Modelling and Analysis of Spatially Correlated Event Time Data using Dynamic Modeling and Geostatistical Formulation

Consider units located at n spatially correlated geographical areas described by their longitude and latitude in a two-dimensional surface. The locations are monitored by the occurrence of an event such as pandemic, epidemic, migration, to name a few. We consider two scenarios. The first one is where one unit is located in the area and the event of interest is allowed to recur over a random monitoring window.  The other scenario is when many units are located in one area and each one is allowed to experience the event one time or being censored. In each case, data on event times as well possibly time varying covariates are collected. The data is analyzed using counting processes and geostatistical formulation that led to a class of weighted pairwise semiparametric estimating functions.  We outline how the parameters of the involved models which include regression type as well spatial correlation are estimated; and their asymptotic properties obtained. Results of simulation studies and real data applications that well describes each scenario are presented.