Regularized estimation in the accelerated failure time model with high-dimensional covariates

Biometrics

Volumn 62, Issue 3, 2006, Pages 813-820

  Huang, Jian ^a   Ma, Shuangge ^b   Xie, Huiliang ^a  

^a UNIVERSITY OF IOWA   (United States)

^b UNIVERSITY OF WASHINGTON   (United States)

Author keywords

Cross validation; LASSO; Threshold gradient directed regularization; Variable selection; Weighted least squares

Indexed keywords

BIOMETRICS;

COVARIATES; CROSS VALIDATION; FAILURE TIME; HIGH-DIMENSIONAL; LASSO; REGULARISATION; THRESHOLD-GRADIENT-DIRECTED REGULARIZATION; TIME MODELING; VARIABLES SELECTIONS; WEIGHTED LEAST-SQUARES;

LEAST SQUARES APPROXIMATIONS;

AKAIKE INFORMATION CRITERION; BOOTSTRAPPING; COVARIANCE ANALYSIS; LEAST SQUARES METHOD; NUMERICAL MODEL; SIMULATION;

ACCELERATED FAILURE TIME MODEL; ARTICLE; LINEAR REGRESSION ANALYSIS; MATHEMATICAL MODEL; MULTIVARIATE ANALYSIS OF COVARIANCE; PREDICTION; SIMULATION; STATISTICAL ANALYSIS; VALIDATION PROCESS;

EID: 33748771184     PISSN: 0006341X     EISSN: 15410420     Source Type: Journal    
DOI: 10.1111/j.1541-0420.2006.00562.x     Document Type: Article

References (31)

1. Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In Second International Symposium on Information Theory, B. N. Petrov and F. Csake (eds), 267-281. Budapest: Akademiai Kaido.
2. Andersen, P. K. and Gill, R. D. (1982). Cox's regression model for counting processes: A large sample study. Annals of Statistics 10, 1100-1120.
3. Buckley, J. and James, I. (1979). Linear regression with censored data. Biometrika 66, 429-436.
4. Cox, D. R. (1972). Regression models and life-tables (with discussion). Journal of the Royal Statistical Society, Series B 34, 187-220.
5. Efron, B. and Tibshirani, R. (1993). An Introduction to the Bootstrap. New York: Chapman and Hall.
6. Efron, B., Hastie, T., Johnstone, I., and Tibshirani, R. (2004). Least angle regression. Annals of Statistics 32, 407-499.
7. Fleming, T. R. and Harrington, D. P. (1991). Counting Processes and Survival Analysis. New York: Wiley.
8. Friedman, J. H. and Popescu, B. E. (2004). Gradient directed regularization for linear regression and classification. Technical Report, Department of Statistics, Stanford University, Stanford, California. Available at http:// www-stat.stanford.edu/~jhf/PathSeeker.html
9. Friedman, J. H., Hastie, T., and Tibshirani, R. (2000). Additive logistic regression: A statistical view of boosting. Annals of Statistics 28, 337-374.
10. Gui, J. and Li, H. (2005a). Penalized Cox regression analysis in the high-dimensional and low-sample size settings, with applications to microarray gene expression data. Bioinformatics 21, 3001-3008.
11. Gui, J. and Li, H. (2005b). Threshold gradient descent method for censored data regression with applications in pharmacogenomics. Proceedings of the Pacific Symposium on Biocomputing 2005. Available at http://helix-web. stanford.edu/psb05
12. Hastie, T., Tibshirani, R., and Friedman, J. (2001). The Elements of Statistical Learning. New York: Springer-Verlag.
13. Jin, Z., Lin, D. Y., Wei, L. J., and Ying, Z. L. (2003). Rank-based inference for the accelerated failure time model. Biometrika 90, 341-353.
14. Kalbfleisch, J. D. and Prentice, R. L. (1980). The Statistical Analysis of Failure Time Data. New York: Wiley.
15. Kim, Y. and Kim, J. (2004). Gradient LASSO for feature selection. Proceedings of the 21st International Conference on Machine Learning. Available at http://www.aicml.cs.ualberta.ca/ banff04/icm1/pages/proceedings.htm
16. Knight, K. and Fu, W. (2000). Asymptotics for LASSO-type estimators. Annals of Statistics 28, 1356-1378.
17. Prentice, R. L. (1978). Linear rank tests with right censored data. Biometrika 65, 167-179.
18. Ritov, Y. (1990). Estimation in a linear regression model with censored data. Annals of Statistics 18, 303-328.
19. Stone, M. (1974). Cross-validatory choice and assessment of statistical predictions (with discussion). Journal of the Royal Statistical Society, Series B 36, 111-147.
20. Stute, W. (1993). Consistent estimation under random censorship when covariables are available. Journal of Multivariate Analysis 45, 89-103.
21. Stute, W. (1996). Distributional convergence under random censorship when covariables are present. Scandinavian Journal of Statistics 23, 461-471.
22. Stute, W. and Wang, J. L. (1993). The strong law under random censorship. Annals of Statistics 14, 1351-1365.
23. Tibshirani, R. (1996). Regression shrinkage and selection via the LASSO. Journal of the Royal Statistical Society, Series B 58, 267-288.
24. Tibshirani, R. (1997). The LASSO method for variable selection in the Cox model. Statistics in Medicine 16, 385-395.
25. Tsiatis, A. A. (1990). Estimating regression parameters using linear rank tests for censored data. Annals of Statistics 18, 354-372.
26. Van der Vaart, A. W. and Wellner, J. A. (1996). Weak Convergence and Empirical Processes: With Applications to Statistics. New York: Springer.
27. Wahba, G. (1990). Spline Models for Observational Data. CBMS-NSF Regional Conference Series in Applied Mathematics, Volume 59. Philadelphia: SIAM.
28. Wei, L. J. (1992). The accelerated failure time model: A useful alternative to the Cox regression model in survival analysis. Statistics in Medicine 11, 1871-1879.
29. Wei, L. J., Ying, Z. L., and Lin, D. Y. (1990). Linear regression analysis of censored survival data based on rank tests. Biometrika 77, 845-851.
30. Ying, Z. L. (1993). A large sample study of rank estimation for censored regression data. Annals of Statistics 21, 76-99.
31. Zou, H. and Hastie, T. (2005). Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society, Series B 67, 301-320.