| dc.contributor.advisor | 陳麗霞 | zh_TW |
| dc.contributor.advisor | Chen,Li-Shya | en_US |
| dc.contributor.author (Authors) | 陳志豪 | zh_TW |
| dc.contributor.author (Authors) | Chen,Chih-Hao | en_US |
| dc.creator (作者) | 陳志豪 | zh_TW |
| dc.creator (作者) | Chen,Chih-Hao | en_US |
| dc.date (日期) | 2004 | 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) | G0923540061 | en_US |
| dc.identifier.uri (URI) | https://nccur.lib.nccu.edu.tw/handle/140.119/30940 | - |
| 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) | 92354006 | zh_TW |
| dc.description (描述) | 93 | zh_TW |
| dc.description.abstract (摘要) | 共變數的值會隨著時間而改變時，我們稱之為時間相依之共變數。時間相依之共變數往往具有重複測量的特性，也是長期資料裡最常見到的一種共變數形態；在對時間相依之共變數進行重複測量時，可以考慮每次測量的間隔時間相同或是間隔時間不同兩種情形。在間隔時間相同的情形下，我們可以忽略間隔時間所產生的效應，利用分組的Cox模式或是合併的羅吉斯迴歸模式來分析，而合併的羅吉斯迴歸是一種把資料視為“對象 時間單位”形態的分析方法；此外，分組的Cox模式和合併的羅吉斯迴歸模式也都可以用來預測存活機率。在某些條件滿足下，D’Agostino等六人在1990年已經證明出這兩個模式所得到的結果會很接近。 當間隔時間為不同時，我們可以用計數過程下的Cox模式來分析，在計數過程下的Cox模式中，資料是以“對象 區間”的形態來分析。2001年Bruijne等人則是建議把間隔時間也視為一個時間相依之共變數，並將其以B-spline函數加至模式中分析；在我們論文的實證分析裡也顯示間隔時間在延伸的Cox模式中的確是個很顯著的時間相依之共變數。延伸的Cox模式為間隔時間不同下的時間相依之共變數提供了另一個分析方法。至於在時間相依之共變數的預測方面，我們是以指數趨勢平滑法來預測其未來時間點的數值；利用預測出來的時間相依之共變數值再搭配延伸的Cox模式即可預測未來的存活機率。 | zh_TW |
| dc.description.abstract (摘要) | It is so called “time-dependent covariates” that the values of covariates change over time. Time-dependent covariates are measured repeatedly and often appear in the longitudinal data. Time-dependent covariates can be regularly or irregularly measured. In the regular case, we can ignore the TEL(time elapsed since last observation) effect and the grouped Cox model or the pooled logistic regression model is employed to anlalyze. The pooled logistic regression is an analytic method using the“person-period”approach. The grouped Cox model and the pooled logistic regression model also can be used to predict survival probablity. D’Agostino et al. (1990) had proved that pooled logistic regression model is asymptotically equivalent to the grouped Cox model. If time-dependent covariates are observed irregularly, Cox model under counting process may be taken into account. Before making the prediction we must turn the original data into“person-interval”form, and this data form is also suitable for the prediction of grouped Cox model in regular measurements. de Bruijne et al.(2001) first considered TEL as a time-dependent covariate and used B-spline function to model it in their proposed extended Cox model. We also show that TEL is a very significant time-dependent covariate in our paper. The extended Cox model provided an alternative for the irregularly measured time-dependent covariates. On the other hand, we use exponential smoothing with trend to predict the future value of time-dependent covariates. Using the predicted values with the extended Cox model then we can predict survival probablity. | 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 定期測量下的模式配置與預測 5 第一節 有時間相依之共變數下的Cox模式 5 2-1-1 