Sieve estimation of Cox models with latent structures

Area of Science:

• Statistics
• Biostatistics
• Survival Analysis

Background:

• The Cox proportional hazards model is widely used for survival data analysis.
• Estimating regression structures in the Cox model with right-censored data presents challenges, especially with unknown nonparametric components.
• Existing methods may struggle to simultaneously identify and estimate both linear and nonparametric covariate effects.

Purpose of the Study:

• To propose a novel semiparametric pursuit method for sieve estimation in the Cox model.
• To simultaneously identify and estimate linear and nonparametric covariate effects using B-spline expansions and penalized group selection.
• To address the challenge of unknown regression structures in survival data analysis.

Main Methods:

• Utilized a semiparametric pursuit approach for simultaneous identification and estimation.
• Employed B-spline expansions for nonparametric covariate effects.
• Implemented a penalized group selection method with concave penalties and a modified blockwise majorization descent algorithm for computation.

Main Results:

• Demonstrated the consistency of estimators for both linear effects and the nonparametric component.
• Established the asymptotic normality of the estimator for linear effects.
• Simulation studies confirmed the method's good performance in finite sample situations.

Conclusions:

• The proposed semiparametric pursuit method offers a robust approach for sieve estimation in the Cox model with unknown structures.
• The method effectively handles right-censored data and simultaneously estimates diverse covariate effects.
• The developed algorithm is efficient, easy to implement, and validated by simulation and real-world data application (primary biliary cirrhosis).