Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Penalized variable selection for accelerated failure time models

  • Park, Eunyoung (Department of Statistics, Pukyong National University) ;
  • Ha, Il Do (Department of Statistics, Pukyong National University)
  • Received : 2018.03.19
  • Accepted : 2018.09.15
  • Published : 2018.11.30
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Abstract

The accelerated failure time (AFT) model is a linear model under the log-transformation of survival time that has been introduced as a useful alternative to the proportional hazards (PH) model. In this paper we propose variable-selection procedures of fixed effects in a parametric AFT model using penalized likelihood approaches. We use three popular penalty functions, least absolute shrinkage and selection operator (LASSO), adaptive LASSO and smoothly clipped absolute deviation (SCAD). With these procedures we can select important variables and estimate the fixed effects at the same time. The performance of the proposed method is evaluated using simulation studies, including the investigation of impact of misspecifying the assumed distribution. The proposed method is illustrated with a primary biliary cirrhosis (PBC) data set.

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References

  1. Cai T, Huang J, and Tian L (2009). Regularized estimation for the accelerated failure time model, Biometrics, 65, 394-404. https://doi.org/10.1111/j.1541-0420.2008.01074.x
  2. Cox DR (1972). Regression models and life-tables, Journal of the Royal Statistical Society-Series B, 34, 187-220.
  3. 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
  4. 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
  5. Ha ID, Jeong JH, and Lee Y (2017). Statistical Modelling of Survival Data with Random Effects: h-Likelihood Approach, Springer, Singapore.
  6. Ha ID, Lee Y, and Song JK (2002). Hierarchical likelihood approach for mixed linear models with censored data, Lifetime Data Analysis, 8, 163-176. https://doi.org/10.1023/A:1014839723865
  7. Ha ID, Pan J, Oh S, and Lee Y (2014). Variable selection in general frailty models using penalized h-likelihood, Journal of Computational and Graphical Statistics, 23, 1044-1060. https://doi.org/10.1080/10618600.2013.842489
  8. Huang J and Ma S (2010). Variable selection in the accelerated failure time model via the bridge method, Lifetime Data Analysis, 16, 176-195. https://doi.org/10.1007/s10985-009-9144-2
  9. Huang J, Ma S, and Xie H (2006). Regularized estimation in the accelerated failure time model with high-dimensional covariates, Biometrics, 62, 813-820. https://doi.org/10.1111/j.1541-0420.2006.00562.x
  10. Hutton JL and Monaghan PF (2002). Choice of parametric accelerated life and proportional hazard models for survival data: asymptotic results, Lifetime Data Analysis, 8, 375-393. https://doi.org/10.1023/A:1020570922072
  11. Klein JP and Moeschberger S (2003). Survival Analysis: Techniques for Censored and Truncated Data (2nd ed), Springer, Berlin.
  12. Lawless JF (1982). Statistical Models and Methods for Lifetime data (1st ed), Wiley, New York.
  13. Reid N (1994). A conversation with Sir David Cox, Statistical Science, 9, 439-455. https://doi.org/10.1214/ss/1177010394
  14. Royston P (2001). The lognormal distribution as a model for survival time in cancer, with an emphasis on prognostic factors, Statistica Neerlandica, 55, 89-104. https://doi.org/10.1111/1467-9574.00158
  15. Tibshirani R (1996). Regression shrinkage and selection via the Lasso, Journal of the Royal Statistical Society B, 58, 267-288.
  16. Tibshirani R (1997). The LASSO method for variable selection in the Cox model, Statistics in Medicine, 16, 385-395. https://doi.org/10.1002/(SICI)1097-0258(19970228)16:4<385::AID-SIM380>3.0.CO;2-3
  17. Wang H, Li R, and Tsai CL (2007). Tuning parameter selectors for the smoothly clipped absolute deviation method, Biometrika, 94, 553-568. https://doi.org/10.1093/biomet/asm053
  18. Wang X and Song L (2011). Adaptive lasso variable selection for the accelerated failure models, Communications in Statistics - Theory and Methods, 40, 4372-4386. https://doi.org/10.1080/03610926.2010.513785
  19. Xu J, Leng C, and Ying Z (2010). Rank-based variable selection with censored data, Statistics and computing, 20, 165-176. https://doi.org/10.1007/s11222-009-9126-y
  20. Zhang HH and Lu W (2007). Adaptive LASSO for Cox's proportional hazards model, Biometrika, 94, 691-703. https://doi.org/10.1093/biomet/asm037
  21. Zhang Z, Sinha S, Maiti T, and Shipp E (2018). Bayesian variable selection in the accelerated failure time model with an application to the surveillance, epidemiology, and end results breast cancer data, Statistical Methods Medical Research, 27, 971-990. https://doi.org/10.1177/0962280215626947
  22. Zhou M (2005). Empirical likelihood analysis of the rank estimator for the censored accelerated failure time model, Biometrika, 92, 492-498. https://doi.org/10.1093/biomet/92.2.492
  23. Zou H (2006). The adaptive Lasso and its oracle properties, Journal of American Statistical Association, 101, 1418-1429. https://doi.org/10.1198/016214506000000735