A Two-Stage Estimation Approach to Cox Regression Under the Five-Parameter Spline Model

The Cox proportional hazards model is one of the most popular regression models for censored survival data. In the Cox model, the baseline hazard function is often modeled by cubic spline functions. However, the penalized likelihood estimation for fitting cubic spline models is computationally challenging. In this paper, we propose a computationally simple approach to implement the cubic spline model without penalizing the likelihood. The proposed method consists of two stages under the five-parameter spline model. The first stage estimates a scale parameter for a given shape model. The second stage adopts a model selection from 13 candidate shape models. We implement the proposed methods in our new R package “splineCox” (version 0.0.3) and it has been made available in CRAN. We conduct simulation studies to assess the performance of the proposed method. To illustrate the advantage of the proposed model, we analyze a life test dataset on electrical insulations and a gene expression dataset on lung cancer patients.