Joint Modeling of Multiple Spatial Temporal Outcomes

在公共卫生、环境和生态研究中，在相同空间位置测量的变量可能相互关联，因此，在所考虑的整个区域，这些变量的空间结构非常相似，这表明它们可能具有共同的空间风险面。利用风险的这种共性可能有助于获得局部区域风险估计的准确性，特别是对于罕见疾病。在许多科学研究领域，对空间上的函数曲线聚类方法也有很高的需求，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研究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。将开发一种综合方法，将这两个领域的建模技术相结合，用于测试多个结果之间的共同聚类模式。这种方法将非常有助于确定共同的潜在风险因素，如社会结构和政策执行的变化，推动共同的集群模式。共同空间因素模型将被扩展到模拟时空相关的多个零重结局，如低出生体重和早产的计数。此外，联合建模框架的空间相关的纵向和生存的结果，这将被应用到共同建模野火的持续时间和火灾发生的不列颠哥伦比亚省森林火灾数据。为了推进在空间上聚类函数曲线的方法，贝叶斯分层模型将被开发，并与传统方法进行比较，在聚类成员的错误分类及其对协变量效应的影响方面。建模策略还将应用于对事件时间数据的风险函数进行聚类。还将开发考虑风险面不连续性的方法，以确定与周围区域相比具有显著不同的时间模式的区域聚类。 **********************

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. **********************