Dimension reduction and variable selection in case control studies via regularized likelihood optimization

Electronic Journal of Statistics

Volumn 3, Issue , 2009, Pages 1257-1287

  Bunea, Florentina ^a   Barbu, Adrian ^a  

^a FLORIDA STATE UNIVERSITY   (United States)

Author keywords

Bisection method; Case control studies; Dimension reduction; Lasso; Logistic regression; Model selection; Prospective sampling; Regularization; Retrospective sampling

Indexed keywords

EID: 84995308283     PISSN: 19357524     EISSN: None     Source Type: Journal    
DOI: 10.1214/09-EJS537     Document Type: Article

References (28)

1. Anderson, J. A.(1972) Separate sample logistic discrimination. Biometrika, 59, 19-35.
2. Barron, A., Birgé, L. and Massart, P. (1999) Risk bounds for model selection via penalization. Probability Theory and Related Fields, 113, 301-413.
3. Breslow, N. E., Robins, J. M. and Wellner, J. A. (2000) On the semi-parametric efficiency of logistic regression under case-control sampling, Bernoulli, 6(3), 447-455.
4. Bunea, F. (2008) Honest variable selection in linear and logistic models via ℓ1 and ℓ1 + ℓ2 penalization, Electronic Journal of Statistics, 2, 1153-1194.
5. Bunea, F. and McKeague, I. (2005) Covariate Selection for Semiparametric Hazard Function Regression Models, Journal of Multivariate Analysis, 92, 186-204.
6. Burden, R.L. and Faires, J.D. (2001), Numerical analysis, 7th ed., Pacific Grove, CA: Brooks/Cole.
7. Carroll, R. J., Wang, S. and Wang, C. Y. (1995) Prospective Analysis of Logistic Case-Control Studies. Journal of the American Statistical Association, 90(429), 157-169.
8. Chen, Y-H., Chatterjee, N. and Carroll, R. J. (2009) Shrinkage Estimators for Robust and Efficient Inference in Haplotype-Based Case-Control Studies. Journal of the American Statistical Association, 104(485), 220-233.
9. Devroye, L. and Lugosi, G. (2001) Combinatorial methods in density estimation, Springer-Verlag.
10. Farewell, V. T. (1979) Some results on the estimation of logistic models based on retrospective data. Biometrika, 66, 27-32.
11. Gill, R. D., Vardi, Y. and Wellner, J. A. (1988). Large sample theory of empirical distributions in biased sampling models. Ann. Statist. 16, 1069-1112.
12. Hastie, T., Rosset S., Tibshirani, R, and Zhu J. (2004). The Entire Regularization Path for the Support Vector Machine. J. Mach. Learn. Res. 5, 1391-1415.
13. Koh, K., Seung-Jean K., and Boyd, S. (2007) An Interior-Point Method for Large-Scale L1-Regularized Logistic Regression. J. Mach. Learn. Res. 8, 1519-1555.
14. Leng, C., Lin, Y., and Wahba, G. (2006). A note on the lasso and related procedures in model selection. Statistica Sinica 16, 1273-1284.
15. Meier, L., van de Geer, S. and Bühlmann, P. (2009) High-dimensional additive modeling, Ann. Statist., to appear.
16. Murphy, S. A. and van der Vaart, A. W. (2001) Semiparametric mix-tures in case-control studies, Journal of Multivariate Analysis, 79, 1-32.
17. Osius, G. (2009) Asymptotic inference for semiparametric association models, Ann. Statist., 37 (1), 459-489.
18. Park, M.Y. and Hastie, T., (2006). Regularization path algorithms for detecting gene interactions, Manuscript. Available from www-stat.stanford.edu/∼hastie/Papers/glasso.pdf.
19. Park, M.Y. and Hastie, T., (2007). L1-regularization path algorithm for generalized linear models. Journal of the Royal Statistical Society: Series B, 69(4), 659-677.
20. Prentice, R. L. and Pyke, R. (1979) Logistic disease incidence models and case-control studies. Biometrika, 66(3), 403-411.
21. Qin, J. and Zhang, B. (1997) A goodness-of-fit test for logistic re-gression models based on case-control data Biometrika, 84(3), 609-618.
22. Ravikumar, P., Wainwright, M. J. and Lafferty, J. (2008) High-dimensional graphical model selection using ℓ1-regularized logistic regression. Technical Report, UC Berkeley, Dept of Statistics.
23. Rosset, S (2005). Tracking curved regularized optimization solution paths. Advances in Neural Information Processing Systems 17 2005.
24. Rosset, S and Zhu, J. (2007) Piecewise linear regularized solution paths, The Ann. Statist., 35(3), 1012-1030.
25. Shi, W., Lee, K. E. and Wahba, G. (2007) Detecting disease-causing genes by LASSO-Patternsearch algorithm. BMC Proceedings 2007, 1(Suppl 1), S60.
26. van de Geer, S. (2008) High-dimensional generalized linear models and the Lasso. The Ann. Statist., 36(2), 614-645.
27. Wegkamp, M. H. (2007) Lasso type classifiers with a reject option. Electronic Journal of Statistics, 1, 155-168.
28. Wu, T.T., Chen, Y. F., Hastie, T., Sobel, E. and Lange, K. (2009) Genome-wide association analysis by lasso penalized logistic regression. Bioinformatics, 25(6), 714-721.