  To analyze the impacts of certain types of public health interventions we
need to estimate the treatment effects and outcomes as these apply to
heterogeneous open populations. Dynamically modifying populations containing
risk groups that can react very differently to changes in covariates are
inferentially challenging. Here we propose a novel Bayesian graphical model
called the Reduced Dynamic Chain Event Graph (RDCEG) customized to such
populations. These models generalize the tree-based Chain Event Graphs to a
particular class of graphically supported semi-Markov processes. They provide
an interface between natural language explanations about what might be
happening to individuals and a formal statistical analysis. Here we show how
the RDCEG is able to express the different possible progressions of each
vulnerable individual as well as hypotheses about probabilistic symmetries
within these progressions across different individuals within that population.
We demonstrate how well-developed Bayesian Network technologies can be
transferred almost seamlessly to this class. Our work is motivated by the
challenge of modeling non-pharmacological interventions for recurrent event
processes. We illustrate our methodology in two settings: an intervention to
reduce falls among the elderly and a trial to examine effects of deferred
treatment among individuals presenting with early epilepsy.
