Functional Principal Component Analysis of Spatiotemporal Point Processes With Applications in Disease Surveillance

• 成果类型: Article
• 署名作者: Li, Yehua; Guan, Yongtao
• 署名单位: Iowa State University; Iowa State University; University of Miami
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2014.885434
• 发表日期: 2014
• 页码: 1205-1215
• 关键词: gaussian cox processes; longitudinal data; Dimension Reduction; regression splines; residual analysis; PROCESS MODELS; asymptotics; likelihood; intensity; patterns

摘要

In disease surveillance applications, the disease events are modeled by spatiotemporal point processes. We propose a new class of semiparametric generalized linear mixed model for such data, where the event rate is related to some known risk factors and some unknown latent random effects. We model the latent spatiotemporal process as spatially correlated functional data, and propose Poisson maximum likelihood and composite likelihood methods based on spline approximations to estimate the mean and covariance functions of the latent process. By performing functional principal component analysis to the latent process, we can better understand the correlation structure in the point process. We also propose an empirical Bayes method to predict the latent spatial random effects, which can help highlight hot areas with unusually high event rates. Under an increasing domain and increasing knots asymptotic framework, we establish the asymptotic distribution for the parametric components in the model and the asymptotic convergence rates for the functional principal component estimators. We illustrate the methodology through a simulation study and an application to the Connecticut Tumor Registry data. Supplementary materials for this article are available online.