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，从而使所考虑区域内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表面的特征。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精确度，特别是对罕见疾病。在许多科学研究领域中，空间函数曲线的聚类方法也是非常需要的，作为进一步流行病学调查的有用的筛查工具。我提出的研究计划旨在促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函数数据的聚类。将开发一种融合这两个领域的建模技术的综合方法，以测试多个结果的共同集群模式。这种方法将非常有助于识别共同的潜在风险因素，例如推动共同集群模式的社会结构和政策执行的变化。公共空间因素模型将被扩展到时空相关的多个零-重结果的建模，例如低出生体重和早产的计数。此外，还将开发空间相关的纵向结果和生存结果的联合建模框架，该框架将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事件的联合建模。为了推进函数曲线在空间上的聚类方法，将发展贝叶斯层次模型，并将其与传统方法进行比较，以考察聚类成员的错误分类及其对协变量效应的影响。该建模策略还将应用于对事件间隔时间数据的风险函数进行聚类。还将开发考虑风险表面中不连续性的方法，以识别与周围地区相比具有显著不同时间模式的区域的聚集性。

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.