  Consider a subject or unit being monitored over a period of random duration
in a longitudinal time-to-event study in a biomedical, public health, or
engineering setting. As time moves forward, 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 containing 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 represents this unit's
lifetime. Aside from being affected by the covariate vector, there is a synergy
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 affected by the other processes. To exploit this synergy in order to
obtain more realistic models and enhance inferential performance, a joint
stochastic model for these components is proposed and the proper statistical
inference methods for this model are developed. This joint model has the
potential of facilitating precision interventions, thereby enhancing precision
or personalized medicine. A stochastic process approach, using counting
processes and continuous-time Markov chains, is utilized, which allows for
modeling the dynamicity arising from the synergy among the model components and
the impact of performed interventions after event occurrences and the
increasing number of event occurrences. Likelihood-based inferential methods
are developed based on observing a sample of these units. Properties of the
inferential procedures are examined through simulations and illustrated using
some real data sets.
