隨機右設限存活資料之下根據聯合信賴域所做的多重比較

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王光祿(KuangLu Wang) 查詢紙本館藏

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論文名稱

隨機右設限存活資料之下根據聯合信賴域所做的多重比較
(Multiple comparison procedures based on simultaneous confidence regions for random right-censored survival data)

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摘要(中)

多重比較法(multiple comparison procedure)是評估多個處理效應異同的多重決策。因聯合信賴域(simultaneous confidence region)除了能夠用作檢定，且可提供各處理組存活差異大小的訊息。所以，本文首先針對不具共變數的隨機右設限(right censored)存活資料，分別建構存活百分位數差異和限制平均壽命差異的聯合信賴域，然後，針對具共變數的隨機右設限存活資料，分別在分層Cox模式(stratified Cox model)和不分層Cox模式(unstratified Cox model)之下，建構條件存活百分位數差異和條件限制平均壽命差異的聯合信賴域。在比例風險和非比例風險二種模式，本文模擬研究上述所提信賴域的覆蓋機率(coverage)及平均距離(averaged absolute deviance)。最後，藉由實例分析說明本文所提各種方法的應用。

摘要(英)

The multiple comparison procedures are multiple decisions that assess the differences of the effects for more than two treatment groups, simultaneously. Because the simultaneous confidence regions can not be only used for the problems of hypotheses testing, but also provide the information about the magnitudes of the differences between the survival indices of each treatment group. Therefore, for random right-censored survival data without covariates, the simultaneous confidence regions for the differences between the survival percentiles and the differences between the restricted mean life times are constructed, firstly. Next, for random right-censored survival data with covariates, the simultaneous confidence regions for the differences between the conditional survival percentiles and the differences between the conditional restricted mean life times are constructed under the stratified Cox model and the unstratified Cox model, respectively. In the simulation study, the cases of proportional hazards and nonproportional hazards are considered, and the coverages and the averaged absolute deviances between the lower bounds and the true parameters are then provided. Finally, the use of the proposed procedures in this article is illustrated with a right-censored survival data

關鍵字(中)

★ 多重比較
★ 右設限
★ 限制平均壽命
★ 存活百分位數
★ 分層比例風險模式

關鍵字(英)

★ multiple comparison
★ right-censored
★ stratified proportional hazards model
★ survival percentile
★ restricted mean life time

論文目次

第一章緒論 ............................................ 1
1.1 研究動機與目的 ...................................... 1
1.2 文獻回顧 ............................................ 4
1.2.2 累積風險函數之Nelson-Aalen估計式的聯合弱收斂 ..... 5
1.2.2 分層Cox模式下基準累積風險函數估計式的聯合弱收斂 .. 6
1.2.3 不分層Cox模式下基準累積風險函數估計式的弱收斂 .... 9
第二章不具共變數之多重比較 .............................. 11
2.1 根據存活百分位數的多重比較 .......................... 11
2.1.1 多個處理組和對照組的比較 ......................... 11
2.1.2 相鄰處理組的比較 ................................. 16
2.2 根據限制平均壽命的多重比較 .......................... 17
2.2.1 多個處理組和對照組的比較 ......................... 17
2.2.2 相鄰處理組的比較 ................................. 20
2.2.3 限制時間點的決定 ................................. 22
第三章具共變數之多重比較 ................................ 24
3.1 分層Cox模式下根據條件存活百分位數的多重比較 ......... 24
3.1.1 多個處理組和對照組的比較 ......................... 24
3.1.2 相鄰處理組的比較 ................................. 29
3.2 分層Cox模式下根據條件限制平均壽命的多重比較 ......... 31
3.2.1 多個處理組和對照組的比較 ......................... 31
3.2.2 相鄰處理組的比較 ................................. 34
3.3 不分層Cox模式下根據條件存活百分位數的多重比較 ....... 36
3.3.1 多個處理組和對照組的比較 ......................... 36
3.3.2 相鄰處理組的比較 ................................. 40
3.4 不分層Cox模式下根據條件限制平均壽命的多重比較 ....... 42
3.4.1 多個處理組和對照組的比較 ......................... 42
3.4.2 相鄰處理組的比較 ................................. 45
第四章模擬研究 .......................................... 48
4.1 不具共變數多重比較之模擬研究 ........................ 48
4.2 具共變數多重比較之模擬研究 .......................... 50
第五章實例分析 .......................................... 53
第六章結語 ............................................ 59
參考文獻 .................................................. 61
附錄 ...................................................... 66

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指導教授

陳玉英(Yuh-Ing Chen)

審核日期

2009-7-13

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