Joint Modeling of Multiple Spatial Temporal Outcomes

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.