A relatively new approach to spatial modeling is the copula-based approach, which has thus far been applied only to geostatistical data, i.e., data observed over a continuous spatial domain. The chief advantage of copula-based modeling is modularity. The dependence structure and the marginal distributions can be modeled separately and then joined by way of the probability integral transform. This approach can, in principle, allow copula-based areal models to overcome many of the problems associated with the most commonly used areal models. Specifically, we expect copula-based areal models (1) to be flexible and intuitive, (2) to permit positive spatial dependence for all types of data, (3) to be ow dimensional, (4) to permit efficient computation (so that large datasets can be handled), and (5) to provide reliable spatial regression inference (because spatial confounding is impossible). In this project, we will develop various copula models for areal data, and we will develop approaches to frequentist and Bayesian inference for the models. The performance of the copula models will be compared to one another and to existing areal models by way of an extensive simulation study and application to current SEER data for HPV-related cancers. We will also implement R software for fitting the copula models to data. The new routines (and thorough documentation) will be added to existing R package ngspatial, which is freely available from the Comprehensive R Archive Network.
Copula models for disease mapping have the potential to provide a more accurate description of cancer risk. New, user-friendly software will enable a diverse community of practitioners to apply copula models to spatially aggregated cancer data.