| dc.contributor.advisor | 陳麗霞 | zh_TW |
| dc.contributor.author (Authors) | 黃惠芬 | zh_TW |
| dc.creator (作者) | 黃惠芬 | zh_TW |
| dc.date (日期) | 2006 | en_US |
| dc.date.accessioned | 2009-09-14 | - |
| dc.date.available | 2009-09-14 | - |
| dc.date.issued (上傳時間) | 2009-09-14 | - |
| dc.identifier (Other Identifiers) | G0094354012 | en_US |
| dc.identifier.uri (URI) | https://nccur.lib.nccu.edu.tw/handle/140.119/30916 | - |
| dc.description (描述) | 碩士 | zh_TW |
| dc.description (描述) | 國立政治大學 | zh_TW |
| dc.description (描述) | 統計研究所 | zh_TW |
| dc.description (描述) | 94354012 | zh_TW |
| dc.description (描述) | 95 | zh_TW |
| dc.description.abstract (摘要) | 再發事件資料常見於醫學、工業、財經、社會等等領域中，對再發資料分析研究時，我們往往無法確知再發事件發生的時間或是發生次數的分配。因此，本論文探討的是分析再發事件的無母數方法，包括Nelson提出的平均累積函數(mean cumulative function)估計量，及Wang、Chiang與Huang介紹的發生率(occurrence rate)之核函數(kernel function)估計量。 就平均累積函數估計量來說，藉由Nelson導出的變異數及自然(naive)變異數，可分別求得平均累積函數的區間估計。本文利用靴環法(bootstrap)計算出平均累積函數在不同時點的變異數，再與Nelson變異數及自然變異數比較，結果顯示Nelson變異數與靴環法算出的變異數較接近。因此，應依據Nelson變異數建構出事件發生累積次數之漸近信賴區間。 本論文亦介紹了兩個或多個母體的平均累積函數的比較方法，包含固定時點之比較與整條曲線之比較。在固定時點之下，比較方法分別為平均累積函數成對差異之漸近信賴區間及靴環信賴區間、變異數分析比較法，與排列檢定法；而整條曲線比較方法包含：類似 統計量、Lawless-Nadeau檢定。這些方法應用在本論文所採之實證資料時，所得到的檢定結論是一致的。 | zh_TW |
| dc.description.abstract (摘要) | Recurrent event data arise in many fields, such as medicine, industry, economics, social sciences and so on. When studying recurrent event data, we usually don’t know the exact joint or marginal distributions of the occurrence times or the number of events over time. So, in this article we talk about some nonparametric methods, such as the mean cumulative function (MCF) discussed by Nelson, and kernel estimation of the rate function introduced by Wang, Chiang and Huang. As to the estimator of MCF, we can compute the confidence interval by Nelson’s variance and naive variance. We use bootstrap method to compare the performance of Nelson variance of the estimated MCF and naive variance of the estimated MCF. The results show that Nelson variance is better than naive variance, so we should construct the confidence limits for the MCF by Nelson’s variance except when only grouped data are available. We also introduce methods for comparing MCFs, including pointwise comparison of MCFs and comparison of entire MCFs. Methods for pointwise comparing MCFs include approximate confidence limits for difference between two MCFs, analysis-of-variance comparison, permutation test, and bootstrap’s confidence limits for difference between two MCFs. Methods for comparing entire MCFs include a statistic like Hoetelling’s , and Lawless-Nadeau test. Finally, all approaches are employed to analyze a real data, and the conclusions concordance with each other. | en_US |
| dc.description.tableofcontents | 第一章 緒論................................1 第一節 研究動機與目的.......................1 第二節 文獻回顧 ...........................2 第三節 論文架構 ...........................4 第二章 再發事件無母數估計 ...................5 第一節 平均累積函數.........................5 2-1-1 平均累積函數及估計......................5 2-1-2 平均累積函數之變異數估計.................9 第二節 發生率..............................15 2-2-1 發生率函數及平滑估計量..................15 2-2-2 發生率函數之變異數估計..................18 第三節 利用靴環法估計MCF 變異數...............21 第四節 