  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 recurrent events of
several types and a longitudinal marker transitions over a discrete
state-space. In addition, its "health" status also transitions over a discrete
state-space with at least one absorbing state. A vector of covariates will also
be associated with this unit. Of major interest for this unit is the
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. The developed procedures are illustrated using a real data
set.
