Approximate methods in Bayesian point process spatial models.

A range of point process models which are commonly used in spatial epidemiology applications for the increased incidence of disease are compared. The models considered vary from approximate methods to an exact method. The approximate methods include the Poisson process model and methods that are based on discretization of the study window. The exact method includes a marked point process model, i.e., the conditional logistic model. Apart from analyzing a real dataset (Lancashire larynx cancer data), a small simulation study is also carried out to examine the ability of these methods to recover known parameter values. The main results are as follows. In estimating the distance effect of larynx cancer incidences from the incinerator, the conditional logistic model and the binomial model for the discretized window perform relatively well. In explaining the spatial heterogeneity, the Poisson model (or the log Gaussian Cox process model) for the discretized window produces the best estimate.