Inference on Spatio-Temporal Log-Gaussian Cox Processes for Spatially Aggregated Disease Incidence Data

受利用常规收集的调查数据了解疾病风险的空间差异这一问题的推动，该项目旨在开发跨越长时间段的空间聚集数据的模型和统计推断方法。在研究疾病风险的小区域变异时，需要高分辨率的疾病风险预测，无法获得确切的病例位置这一事实变得重要。此外，通常提供数据的人口普查地区和邮政地区的规模差别很大，在城市地区信息量很大，在人口较少的地区受到严格审查，这些地区在地图上占据主导地位。对小区域或罕见结果的研究需要很长的研究时间才能积累足够的病例。这带来了风险随时间变化的问题，以及人口普查和邮政地区的变化。 该项目将以申请人以前的工作为基础，首先扩展模型，以考虑风险随时间的变化，其次改进统计推断方法，以考虑到向时空模型转变所产生的更高维度。将现有的马尔可夫随机场近似推广到具有稀疏精度矩阵的马尔可夫时空过程。马尔可夫链蒙特卡罗推论将通过使用最近发展起来的一些方法来改进，如Rymann流形，朗之万MCMC。 开发这些方法的目的是为了解决应用文献中的实质性问题，维持和加强现有的关于北卡罗来纳州梅毒、多伦多狼疮和安大略省西部间皮瘤肺癌的合作。作为这项工作的结果，疾病地图中的更多种类的问题将能够得到解决，特别是在病例数量低、聚集不规律以及存在时空相互作用的情况下。

Motivated by the problem of understanding spatial variations in disease risk using routinely collected survey data, this project aims to develop models and statistical inference methods for spatially aggregated data spanning long time periods. When studying small-area variations in disease risk, where prediction of disease risk at a high resolution is required, the fact that exact case locations are unavailable becomes important. Further, the census regions and postal regions on which data are typically made available vary greatly in size being highly informative in urban areas and heavily censored in the less populated ares which dominate maps. Studies on small regions or rare outcomes require long study periods to accumulate sufficient cases. This introduces the problem of risk changing over time as well as changes to census and postal regions. This project will build on the applicant's previous work by first extending the models to allow for changes in risk over time, and second by improving the method of statistical inference to allow for the higher dimensionality resulting from the shift to a spatio-temporal model. The existing Markov random field approximation to continuous spatial surfaces will be extended to approximate Markovian spatio-temporal processes with sparse precision matrices. Markov Chain Monte Carlo inference will be improved by using a number of recently developed methods such as Remiann manifold Langevin MCMC. The methods will be developed with the aim of addressing substantive problems in the applied literature, with existing collaborations concerning Syphilis in North Carolina, Lupus in Toronto, and Mesothelioma lung cancer in western Ontario maintained and built upon. As a result of this work, a greater variety of problems in disease mapping will be able to be addressed, notably when case counts are low, aggregation is irregular, and spatio-temporal interactions are present.