INFERENCE FOR EXTREMES IN DISEASE MAPS OF SMALL AREAS

描述(申请人的描述)疾病-发病率或疾病-死亡率 数据通常在较小的区域内报告，并使用全息图显示 地图，例如，在癌症地图集中。发病率极高的地区可能 受到进一步的审查，试图找出可能的风险 各种因素。然后可以进行病例对照研究，以估计 特定风险因素的影响。这项研究计划旨在 从长远来看，探讨与以下方面有关的一些统计问题 显示、分析和解释疾病发病率或 疾病死亡率数据。这项小额拨款申请的具体目的 包括改进小区域估计，重点是识别区域 与极端的比率，并确定地区，如果有的话，展示 由于机会波动，利率超出了预期。它是 预计这项研究将导致构建点级 将流行病学机制转化为小区域数据的模型，并且 使用地理信息系统实现数据和结果的可视化。 本应用程序目标的主要研究工具是贝叶斯 小区域疾病发病率数据的分层模型。三种方法 极值推理是要研究的：直接推理 从小区域发病率的后验分布来看，受限的 基于平方误差损失的贝叶斯估计和基于贝叶斯估计的 关于强调极值的损失函数。

DESCRIPTION (Applicant's Description) Disease-incidence or disease-mortality data are often reported for small areas and displayed using a choropleth map, e.g., in cancer atlases. Areas with extremely high incidence rates may be subject to further scrutiny in an attempt to identify possible risk factors. Case-control studies may then be carried out to estimate the effects of a particular risk factor. This research program is intended to explore, over the long term, a number of statistical issues related to the display, analysis, and interpretation of disease-incidence or disease-mortality data. The specific aims of this small grant application include improved small-area estimation with a focus on identifying regions with extreme rates, and identification of the regions, if any, that exhibit rates beyond what might be expected due to chance fluctuations. It is expected that this research will lead into building point-level epidemiological mechanisms into a model for small-area data, and the visualization of data and results using a Geographic Information System. The primary research tool for the goals of this application is a Bayesian hierarchical model for small-area disease incidence data. Three approaches to inference for extreme values are to be investigated: inference directly from the posterior distribution of small-area disease rates, constrained Bayesian estimation using squared-error loss, and Bayesian estimation based on loss functions emphasizing extrema.