兩組樣本之比較方法.....................25 2-4-1 固定時點之比較方法......................25 2-4-2 整條平均累積函數之比較方法...............26 第三章 實證分析.............................29 第一節 估計量之比較...........................29 3-1-1 與MCF有關的估計量之比較.................29 3-1-2 再發率與發生率估計結果之比較.............34 3-1-3 MCF與CORF估計結果之比較.................38 第二節 三組樣本之比較.........................40 3-2-1 固定時點之比較.........................41 3-2-2 整條平均累積函數之比較..................47 第四章 結論.................................50 參考文獻.....................................52 圖表目錄 圖2-1 再發事件累積次數的離散分配..........................6 圖2-2 MCF估計值.........................................8 圖 3-1 各時點的MCF之95%漸近Nelson與自然區間估計...........29 圖 3-2 Nelson與自然變異數估計............................30 圖 3-3 MCF估計量抽人靴環法的在再抽樣結果...................31 圖 3-4 MCF估計量抽時間靴環法再抽樣結果.....................31 圖 3-5 MCF估計量分散靴環法再抽樣結果.......................31 圖 3-6 三種靴環法估計出MCF之比較..........................32 圖 3-7 MCF估計量之變異數比較..............................33 圖 3-8 四種 區間估計之比較................................34 圖 3-9 依區間ORF核函數估計(h在整個歷程相同)............... 36 圖 3-10 依區間ORF核函數估計(h在各時間不同) ................36 圖 3-11 依區間ORF核函數估計與 比較(h固定) ................37 圖 3-12 依區間ORF核函數估計與 比較(h不固定)................37 圖 3-13 依時點之ORF估計與 比較(h不固定)....................37 圖 3-14 依時點之ORF估計與 比較(h不固定)....................37 圖 3-15 未修勻之ORF估計與 比較............................38 圖 3-16 依區間修勻CORF估計結果與MCF比較(h不固定)...........39 圖 3-17 依區間修勻CORF估計結果與MCF比較(h固定).............39 圖 3-18 三種治療方法的估計腫瘤平均累積次數..................40 圖 3-19 安慰劑與Thiotepa腫瘤平均累積次數差異的漸近95%信賴區間 .................................................41 圖 3-20 維他命B6與Thiotepa腫瘤平均累積次數差異的漸近95%信賴區間 .................................................42 表 3-1 安慰劑與Thiotepa MCF差異檢定之Q統計量...............42 表 3-2 維他命B6與Thiotepa MCF的差異檢定之Q統計量...........43 圖 3-21 抽人靴環法所建立安慰劑與Thiotepa腫瘤平均累積次數差異的信 賴區. ...................................................45 圖 3-22 抽人靴環法所建立維他命B6與Thiotepa腫瘤平均累積次數差異的信賴區間 .................................................45 圖 3-23 排列檢定估計之安慰劑與Thiotepa的腫瘤平均累積次數差異的95%信賴區間 .................................................46 圖 3-24 排列檢定估計之維他命B6與Thiotepa的腫瘤平均累積次數差異的95%信賴區間...............................................47 | zh_TW |
| dc.language.iso | en_US | - |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#G0094354012 | en_US |
| dc.subject (關鍵詞) | 再發事件 | zh_TW |
| dc.subject (關鍵詞) | 平均累積函數 | zh_TW |
| dc.subject (關鍵詞) | 發生率函數 | zh_TW |
| dc.subject (關鍵詞) | 核函數 | zh_TW |
| dc.subject (關鍵詞) | 靴環法 | zh_TW |
| dc.subject (關鍵詞) | 排列檢定 | zh_TW |
| dc.subject (關鍵詞) | 變異數分析比較法 | zh_TW |
| dc.subject (關鍵詞) | Lawless-Nadeau檢定 | zh_TW |
| dc.subject (關鍵詞) | 類似 Hoetelling`s T square | zh_TW |
| dc.subject (關鍵詞) | recurrent events | en_US |
| dc.subject (關鍵詞) | mean cumulative function | en_US |
| dc.subject (關鍵詞) | rate function | en_US |
| dc.subject (關鍵詞) | bootstrap | en_US |
| dc.subject (關鍵詞) | permutation test | en_US |
| dc.subject (關鍵詞) | analysis-of-variance comparison | en_US |
| dc.subject (關鍵詞) | Lawless-Nadeau test | en_US |
| dc.subject (關鍵詞) | statistic like Hoetelling`s T square | en_US |
| dc.subject (關鍵詞) | kernel estimation | en_US |
| dc.title (題名) | 再發事件資料之無母數分析 | zh_TW |
| dc.type (資料類型) | thesis | en |
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