Semiparametric Joint Modeling for Survival Analysis with Longitudinal Covariates

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.