Copula Models for Spatial Epidemiology of Cancer

描述（由申请人提供）：一种相对较新的空间建模方法是基于copula的方法，迄今为止仅应用于地质统计数据，即在连续空间域上观察到的数据。基于copula的建模的主要优点是模块化。依赖结构和边际分布可以分别建模，然后用概率积分变换的方法结合起来。原则上，这种方法可以允许基于copula的面积模型克服与最常用的面积模型相关的许多问题。具体来说，我们期望基于copula的面模型(1)灵活直观，(2)允许所有类型的数据具有正的空间依赖性，(3)低维，(4)允许高效计算（以便处理大型数据集），以及(5)提供可靠的空间回归推理（因为空间混淆是不可能的）。在这个项目中，我们将为实际数据开发各种联结模型，我们将为这些模型开发频率论和贝叶斯推理的方法。通过广泛的模拟研究和应用于hpv相关癌症的当前SEER数据，将copula模型的性能相互比较并与现有的区域模型进行比较。我们还将实现R软件来拟合数据的copula模型。新的例程（和完整的文档）将被添加到现有的R包ngspatial中，它可以从综合R档案网络免费获得。

DESCRIPTION (provided by applicant): 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.