Variable selection method for high-dimensional survival error-in-variable data

doi:10.7523/j.ucas.2021.0016

Abstract

Abstract: Analysis with censored survival data plays an important role in high-dimensional sparse modeling. Much theoretical and applied work is based on clean data. However, we often face corrupted data with missing data or error-in-variable data and as a result analysis on error-in-variable data is more useful. While in the known literature, relatively few work has been done on high-dimensional survival data variable selecting with measurement error. In this situation, we propose a new method to select variables in high-dimensional additive hazards model with error-in-variable data, which combines the pseudoscore function and the nearest positive semi-definite projection. Our numerical studies and real data analysis show that the method has good performance and can select the nonzero coefficients successfully.

Key words: variable selection, high-dimensional, additive hazard model, error-in-variable data

CLC Number:

O212.1

ZHANG Jiarui, WU Yaohua. Variable selection method for high-dimensional survival error-in-variable data[J]. Journal of University of Chinese Academy of Sciences, 2023, 40(1): 12-20.

References

[1] Tibshirani R. Regression shrinkage and selection via the lasso[J]. Journal of the Royal Statistical Society: Series B(Methodolo gieal), 1996, 58(1): 267-288. DOI:10.1111/j.2517-6161.1996.tb02080.x.
[2] Fan J Q, Li R Z. Variable selection via nonconcave penalized likelihood and its oracle properties[J]. Journal of the American Statistical Association, 2001, 96(456): 1348-1360.DOI:10.1198/016214501753382273.
[3] Zhang C H. Nearly unbiased variable selection under minimax concave penalty[J]. Annals of Statistics, 2010, 38(2): 894-942.
[4] Bradic J, Fan J Q, Jiang J C. Regularization for cox’s proportional hazards model with np-dimensionality[J]. Annals of Statistics, 2011, 39(6): 3092-3120.DOI:10.1214/11-AOS911.
[5] Gorst-Rasmussen A, Scheike T. Independent screening for single-index hazard rate models with ultrahigh dimensional features[J]. Journal of the Royal Statistical Society: Series B(Statistical Methodology), 2013, 75(2): 217-245.DOI:10.1111/j.1467-9868.2012.01039.x.
[6] Lin W, Lyu J C. High-dimensional sparse additive hazards regression[J]. Journal of the American Statistical Association, 2013, 108(501): 247-264.DOI:10.1080/01621459.2012.746068.
[7] Fan J Q, Lyu J C, Qi L. Sparse high-dimensional models in economics[J]. Annual Review of Economics, 2011, 3: 291-317.DOI:10.1146/annurer-economics-061109-080451.
[8] Loh P L, Wainwright M J. High-dimensional regression with noisy and missing data: provable guarantees with nonconvexity[J]. The Annals of Statistics, 2012, 40(3): 1637-1664.
[9] Datta A, Zou H. CoCoLasso for high-dimensional error-in-variables regression[J]. The Annals of Statistics, 2017, 45(6): 2400-2426.
[10] 刘智凡, 王妙妙, 谢田法，等. 工具变量辅助的变系数测量误差模型的估计[J]. 中国科学院大学学报, 2018, 35(1):1-9.DOI:10.7523/j.issn.2095-6134.2018.01.001.
[11] Song X, Wang C Y. Proportional hazards model with covariate measurement error and instrumental variables[J]. Journal of the American Statistical Association, 2014, 109(508):1636-1646.DOI:10.1080/01621459.2014.896805.
[12] Chen L P, Yi G Y. Semiparametric methods for left-truncated and right-censored survival data with covariate measurement error[J]. Annals of the Institute of Statistical Mathematics, 2021,73(3): 481-517. DOI:10.1007/s10463-020-00755-2.
[13] Chen L P, Yi G Y. Analysis of noisy survival data with graphical proportional hazards measurement error models[J]. Biometrics, 2021,77(3):956-969. DOI:10.1111/biom.13331.
[14] Chen B J, Yuan A, Yi G Y. Variable selection for proportional hazards models with high-dimensional covariates subject to measurement error[J]. The Canadian Journal of Statistics, 2020,49(2):397-420DOI:10.1002/cjs.11568.
[15] Lin D Y, Ying Z L. Semiparametric analysis of the additive risk model [J]. Biometrika, 1994, 81(1): 61-71.DOI:10.1093/biomet/81.1.61.
[16] Leng C L, Ma S G. Path consistent model selection in additive risk model via Lasso[J]. Statistics in Medicine, 2007, 26(20): 3753-3770.DOI:10.1002/sim.2834.
[17] Martinussen T, Scheike T H. Covariate selection for the semiparametric additive risk model[J]. Scandinavian Journal of Statistics, 2009, 36(4): 602-619.
[18] Duchi J, Shalev-Shwartz S, Singer Y, et al. Efficient projections onto the l₁-ball for learning in high dimensions[C]//Proceedings of the 25^th International Conference on Machine Learning-ICML,08. July 5-9, 2008, Helsinki, Finland. New York: ACM Press, 2008: 272-279.DOI:10.1145/1390156.1390191.
[19] van Houwelingen H C, Bruinsma T, Hart A A M, et al. Cross-validated cox regression on microarray gene expression data[J]. Statistics in Medicine, 2006, 25(18): 3201-3216.DOI:10.1002/sim.2353.
[20] van’t Veer L J, Dai H Y, van de Vijver M J, et al. Gene expression profiling predicts clinical outcome of breast cancer[J]. Nature, 2002, 415(6871): 530-536.DOI:10.1038/415530a.