Semiparametric Joint Modeling for Survival Analysis With Longitudinal Covariates
提出一种半参数联合建模方法，将纵向轨迹视为潜在功能模式的随机实现，通过对数线性函数回归模型关联全局生存函数，解决了经典时变协变量模型在条件生存函数定义上的困难。
Characterizing the association between survival time and the dynamic patterns of a longitudinal covariate trajectory is of particular interest in many studies. Classical time-dependent survival models focus mainly on the link between the concurrent covariate value and the instantaneous hazard function. Consequently, the conditional survival function is often not properly defined on the whole time range, which causes difficulty in model estimation and interpretation. In this article, we propose a novel semiparametric joint modeling approach, in which the observed longitudinal trajectory is modeled as a random realization of a latent functional pattern. We assume each latent pattern uniquely indexes a global survival function via a log-linear functional regression model. Because the observational time interval of the longitudinal data depends on the survival time, we propose to jointly model the longitudinal and survival data. By using the latent pattern as an infinite-dimensional shared parameter, our approach extends the classical parametric joint modeling method to a semiparametric setting. We show that the proposed estimator achieves the semiparametric efficiency bound. Simulation studies and a real data application demonstrate the advantageous finite sample performances of our new approach.