A penalized estimation for the Cox model with ordinal multinomial covariates

Abstract

Models dealing with ordinal multinomial(OM) variables have drawn much attention in regression analysis. Studies on the ordinal response variable have been solidly established and widely applied. However, few studies have investigated generalized linear models with OM covariates, especially in high-dimensional situations. For this problem, the detection of pseudo categories for the OM covariates and the selection of other important covariates need to be concerned simultaneously. This paper proposes an $L_1$-norm penalized estimation procedure to detect pseudo categories of OM covariates in high-dimensional($p_n\le n,p_n=O\left(n^{\sigma }\right),0<\sigma \le 1)$) Cox models. The estimation approach is based on the combination of a transformation method of dummy variables and the penalized partial likelihood. Theoretical properties, such as consistency and oracle property of the proposed estimators, are rigorously established under some regularity conditions. The performance of the proposed method is illustrated by analyses on both simulated data and real data.

Keywords:

• Dummy variables
• pseudo-categories
• transformation
• proportional hazards
• $L_1$ penalty

Acknowledgements

The authors thank the Editor, Associate Editor and three referees for their helpful comments that sub- stantially improve this work. This work is partially supported by the National Natural Science Foundation of China, Grant No. 11771066 and No. 72033002. This work is fully supported by the Fundamental Research Funds for the Central Universities, Grant No. 2682020ZT113.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is partially supported by National Natural Science Foundation of China [11771066,72033002]. This work is fully supported by the Fundamental Research Funds for the Central Universities [2682020ZT113].