Penalized variable selection in copula survival models for clustered time-to-event data

A dependence among individual event times within a cluster can be modelled using a copula. Variable selection methods using a penalized likelihood allowing for several penalty functions have been widely studied in various statistical models. To the best of our knowledge, however, there is no literature on variable selection methods for the copula survival models. In this paper, we propose a variable selection procedure in the copula survival models with a parametric (e.g. Weibull) marginal using a one-stage estimation method based on a penalized likelihood. Here, we consider four penalty functions, i.e. LASSO, adaptive LASSO, SCAD and HL (h-likelihood). The performance of the proposed method is demonstrated via simulation study. The usefulness of the new method is illustrated using two well-known clinical data sets.

聚类内个体事件时间之间的相关性可通过连接函数（copula）建模。在各类统计模型中，采用支持多种惩罚函数的惩罚似然的变量选择方法已得到广泛研究。然而，据我们所知，目前尚无针对连接函数生存模型的变量选择方法的相关研究文献。本文中，我们针对采用参数化边际分布（如威布尔（Weibull）分布）的连接函数生存模型，提出了一种基于惩罚似然的单阶段估计变量选择方法。本文共考虑四类惩罚函数，即套索（LASSO）、自适应套索（adaptive LASSO）、平滑剪裁绝对偏差惩罚（SCAD）以及HL（h似然）。我们通过仿真实验验证了所提方法的性能，并利用两个知名临床数据集演示了该新方法的实用性。