Dynamic Long-Term Prediction With Intermediate Event Information: A Flexible Model With Bivariate Time-Varying Coefficients.

The integration of time-to-intermediate event data and the evolving characteristics of patients to enhance long-term prediction has garnered significant interest, driven by the wealth of data generated from longitudinal cohorts. In this paper, we propose sequential/dynamic prediction rules by using regression models with time-varying coefficients. We introduce a class of dynamic models that not only incorporates intermediate event information but also leverages information across different landmark times. To address the challenge of right-censoring, we employ an inverse weighting technique in the estimation process. We establish the asymptotic properties of the estimated parameters and conduct extensive simulations to assess the finite sample performance. Our simulation studies confirm that the proposed method exhibits computational efficiency and yields estimations comparable to those of kernel-based approaches. We apply the proposed method to real-world data from the Atherosclerosis Risk in Communities (ARIC) study and predict mortality while incorporating information regarding a crucial intermediate event, the occurrence of a stroke, and other time-varying covariates dynamically.