臺灣博碩士論文加值系統

近年來存活分析應用於各領域中，所欲探討的事件並不一定會發生，且所觀察到的存活時間並不一定為連續型。當個體不會發生所欲探討的事件時，稱此個體為治癒個體。此外，當每一個個體所提供的存活資料為兩筆以上時，稱此個體內的存活資料為一集群資料，且同一集群內的存活資料具有相依性。但目前尚未有學者對集群離散存活資料於治癒模式下提供參數估計方法，所以本論文針對集群離散存活資料，將應用Yu和Peng (2008)所使用的邊際方法，求Zhao和Zhou (2008)所推導出非等比例治癒模式中參數的估計量。接著以模擬的方式，驗證參數估計量之一致性，且在不同設限比例與不同集群數下，探討參數估計量之表現。最後，以非等比例治癒模型探討植牙資料，利用邊際方法求得參數的估計量，以探討影響植牙發生併發症的因素。

Clustered survival data with a cure fraction arise naturally from biomedicine, econometrics and sociology studies. The mixture cure rate models have been well developed for univariate or multivariate (or clustered) continuous right censored data. When the correlation structure within clusters is not of interest, Yu and Peng (2008) used a marginal regression approach constructed estimating equations for estimating the parameters in mixture cure rate models.
Recently, Zhao and Zhou (2008) proposed discrete-time survival models with long-term survivors (cured individuals) for univariate grouped or discrete-time survival data. However, their methodologies can not be directly applied to clustered discrete-time survival data. Therefore, the marginal regression approach is proposed to construct estimating equations based on a non-proportional cure rate model. The accuracy of the estimators is examined by simulation. In addition, the implementation of the marginal approach to a dental implant study is presented.

摘要.........................................I
Abstract.....................................II
表目錄.......................................V
圖目錄.......................................V
第一章 緒論................................1
第二章 文獻探討............................3
第一節 存活函數與風險函數的關係式..........3
第二節 瑕存活函數..........................5
第三節 符號定義............................5
第四節 連續存活時間之治癒模型..............6
第五節 離散存活時間之治癒模型..............9
第三章 集群離散存活資料之非等比例治癒模型..12
第一節 非等比例治癒模型....................12
第二節 推廣的統計方法......................13
第四章 模擬分析............................16
第一節 模擬設計............................16
第二節 模擬比較............................18
第三節 綜合討論............................19
第五章 實例分析............................23
第一節 資料介紹............................23
第二節 分析結果............................24
第六章 結論與建議..........................28
參考文獻.....................................29
附錄A........................................31
附錄B........................................46

1. Boag, J.W., (1949). Maximum likelihood estimates of the proportion of patients cured by cancer therapy. Journal of the Royal statistical Society B 11, 15-44.
2. Cai, J., Shen, Y., (2000). Permutation tests for comparing marginal survival functions with clustered failure time data. Statistics in Medicine 19, 2963-2973.
3. Chandler, R.E., Bate S., (2007). Inference for clustered data using the independence loglikelihood. Biometrika 94, 1-17.
4. Clayton, D., Cuzick J., (1985). Multivariate generalizations of the proportional hazards model(with discussion) Journal of the Royal Statistical, Series A 148, 82-117.
5. Farewell, V.T., (1982). The use of mixture models for the analysis of survival data with long term survivors. Biometrics 38, 1041-1046.
6. Kalbfleisch, J. D., Prentice, R. L.(1980). The statistical analysis of failure time data. Wiley Series In Probability And Mathematical Statistics.
7. Lipsitz, S. R., Dear, K.B.G., Zhao, L., (1994). Jacknife estimators of variance for parameter estimates from estimating equations with applications to clustered survival data. Biometric 50, 842-846.
8. Wen, M.J., Tseng, C.C., Lee, C.K., (2008). Life table analysis for evaluating curative-effect of one-stage non-submerged dental implant in Taiwan. Journal of Data Science 6, 591-599.
9. Yu, B., Peng, Y.(2008). Mixture cure models for multivariate survival data. Computational Statistics & Data Analysis 52, 1524-1532.
10. Zeger, S.L., Liang, K.Y. (1986). Longitudinal data analysis for discrete and continuous outcomes. Biometrics 42, 121-130.
11. Zhao, X., Zhou, X. (2008). Discrete-time survival models with long-term survivors. Statistics in Medicine 27, 1261-1281.