A family of dynamic models for inference on point processes with applications to epidemic data

Abstract

There has been an increasing interest in the analysis of recurrent events, in particu- lar in the fields of epidemiology and public health. Despite their limited utilization, stochastic models provide great exibility for the analysis of epidemic data. Mod- els and methods for the statistical analysis of recurrent events, for instance, can be especially useful to model the spread of infectious diseases and make inferences on epidemic processes. In this study, we introduce a new family of dynamic models for recurrent event processes, called the family of dynamic modulated Poisson process (DMPP) models. A DMPP model includes internal and external covariates to model carryover effects, and dynamically adapts to change points. Such covariates are par- ticularly useful for modelling event clustering, a phenomenon frequently observed in epidemiology. We develop the maximum likelihood estimation procedure of the model parameters and discuss asymptotic properties of the estimators when a single process is under observation for arbitrarily large time periods. We present the results of an extensive simulation study conducted to investigate the finite sample properties of the estimators, as well as effects of various types of model misspecifications. We demon- strate an application of our model and methods to analyze a real-life infectious disease dataset. Finally, we discuss possible extensions of our model and methods as future research.