1093/biomet/88.1.233
  14. Ha, I. D., Noh, M. and Lee, Y. (2010). Bias reduction of likelihood estimators in semiparametric frailty models. Scandinavian Journal of Statistics, 37, 307-320. https://doi.org/10.1111/j.1467-9469.2009.00671.x
  15. Ha, I.D., Sylvester, R., Legrand, C. and MacKenzie, G. (2011). Frailty modelling for survival data from multi-centre clinical trials. Statistics in Medicine, 30, 2144-2159. https://doi.org/10.1002/sim.4250
  16. Hong, Y. W. (2010). Failure rate of a bivariate exponential distribution. Journal of Korean Data & Information Science Society, 21, 173-177.
  17. Hougaard, P. (2000). Analysis of multivariate survival data, Springer-Verlag, New York.
  18. Kim, H. K., Noh, M. and Ha, I. D. (2011). A study using HGLM on regional di erence of the dead due to injuries. Journal of Korean Data & Information Science Society, 22, 137-148.
  19. Lee, Y. and Nelder, J. A. (1996). Hierarchical generalized linear models (with discussion). Journal of the Royal Statistical Society B, 58, 619-678.
  20. Lee, Y and Nelder, J. A. (2001). Hierarchical generalised linear models: A synthesis of generalised linear models, random-effect models and structured dispersions. Biometrika, 88, 987-1006. https://doi.org/10.1093/biomet/88.4.987
  21. Lee, Y. and Nelder, J. A. and Pawitan, Y. (2006). Generalised linear models with random effects: Unified analysis via h-likelihood, Chapman and Hall, London.
  22. Lu, W. and Zhang, H. H. (2007). Variable selection for proportional odds model. Statistics in Medicine, 26, 3771-3781. https://doi.org/10.1002/sim.2833
  23. Nielsen, G. G., Gill, R. D., Andersen, P. K. and Sorensen, T. I. A. (1992). A counting process approach to maximum likelihood estimation in frailty models. Scandinavian Journal of Statistics, 19, 25-44.
  24. Tibshirani, R. (1996). Regression shrinkage and selection via the Lasso. Journal of the Royal Statistical Society B, 58, 267-288.
  25. Zou, H. (2006). The adaptive Lasso and its oracle properties. Journal of the American Statistical Association, 101, 1418-1429. https://doi.org/10.1198/016214506000000735

피인용 문헌

  1. A visualizing method for investigating individual frailties using frailtyHL R-package vol.24, pp.4, 2013, https://doi.org/10.7465/jkdi.2013.24.4.931
  2. Derivation of the likelihood function for the counting process vol.25, pp.1, 2014, https://doi.org/10.7465/jkdi.2014.25.1.169
  3. Variable selection in Poisson HGLMs using h-likelihoood vol.26, pp.6, 2015, https://doi.org/10.7465/jkdi.2015.26.6.1513
  4. Joint HGLM approach for repeated measures and survival data vol.27, pp.4, 2016, https://doi.org/10.7465/jkdi.2016.27.4.1083
  5. Statistical analysis of recurrent gap time events with incomplete observation gaps vol.25, pp.2, 2014, https://doi.org/10.7465/jkdi.2014.25.2.327
  6. Analysis of multi-center bladder cancer survival data using variable-selection method of multi-level frailty models vol.27, pp.2, 2016, https://doi.org/10.7465/jkdi.2016.27.2.499