本研究是針對卵巢癌的主要風險因子作統計相關分析，共分成兩個部分，第一個部分是在區分卵巢癌患者的中度惡性與惡性腫瘤，考慮在知道腫瘤標記(Tumor marker)與超音波掃描(Ultrasound Imaging)的資訊下，建立邏輯斯(Logistic)迴歸來分類，其重要性在於若能準確分辨出中度惡性腫瘤，在治療上可以考慮比較保守的處置方式，對於較年輕的患者也可以考慮保留其生育能力。第二個部分，我們考慮在一個化療療程內，想找出腫瘤標記中的 CA125 與存活之間的相對關係，因此，建立一聯合模型，利用線性混和模型來描述 CA125 的長期追蹤過程，Cox 比例風險模型(Cox proportional hazard model))來描述存活與共變量之間的關係，預測從手術結束後三年時間點的存活率，並建立獨立樣本組別來進行交叉驗證，其中除了變數 CA125 以外，我們也考慮把手術過程中得到的因子加入模型中，這些因子除了具有醫學上的意義，也能增加預測上的準確率。

The aim of this thesis is to use statistical methods to analyze data in ovarian cancer study. The first part of the thesis is to use information about tumor markers and variables from Ultrasound imaging to classify borderline and invasive ovarian tumors. The purpose of this classification analysis is that patients may receive more proper treatment according to the classification result. In the second part, we tried to explore the relationship between longitudinal CA125 profile and hazard using a joint model in primary chemotherapy.
The joint model coupled the Cox proportional hazard model and the linear mixed-effects
model. The survival function for each patient can be obtained by fitting the joint model.
The estimated survival rate can be used to predict whether a patient is in a high-risk or low- risk group. As an example, we used the prediction of patient's three year survival rate to validate our results. In addition to longitudinal CA125, we also added other variables in the model to increase the accuracy of estimating survival probability.

誌謝. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Abstract. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
1 介紹. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 研究動機與背景介紹. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 研究方法與架構. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 統計方法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .6
2.1 邏輯斯迴歸. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 線性混和模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 Cox 比例風險模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.4 聯合模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3 模型分析結果. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.1 邏輯斯迴歸分類結果. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2 聯合模型分類結果. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4 驗證. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.1 邏輯斯迴歸驗證. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.2 聯合模型驗證. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
5 討論與結語 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
參考文獻 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
A 附錄 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

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