空間群聚分析應用於流行病學已行之有年，但國內這方面的研究仍較缺乏，尤其在找出哪些地區有較高疾病發生率的群聚偵測。本文針對台灣鄉鎮市資料的特性，提出一套合適的群聚檢測方法，這個方法使用兩階段的電腦模擬，實證上更容易使用；這個方法除了可找出最大顯著群聚外，也能夠偵測出多個群聚的分佈。本文使用電腦模擬比較本文的方法與目前使用較為廣泛的方法(包括Kulldorff(1995)的spatial scan statistic和Tango(2005)的flexible scan statistic)，以型一誤差、型二誤差及錯誤率三種標準衡量方法的優劣。最後套用台灣癌症死亡率與健保就診次數資料，探討台灣癌症空間群聚與就診情形的變化。 / Spatial cluster analyses have applied in epidemiology for many years. In this topic there still are few researches in Taiwan, especially in detecting the areas which have higher disease intensity. In this paper, we proposed a new cluster detection method which is aimed at Taiwan counties’ data. This method which uses two-stage computer simulation procedures is useful in practice. This method can find the most likely cluster. Besides, it can find multiple clusters. We use computer simulations to compare our method with others (Kulldorff’s spatial scan statistic& Tango’s flexible scan statistic). Type-I error, Type-II error and error rate are criterions of measurement. At last, we use Taiwan cancer mortality data and all the people health insurance data to discuss Taiwan cancer spatial clusters and the change of diagnoses.

本論文的研究目標是建構一個由多標記複合成的最佳疾病診斷工具，所考慮的評估準則為操作者特徵曲線在特定特異度範圍之線下面積(pAUC)。在常態分布假設下，我們推導多標記線性組合之pAUC以及最佳線性組合之必要條件。由於函數本身過於複雜使得計算困難。除此之外，我們也發現其最佳解可能不唯一，以及局部極值存在，這些情況使得現有演算法的運用受限，我們因此提出多重初始值演算法。當母體參數未知時，我們利用最大概似估計量以獲得樣本pAUC以及令其極大化之最佳線性組合，並證明樣本最佳線性組合將一致性地收斂到母體最佳線性組合。在進一步的研究中，我們針對單標記的邊際判別能力、多標記的複合判別能力以及個別標記的條件判別能力，分別提出相關統計檢定方法。這些統計檢定被運用至兩個標記選取的方法，分別是前進選擇法與後退淘汰法。我們運用這些方法以選取與疾病檢測有顯著相關的標記。本論文透過模擬研究來驗證所提出的演算法、統計檢定方法以及標記選取的方法。另外，也將這些方法運用在數組實際資料上。 / The aim of this work is to construct a composite diagnostic tool based on multiple biomarkers under the criterion of the partial area under a ROC curve (pAUC) for a predetermined specificity range. Recently several studies are interested in the optimal linear combination maximizing the whole area under a ROC curve (AUC). In this study, we focus on finding the optimal linear combination by a direct maximization of the pAUC under normal assumption. In order to find an analytic solution, the first derivative of the pAUC is derived. The form is so complicated, that a further validation on the Hessian matrix is difficult. In addition, we find that the pAUC maximizer may not be unique and sometimes, local maximizers exist. As a result, the existing algorithms, which depend on the initial-point, are inadequate to serve our needs. We propose a new algorithm by adopting several initial points at one time. In addition, when the population parameters are unknown and only a random sample data set is available, the maximizer of the sample version of the pAUC is shown to be a strong consistent estimator of its theoretical counterpart. We further focus on determining whether a biomarker set, or one specific biomarker has a significant contribution to the disease diagnosis. We propose three statistical tests for the identification of the discriminatory power. The proposed tests are applied to biomarker selection for reducing the variable number in advanced analysis. Numerical studies are performed to validate the proposed algorithm and the proposed statistical procedures.