疾病群聚是指在一段時間區間或研究區域的子集比起其他時間或地區出現發生率異常高的現象，檢測與評估疾病群聚是否隨機發生是重要的，並且要找到感興趣的潛在危險因子。由於大多數疾病是複雜性疾病，將已知危險因子進行校正，可以獲得更多病因學上的相關資訊，也有助於找尋更多未知的危險因子。本研究的目的在使用Generalized map-based pattern recognition procedure與Spatial scan statistic分析美國紐約州2005-2009年的女性乳癌數據，再使用2021年Wu等人文獻中的相等權重轉換設定與本研究新假設的經過倒數轉換加權設定之多元線性迴歸模型，估計年齡與種族對乳癌發生率在空間分佈中的影響程度。
Grimson在1981年提出Map-based pattern recognition procedure使用高發生率地區模擬相鄰數量頻率分佈表識別發病率強度不同的階層群聚，而Wu與Shete在2020年提出的Generalized map-based pattern recognition procedure擴展上述方法，可以校正危險因子並且可以檢測疾病稀少的群聚，Kulldorff在1997提出Spatial scan statistic以likelihood ratio test檢測主要與次要群聚。兩種方法對疾病群聚有不同敏感度並且可以檢測出不同特色的疾病群聚，因此使用兩種方法進行疾病群聚檢測。
我們使用兩種不同加權設定的多元線性迴歸模型評估乳癌發病率與種族之間的線性關係，考慮種族與高/低風險區域之間的交互作用，並估計年齡與種族在不同空間分佈中的影響程度。在Generalized map-based pattern recognition procedure方法中階層群聚的發病率強度不同，在Spatial scan statistic方法中主要群聚與次要群聚的likelihood ratio也不同，新的加權設定依照發病率強度對county假設排名倒數的權重。使用Freeman-Tukey Transformation使數據更接近常態分佈。以1974-1978年北卡羅萊納州嬰兒猝死症數據證實多元線性迴歸模型在倒數轉換加權設定下的可行性，並以兩種加權設定的迴歸模型分析美國紐約州2005-2009年的女性乳癌數據。
在Generalized map-based pattern recognition procedure分析轉換後的女性乳癌數據的迴歸模型結果中，發現中發生率地區經過Freeman-Tukey Transformation的白人比例每增加10，轉換後病例數會增加0.107每千名女性，低發生率地區比中發生率地區減少133.64%，adjusted R^2為27.93%，高於相等權重轉換迴歸模型的26.12%，以Spatial scan statistic分析相同數據，在最具代表的迴歸模型結果中，發現中發生率地區經過Freeman-Tukey Transformation的白人比例每增加10，轉換後病例數會增加0.166每千名女性，高發生率地區比中發生率地區增加55.72%，低發生率地區比中發生率地區減少62.65%，adjusted R^2為38.45%，高於相等權重轉換迴歸模型的37.84%。認為多元線性迴歸模型在經過倒數轉換加權設定比相等權重轉換設定的配適度更好，因為整體adjusted R^2增加。
種族與年齡皆是女性乳癌的顯著危險因子，從多元線性迴歸結果中發現種族是乳癌的空間相關危險因子而年齡並非空間相關危險因子，女性乳癌的發生有38.45%可以被種族與經由年齡校正的空間分佈解釋，表示還有其他需要關注的危險因子。

The aim of this study is to use the generalized map-based pattern recognition procedure and the spatial scan statistic to detect the clusters of female breast cancer in New York State in 2005-2009, adjusted for age and race, and use the multiple linear regression with different weighting schemes, nominal equal weight transform proposed by Wu et al. in 2021 and new reciprocal transform, to estimate the spatial effects. We use multiple linear regression with different weighting scheme to evaluate the linear relationship between incidence and race, consider the interaction between race and high/low-risk areas, and estimate the spatial effects of age and race in spatial disease clusters. The incidence intensity in hierarchical clusters determined by the generalized map-based pattern recognition procedure is variable. The likelihood ratios of most likely cluster and secondary clusters determined by the spatial scan statistic are different. Using the most representative regression model with the spatial scan statistic and reciprocal transform, we found that compared with medium-risk counties, high-risk counties had significantly higher effect by 55.72%, and low-risk counties had significantly lower effect by 62.65%. Race and interaction variables between race and high/low-risk areas determined by the spatial scan statistic explained 38.45% of the incidence of female breast cancer. In the applications to sudden infant death syndrome and female breast cancer, the results show that the regression model with reciprocal transform according to incidence intensity performes a better fit to the data than the one with nominal equal weight transform.

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