Semiparametric estimation with spatially correlated recurrent events

This article pertains to the analysis of recurrent event data in the presence of spatial correlation. Consider units located at n possibly spatially correlated geographical areas described by their longitude and latitude and monitored for the occurrence of an event that can recur. We propose a new class of semiparametric models for recurrent events that simultaneously account for risk factors and correlation among the spatial locations, and that subsumes the current methods. Since the parameters involved in the models are not directly estimable because of the high dimension of the likelihood, we use composite likelihood approach for estimation. The approach leads to estimates with population interpretation where their large sample properties are obtained under a reasonable set of regularity conditions. Simulation studies suggest that the resulting estimators have a very good finite sampling properties. The methods are illustrated using spatial data on recurrent esophageal cancer in the northern region of France and recurrent wildfire data in the province of Alberta, Canada.