Joint Modeling of Multiple Spatial Temporal Outcomes

在公共卫生、环境和生态研究中，在同一空间位置测量的变量可能是相互关联的，因此所考虑的区域内这些变量的空间结构非常相似，表明它们可能具有共同的空间风险面。在风险中采用这种共性可能有助于获得局部地区风险估计的准确性，特别是对于罕见疾病。空间聚类功能曲线的方法在许多科学研究领域也有很高的需求，作为进一步流行病学调查的有用筛选工具。****我提出的研究计划旨在进一步推进这两个相关主题的方法：多个空间结果的联合建模和空间相关功能数据的聚类。将开发一种混合了这两个领域的建模技术的集成方法，用于测试跨多个结果的公共聚类模式。这种方法将非常有助于确定共同的潜在风险因素，如推动共同聚类模式的社会结构和政策执行的变化。将常用的空间因子模型扩展到时空相关的多重零重结果，如低出生体重和早产计数。此外，还将开发纵向和生存结果空间相关的联合建模框架，将其应用于不列颠哥伦比亚省森林火灾数据的野火持续时间和着火发生的联合建模。为了改进空间上聚类功能曲线的方法，将开发贝叶斯层次模型，并在聚类隶属度的错误分类及其对协变量效应的影响方面与传统方法进行比较。该建模策略还将应用于事件数据时间的聚类风险函数。还将开发考虑风险面不连续性的方法，以识别与周围区域相比具有明显不同时间模式的区域的聚类。**********************

In public health, environmental and ecological studies, variables measured at the same spatial locations may be correlated so that the spatial structures of such variables across the region under consideration are very similar, indicating that they may be characterized by a common spatial risk surface. Employing such a commonality in risks may be useful for gaining precision of local area risk estimates, especially for rare diseases. Methods for clustering functional curves over space are also in high demand in many areas of scientific research as a useful screening tool for further epidemiological investigations.****My proposed research program aims at furthering methods in those two related topics: joint modeling of multiple spatial outcomes and clustering of spatially correlated functional data. An integrated approach blending the modeling techniques from those two areas will be developed for testing common clustering pattern across multiple outcomes. Such an approach will be very helpful for identifying common latent risk factors, such as variations in social structure and policy implementation driving the common clustering patterns. The common spatial factor model will be extended to model spatial-temporal correlated multiple zero-heavy outcomes, such as counts of low birth weight and premature birth. In addition, a joint modeling framework of spatially correlated longitudinal and survival outcomes will be developed, which will be applied to jointly modeling the duration of wildfire and occurrence of fire ignition for British Columbia forestry fire data. To advance the methods for clustering functional curves over space, Bayesian hierarchical models will be developed and compared with conventional methods, in terms of misclassification of the cluster membership and their impact on covariate effects. The modeling strategy will also be applied to clustering hazard functions for time to event data. Methods accounting for discontinuities in the risk surface will also be developed to identify clustering of regions with substantially different temporal patterns compared with surrounding regions. **********************