連續型的Cox模式 5 2-1-2 分組的Cox模式 7 第二節 合併的羅吉斯迴規模式 9 2-2-1 PRO法與合併的羅吉斯迴歸模式 9 2-2-2 合併的羅吉斯迴歸之數學形式 11 第三章 不定期測量下的模式配置與預測 12 第一節 計數過程下的Cox模式 12 3-1-1 計數過程簡介 12 3-1-2 Cox模式在計數過程下的部分概似函數 14 第二節 有時間相依之共變數下的延伸Cox模式 16 3-2-1 延伸的Cox模式 16 3-2-2 B-spline曲線之介紹 18 3-2-3 存活機率之預測 19 第三節 時間相依之共變數的預測 21 3-3-1 核密度估計 21 3-3-2 核迴歸 22 3-3-3 局部多項式估計 24 3-3-4 指數趨勢平滑法 26 第四章 實例分析 27 第一節 定期測量下的模式配置與預測 27 第二節 不定期測量下的模式配置與預測 34 第五章 結論與建議 42 第一節 結 論 42 第二節 未來研究方向 43 參考文獻 44 附錄 45 | zh_TW |
| dc.language.iso | en_US | - |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#G0923540061 | en_US |
| dc.subject (關鍵詞) | 分組的Cox模式 | zh_TW |
| dc.subject (關鍵詞) | 合併的羅吉斯迴歸模式 | zh_TW |
| dc.subject (關鍵詞) | 計數過程 | zh_TW |
| dc.subject (關鍵詞) | 間隔時間 | zh_TW |
| dc.subject (關鍵詞) | B-spline函數 | zh_TW |
| dc.subject (關鍵詞) | 延伸的Cox模式 | zh_TW |
| dc.subject (關鍵詞) | 指數趨勢平滑法 | zh_TW |
| dc.subject (關鍵詞) | Grouped Cox model | en_US |
| dc.subject (關鍵詞) | Pooled logistic regression | en_US |
| dc.subject (關鍵詞) | Counting process | en_US |
| dc.subject (關鍵詞) | TEL | en_US |
| dc.subject (關鍵詞) | B-spline function | en_US |
| dc.subject (關鍵詞) | Extended Cox model | en_US |
| dc.subject (關鍵詞) | Exponential smoothing with trend | en_US |
| dc.title (題名) | Cox模式有時間相依共變數下預測問題之研究 | zh_TW |
| dc.type (資料類型) | thesis | en |
| dc.relation.reference (參考文獻) | Allison,P.D. (1995). Survival Analysis Using the SAS System. SAS Publishing. | zh_TW |
| dc.relation.reference (參考文獻) | D’Agostino,R.B., Lee,M.L.T., Belander,A.J., Cupples,L.A., Anderson,K., and Kannel,W.B. (1990). Relation of pooled logistic regression to time dependent Cox regression analysis:the Framingham heart study. Statistics in Medicine 9,1501-1515. | zh_TW |
| dc.relation.reference (參考文獻) | de Bruijne,M.H.J., Cessie,S.L., Nelemans,H.C., and Van Houwelingen,H.C. (2001). On the use of Cox regression in the presence of an irregularly observed time-dependent covariate. Statistics in Medicine 20,3817-3829. | zh_TW |
| dc.relation.reference (參考文獻) | de Bruijne,M.H.J., Sijpkens,Y.W., Paul,L.C., Westendorp,R.G., van Houwelingen,H.C., and Zwinderman,A.H. (2003). Predicting kidney graft failure using time-dependent renal function covariates. Journal of Clinical Epidemiology 56,85-100. | zh_TW |
| dc.relation.reference (參考文獻) | Eilers,P.H.C. and Marx,B.D. (1996). Flexible smoothing with B-splines and penalties. Statistical Science 2,89-121. | zh_TW |
| dc.relation.reference (參考文獻) | Fleming,T.R.and Harrington,D.P. (1991). Counting Process and Survival Analysis. John Wiley and Sons,Inc.,New York. | zh_TW |
| dc.relation.reference (參考文獻) | Simonoff,J.S. (1996). Smoothing Methods in Statistics.Springer. | zh_TW |
| dc.relation.reference (參考文獻) | Kalbfleisch,J.D. and Prentice,R.L. (1980). The Statistical Analysis of Failure Time Data. John Wiley and Sons,Inc.,New York. | zh_TW |
| dc.relation.reference (參考文獻) | Therneau,T.M. and Grambsch,P.M. (2000). Modeling Survival Data:Extending the Cox Model. Springer. | zh_TW |
