Modeling past event feedback through biomarker dynamics in the multi-state event analysis for cardiovascular disease data

In cardiovascular studies, we often observe ordered multiple events along disease progression, which are essentially a series of recurrent events and terminal events with competing risk structure. One of the main interest is to explore the event specific association with the dynamics of longitudinal biomarkers. New Statistical challenge arises when the biomarkers carry information from the past event history, providing feedbacks for the occurrences of future events, and particularly when these biomarkers are only intermittently observed with measurement errors. In this paper, we propose a novel modelling framework where the recurrent events and terminal events are modelled as multi-state process and the longitudinal covariates that account for event feedbacks are described by random effects models. Considering the nature of long-term observation in cardiac studies, flexible models with semiparametric coefficients are adopted. To improve computation efficiency, we develop an one-step estimator of the regression coefficients and derive their asymptotic variances for the computation of the confidence intervals, based on the proposed asymptotically unbiased estimating equation. Simulation studies show that the naive estimators which either ignore the past event feedbacks or the measurement errors are biased. Our method achieves better coverage probability, compared to the naive methods. The model is motivated and applied to a dataset from the Atherosclerosis Risk in Communities Study,