比例風險假設檢定之探討

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劉恒秀(Heng-hsiu Liu) 查詢紙本館藏

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統計研究所

論文名稱

比例風險假設檢定之探討
(Discussion on testing proportional hazards assumption)

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摘要(中)

一般而言，存活資料若通過比例風險假設 (proportional hazards assumption)，Cox比例風險模型即為模型配適之最佳選擇，但如此作法是否真的能保證Cox比例風險模型為最佳配適？因此，本研究針對此一疑問，做大量的統計模擬，尋找是否有資料來自於非Cox比例風險模型，但卻可以通過比例風險假設；另一方面，以針對文獻上三種不同方法分別為Schoenfeld殘差檢定 (Schoenfeld residuals te- st)、資料驅動平滑檢定 (Data-driven smooth test) 和分數過程檢定 (score process test)，比較其檢定力之差異以及未通過比例風險假設的比例是否有一定的趨勢存在，再藉由擴充風險模型做模型選擇後的結果比較三種比例風險假設的結果是否一致。我們建議在選擇模型配適資料時，不能只靠比例風險假設的方法，來選擇資料適合的模型。最後，在實例分析的部份，我們使用五筆生物醫學相關的資料來驗證上述所提及的檢定方法所產生的疑問。

摘要(英)

Generally speaking, if the survival data satisfy the proportional hazards, Cox pro- portional hazards model is the best choice of the model fit. However, can we guarantee that Cox proportional hazards model is the best choice under this circumstance? Therefore, focusing on this issue, we do lots of statistical simulation to look for any data deviating from the nonproportional hazards model yet satisfying the proportional hazards assumption. On the other hand, for the three different methods in the literature, namely Schoenfeld residual test, Data-driven smooth test and score process test, we compare the difference with the power of these tests and there is an obvious proportion tendency for those satisfying the proportional hazards assumption. Then through use the Extended hazard model as the more general model, we compare three proportional hazards assumptions and check if the results are consistent. When we choose models to fit the data, we can not solely depend on the three methods to select the appropriate model. Finally, we use five biomedical data sets to illustrate the issue raised.

關鍵字(中)

★ Schoenfeld殘差檢定
★ 資料驅動平滑檢定
★ 分數過程檢定

關鍵字(英)

★ score process test
★ Schoenfeld residuals test
★ Data-driven smooth test

論文目次

中文摘要 i
英文摘要 ..ii
致謝辭 ..iii
目錄 iv
表目錄 ..vi
符號表 viii
第一章緒論 1
第二章統計方法 10
2.1 Schoenfeld 殘差檢定 (Schoenfeld residual test) .. .12
2.2 資料驅動平滑檢定 (Data‐driven smooth test) .. . 13
2.3 分數過程檢定 (Score process test) ..19
第三章統計模擬 23
3.1 模擬方法 ..24
3.1.1 時間獨立共變數 .24
3.1.2 時間相依共變數 .26
3.2 模擬結果 ..29
3.2.1 時間獨立共變數 .29
3.2.2 時間相依共變數 .40
第四章實例研究 45
4.1 舌癌 ..45
4.2 骨髓移植 ..48
4.3 人類後天免疫缺乏病毒 51
4.4 硼中子捕獲療法 .54
4.5 咽喉癌 56
第五章結論與討論 59
參考文獻 61

參考文獻

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指導教授

曾議寬(Yi-Kuan Tseng)

審核日期

2011-6-24

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