We consider a general semiparametric hazards regression model that encompasses the Cox proportional hazards model and the accelerated failure time model for survival analysis. To overcome the nonexistence of the maximum likelihood, we derive a kernel-smoothed profile likelihood function and prove that the resulting estimates of the regression parameters are consistent and achieve semiparametric efficiency. In addition, we develop penalized structure selection techniques to determine which covariates constitute the accelerated failure time model and which covariates constitute the proportional hazards model. The proposed method is able to estimate the model structure consistently and model parameters efficiently. Furthermore, variance estimation is straightforward. The proposed estimation performs well in simulation studies and is applied to the analysis of a real data set.
Keywords: Cox proportional hazards model; accelerated failure time model; efficiency; kernel-smoothed profile likelihood function; model selection; penalized likelihood.
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