臺灣博碩士論文加值系統

平均餘命(residual lifetime)或餘命的分位數(quantile)的估計在癌症醫學研究越來越重要，因為它提供了比風險函數或存活機率在治療效果上更直覺的訊息。在醫學上，經常利用多重比較法(multiple comparison procedure)評估多個處理效應的異同。因聯合信賴域不但能夠進行檢定，能有提供多個處理之間差異的範圍。因此，本文針對多組右設限存活資料，分別根據無母數推論方法(nonparametric method)及經驗概似比檢定(empirical likelihood ratio test)統計量建立各處理組與對照組的餘命分位數比值的聯合信賴域。接著透過模擬方法研究兩方法所建立的聯合信賴域在覆蓋機率(coverage probability)及平均覆蓋面積(coverage area)的表現。最後，引用實際資料說明此方法的應用。

關鍵詞：設限存活資料；信賴域；最小距離統計量；多重比較；餘命分位數

The estimation of mean residual lifetime or quantile residual lifetime is becoming more critical in cancer research, since it provides patients and physicians with information about the efficacy of the treatment therapies in a more straightforward way using the hazard function or probability of survival. In medical study, the multiple comparison procedures are the commonly used multiple decisions that assess the differences of the effects for several treatment groups, simultaneously. Because the simultaneous confidence regions maybe used for hypotheses testing, as well as providing the information about magnitudes of the differences between the survival indices of each treatment group. In this project for censored survival data, we consider the construction of the simultaneous confidence regions for the ratios of quantile residual lifetimes between the treatment group and the control group based on the nonparametric method and the empirical likelihood ratio tests. The performance of the associated coverage probability and the average coverage area will be investigated via a simulation study. The use of the proposed procedure will be illustrated using real data sets.

Keywords : censored survival data; confidence region; minimum dispersion statistic; multiple comparison; quantile residual lifetime

目錄
Abstract
摘要
背景及研究目的 P.1~2
第二章 文獻回顧
2.1無母數推論 P.3~6
2.2經驗概似比推論 P.6~8
第三章 多組餘命分位數比值的聯合信賴域
3.1無母數聯合信賴域 P.9~12
3.2經驗概似比聯合信賴域 P.12~14
第四章 模擬研究
4.1模擬方法 P.15~18
4.2模擬結果 P.19~23
第五章 資料分析
5.1資料介紹 P.24~25
5.2資料分析
5.2.1整體的治療效果分析 P.26~27
5.2.2不同性別之下治療方式的差異 P.27~31
5.2.3不同年齡之下治療方式的差異 P.31~35
5.2.4大腸癌侵犯淋巴結個數來看治療方式的差異 P.36~40
第六章 結論與建議 P.41
參考文獻 P.42~43
附錄P.44~46

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