New inference procedures for semiparametric varying-coefficient partially linear Cox models. (English) Zbl 1442.62531

Summary: In biomedical research, one major objective is to identify risk factors and study their risk impacts, as this identification can help clinicians to both properly make a decision and increase efficiency of treatments and resource allocation. A two-step penalized-based procedure is proposed to select linear regression coefficients for linear components and to identify significant nonparametric varying-coefficient functions for semiparametric varying-coefficient partially linear Cox models. It is shown that the penalized-based resulting estimators of the linear regression coefficients are asymptotically normal and have oracle properties, and the resulting estimators of the varying-coefficient functions have optimal convergence rates. A simulation study and an empirical example are presented for illustration.


62P10 Applications of statistics to biology and medical sciences; meta analysis
62N02 Estimation in survival analysis and censored data
62G05 Nonparametric estimation
62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
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