Semiparametric Joint Modeling for Survival Analysis with Longitudinal Covariates

Area of Science:

• Biostatistics
• Longitudinal Data Analysis
• Survival Analysis

Background:

• Classical time-dependent survival models struggle with defining conditional survival functions over the entire time range when linked to dynamic longitudinal covariates.
• This limitation complicates model estimation and interpretation in studies analyzing survival time and covariate trajectories.

Purpose of the Study:

• To propose a novel semiparametric joint modeling approach for analyzing the association between longitudinal covariate patterns and survival time.
• To address the limitations of classical models in defining conditional survival functions and improve model interpretability.

Main Methods:

• Modeled longitudinal trajectories as random realizations of latent functional patterns.
• Used a log-linear functional regression model to link latent patterns to global survival functions.
• Jointly modeled longitudinal and survival data, treating the latent pattern as an infinite-dimensional shared parameter to extend parametric joint modeling to a semiparametric setting.

Main Results:

• The proposed semiparametric joint modeling approach achieves the semiparametric efficiency bound.
• Simulation studies and a real data application demonstrated favorable finite sample performance.

Conclusions:

• The novel semiparametric joint modeling approach offers a robust method for characterizing the association between dynamic longitudinal covariate patterns and survival time.
• This approach enhances the definition and interpretation of conditional survival functions, providing a valuable tool for biostatistical research.