Piaomu Liu | Searcharxiv

arXiv2021

Joint Dynamic Models and Statistical Inference for Recurrent Competing Risks, Longitudinal Marker, and Health Status

Consider a subject or unit in a longitudinal biomedical, public health, engineering, economic, or social science study which is being monitored over a possibly random duration. Over time this unit experiences competing recurrent events and a longitudinal marker transitions over a discrete state-space. In addition, its ``health or performance'' status also transitions over a discrete state-space with some states possibly absorbing states. A vector of covariates will also be associated with this unit. If there are absorbing states, of interest for this unit is its time-to-absorption of its health status process, which could be viewed as the unit's lifetime. Aside from being affected by its covariate vector, there could be associations among the recurrent competing risks processes, the longitudinal marker process, and the health status process in the sense that the time-evolution of each process is associated with the other processes. To obtain more realistic models and enhance inferential performance, a joint dynamic stochastic model for these components is proposed and statistical inference methods are developed. This joint model, formulated via counting processes and continuous-time Markov chains, has the potential of facilitating `personalized' interventions. This could enhance, for example, the implementation and adoption of precision medicine in medical settings. Semi-parametric and likelihood-based inferential methods for the model parameters are developed when a sample of these units is available. Finite-sample and asymptotic properties of estimators of model parameters, both finite- and infinite-dimensional, are obtained analytically or through simulation studies.

stat.ME↗

arXiv2020

Prediction of Time-to-terminal Event (TTTE) in a Class of Joint Dynamic Models

In different areas of research, multiple recurrent competing risks (RCR) are often observed on the same observational unit. For instance, different types of cancer relapses are observed on the same patient and several types of component failures are observed in the same reliability system. When a terminal event (TE) such as death is also observed on the same unit, since the RCRs are generally informative about death, we develop joint dynamic models that simultaneously model the RCRs and the TE. A key interest of such joint dynamic modeling is to predict time-to-terminal event (TTTE) for new units that have not experienced the TE by the end of monitoring period. In this paper, we propose a simulation approach to predict TTTE which arises from a class of joint dynamic models of RCRs and TE. The proposed approach can be applied to problems in precision medicine and potentially many other settings. The simulation method makes personalized predictions of TTTE and provides an empirical predictive distribution of TTTE. Predictions of the RCR occurrences beyond a possibly random monitoring time and leading up to the TE occurrence are also produced. The approach is dynamic in that each simulated occurrence of RCR increases the amount of knowledge we obtain on an observational unit which informs the simulation of TTTE. We demonstrate the approach on a synthetic dataset and evaluate predictive accuracy of the prediction method through 5-fold cross-validation using empirical Brier score.

stat.ME↗