On the maximum penalized full likelihood approach for Cox model with extreme value for heavily censored survival data

In this paper, to deal with heavily censored survival data, a penalized full likelihood (PFL) with extreme value is proposed to estimate the regression coefficients and baseline hazard function in Cox model simultaneously, where multiple penalties are used for variable selection. We present a single-loop algorithm to fit the tail of the baseline distribution beyond a threshold with an extreme value model. The proposed maximum PFL estimators are proved to possess good asymptotic properties, which are validated by simulations and real data analysis.