Assessing the Role of Time-Varying Covariates in Survival and Hazard Modeling Across Dynamic Populations

Posted: Jul 26, 2023

• Jordan Morris
• Joseph Kelly
• Julia Foster

Abstract

Survival analysis represents a cornerstone methodology in numerous scientific disciplines, from medical research to engineering reliability and beyond. Traditional survival models, particularly the Cox proportional hazards model, have predominantly treated covariates as static entities measured at baseline. This approach fundamentally ignores the dynamic nature of many real-world processes where covariates evolve over time in complex, non-linear patterns. The integration of time-varying covariates presents both methodological challenges and substantial opportunities for improving predictive accuracy and causal inference. Our research addresses a critical gap in the current literature by developing a comprehensive framework for modeling time-varying covariates as continuous stochastic processes rather than discrete measurements. This perspective shift enables more accurate representation of how covariates influence hazard rates over time. We investigate how different temporal patterns in covariate evolution affect model performance across diverse populations with varying dynamic characteristics. The novelty of our approach lies in the integration of functional data analysis principles with survival modeling, creating a hybrid methodology that captures both the stochastic nature of covariate trajectories and their complex relationship with survival outcomes. We specifically examine how the temporal resolution of covariate measurement interacts with population dynamics to influence model performance, a relationship that has received limited attention in existing literature. This research addresses three primary questions: First, how can we effectively model time-varying covariates as continuous processes rather than discrete measurements? Second, what is the optimal temporal resolution for covariate measurement?