In this paper we propose a class of multistate models for the analysis of multitype recurrent event and failure time data when there are past event feedbacks in longitudinal biomarkers. It can well incorporate various effects, including time-dependent and time-independent effects, of different event paths or the number of occurrences of events of different types.Asymptotic unbiased estimating equations based on polynomial splines approximation are developed. The consistency and asymptotic normality of the proposed estimators are provided. Simulation studies show that the naive estimators which either ignore the past event feedback or the measurement errors are biased.Our method has a better coverage probability of the time-varying/constant coefficients, compared to the naive methods. An application to the dataset from the Atherosclerosis Risk in Communities Study, which is also the motivating example to develop the method, is presented.

Recent work on hierarchical data analysis mainly focuses on the multilevel structure of the mean response. Little research for hierarchical heteroscedasticity was done in the literature. In this paper, we propose a class of hierarchical models with heteroscedasticity and then investigate the semi-parametric statistical inferences. Laplace's approximation is employed to obtain an approximated marginal likelihood function and splines method is used to estimate the unknown functions. We also provide the consistency of the estimators. Simulation studies and real data analysis show that the proposed estimation procedures work well.

In cardiovascular disease studies, a large number of risk factors are measured but it often remains unknown whether all of them are relevant variables and whether the impact of these variables is changing with time or remains constant. In addition, more than one kind of cardiovascular disease events can be observed in the same patient and events of different types are possibly correlated. It is expected that different kinds of events are associated with different covariates and the forms of covariate effects also vary between event types. To tackle these problems, we proposed a multistate modeling framework for the joint analysis of multitype recurrent events and terminal event. Model structure selection is performed to identify covariates with time‐varying coefficients, time‐independent coefficients, and null effects. This helps in understanding the disease process as it can detect relevant covariates and identify the temporal dynamics of the covariate effects. It also provides a more parsimonious model to achieve better risk prediction. The performance of the proposed model and selection method is evaluated in numerical studies and illustrated on a real dataset from the Atherosclerosis Risk in Communities study.

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.