在醫學中常會利用 Cox 比例風險模型來找出影響反應變數的解釋變數，而在本研究中，使用的資料來自高雄榮民總醫院腎臟科，共 101 位微小腎病變的病患資料，且病患皆使用類固醇療法。在這些病患中，找出對於感染風險有影響的危險因子。其中每個病患在開始治療後的每一次回診都會測量一次尿蛋白指數，所以尿蛋白指數為長期追蹤資料，並且利用開始治療後 120 天內的尿蛋白指數趨勢分為三個類別，做為治療效果指標，也是主要考慮的危險因子，同時再考慮其他危險因子對於感染風險的影響。

本文也提供了一個在存活分析中找尋最佳切分點個數及位置的方法，利用概似估計量來決定最佳切分點位置，並透過交叉驗證及蒙地卡羅法來校正 p-value、AIC，進而得到最佳切分點個數。同時提供使用者一個函數，藉此找到最佳切分點個數及最佳切分點位置。將此方法應用在真實資料上，真實資料來自高雄榮民總醫院婦產科，共949位子宮頸癌的病患資料。分析身體質量指數 (BMI)的最佳切分點對於死亡風險的影響。將身體質量指數在不同轉換方式下，配適Cox比例風險模型，由 C_index 作為模型預測能力好壞的標準。最後透過資料模擬驗證我們所提供的方法，並比較模型配適的C_index 表現。

The Cox proportional hazards model is often used in medical science to find the covariates that affect the response.In this study, the data contain 101 patients with idiopathic minimal change disease undergoing immunosuppression therapy from the Department of Nephrology, Kaohsiung Veterans General Hospital.In these patients, we aim to find the risk factors that have an significant impact on the infection.Since the major risk factor, urinary protein index, was measured by each patient at every visit within 120 days after the treatment, we consider it as longitudinal data and divided them into three levels in clinical guideline.In this study, these three levels are regarded as indicators of treatment effectiveness and we took into account other risk factors on the infection.

This paper provided a method to find the optimal number and location of cut points in survival analysis.We determine the location of cut points by using the log-likelihood statistic and correct the p-value and AIC through two-folds cross validation so as to get the optimal number of cut points. Moreover, we also wrote a function to perform this method.And we applied the function to real data including 949 patients with cervical cancer from the Obstetrics and Gynecology Department of Kaohsiung Veterans General Hospital.To analyze the impact of BMI optimal cut points on the risk of death.Besides, BMI was fitted Cox proportional hazard model under different transformation. C_ index was taken as the criterion for the predictions ability of the model. Finally, the method we provided was validated by simulation data, and the performance of C index was compared.

論文審定書 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .i
論文公開授權書. . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
致謝 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .iii
摘要 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .iv
Abstract. . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
1 研究動機與目的. . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
2 資料描述. . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
2.1 微小腎病變. . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
2.1.1 資料處理. . . . . . . . . . . . . . . . . . . . . . . . . . . . .2
2.1.2 變數介紹. . . . . . . . . . . . . . . . . . . . . . . . . . . . .2
2.1.3 連續型變數. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.1.4 離散型變數 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 資料描述-子宮頸癌 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2.1 資料處理 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2.2 Ž變數介紹 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.3 連續型變數 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.4 離散型變數 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3 研究方法
3.1 Kaplan-Meier 存活函數 . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.2 Cox 比例風險模型 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.2.1 Time independent . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.2.2 Time dependent . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.3 一致性指標 (concordance index) . . . . . . . . . . . . . . . . . . . . . . 9
3.4 AIC (Akaike information criterion) . . . . . . . . . . . . . . . . . . . . . 9
3.5 傳統方法 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.6 估計切分點個數及位置 . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.6.1 概似比檢定 Likelihood ratio test . . . . . . . . . . . . . . . . . . 10
3.7 校正型一誤差 Corrected Type I error . . . . . . . . . . . . . . . . . . . . 11
3.7.1 部分概似涵數 Partial likelihood . . . . . . . . . . . . . . . . . . 11
3.8 兩摺交叉驗證及蒙地卡羅法 . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.9 基因演算法 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.10 模擬 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.10.1 資料生成模擬 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.11 計算工具-國網中心 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4 研究結果
4.1 微小腎病變 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.2 切分點程式 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.2.1 真實資料 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.2.2 模擬資料 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
5 結論與結語
參考文獻
A 附錄
A.1 附錄一 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
A.2 附錄二. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
A.3 附錄三 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

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