群集偵測一直是近幾年來是各領域重要的研究問題。傳統的掃描法雖然速度快，但在高相關性資料中會產生許多假警報，而且不能偵測到高盛行率的小群集。而近年來發展的階層模型雖可以偵測群集並同時估計參數，不過須先設定群集個數或群集個數的範圍。本文提出空間及時空相關性模型及所發展的二階段估計法並不需要設定群集個數，經模擬驗證可有效估計模型參數，除了獲得相關性資訊外，偵測率及假警率都有令人滿意的結果。
本文以流行病學上常見的疾病通報資料做驗證。提出的空間相關性模型之實例為紐約州白血病案例。除了偵測到文獻上所提的群集外，由於將相關性納入模型中，可以有效預測保留地點的強度；時空相關性模型之實例為台灣本地腮腺炎及登革熱二種不同傳染途徑的疾病。腮腺炎的時空效應均不明顯，而群集發生地主要是屏東及大台北地區。但近年來台南及高雄也有增加的趨勢，苗栗、雲林、嘉義及花蓮反而減少。登革熱主要的疫區在台南高雄及大台北地區，並且有明顯的時空效應，南部群集多從夏天開始持續到冬天，不過北部的群集不常發生持續的現象。雖然登革熱的個案總數多於腮腺炎，但模型估計的盛行率只有腮腺炎的1/35，顯示此疫一旦發生就迅速蔓延，各級衛生單位須嚴加監控。這二種疾病時空相關性模型的預測值，在個案數多的情況下，模型偏差較簡單時空模型大，反之則有較小的模型偏差，因而可做為監測之用。

Cluster detection is an important problem in many researches. In the case of disease cluster detection, the popular scan statistics of Kulldorff et al is easy to understand and fast to execute, but there are still some drawbacks. It often leads to many false alarms in highly correlation data. Also it cannot detect small clusters even if their infection rates are very high. The spatial hierarchical models proposed by Gangnon and Clayton recently provide information about cluster and spatial/spatial-temporal background. But they do not take into account the possible correlation among the noises. Besides, it has to set the maximum number of clusters which affect the results. In this thesis, we propose spatial and spatial-temporal correlation models and develop the two-stage estimation method which does not need to set the number of clusters in advance. The proposed models are helpful for importation and forecasting purposes. Simulation studies show that they have low false alarm rate and high detection rate.
Our empirical studies are announced disease cases in epidemiology. The upstate New York leukemia data is used for our spatial correlation model. The model provides spatial correlation which makes possible the imputation of missing observation. It can find small clusters which is not possible using scan statistics. The forecast deviance is large when case number rises which hints it potential as a monitoring tool.
For the spatial-temporal correlation model, the mumps and dengue fever in Taiwan, which have different routes of infection, are used. For the mumps data, the spatial and temporal correlations are not clear, and the clusters take place in the north of Taiwan and Ping Tung frequently. Dengue fever clusters usually occur in Tainan, Kaohsiung and Taipei, and the spatial and temporal correlations of dengue fever are significant. The clusters which occur in southern Taiwan last quite long, often starting in summer and vanishing in winter. The clusters in northern Taiwan are usually not sustained. Dengue fever infects fast, so the department of health has to pay close attention as long as one case takes place.
Similarly the prediction deviances, for both diseases, are large when the number of cases increases, indicating its potential usage as a monitoring tool.

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