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系統識別號 U0002-1507201211374600
中文論文名稱 現狀數據在比例勝算比治癒模型下之分析
英文論文名稱 Analysis of Current Status Data under Proportional Odds Cure Model
校院名稱 淡江大學
系所名稱(中) 數學學系碩士班
系所名稱(英) Department of Mathematics
學年度 100
學期 2
出版年 101
研究生中文姓名 劉慶鴻
研究生英文姓名 Ching-Hung Liu
學號 698190088
學位類別 碩士
語文別 中文
口試日期 2012-06-20
論文頁數 30頁
口試委員 指導教授-溫啟仲
委員-黃逸輝
委員-吳裕振
中文關鍵字 白內障  現狀數據  比例勝算比治癒模型 
英文關鍵字 Cataract  current status data  proportional odds cure model 
學科別分類 學科別自然科學數學
中文摘要 具有治癒子群的存活資料在右設限資料上已經被廣泛地研究,但較少對於現狀數據的研究。 我們的研究動機來自於一個關於白內障資料的橫斷面研究,其中白內障的發生是現狀設限的,且似乎有一個比例的研究對象似乎不會罹患白內障。 我們利用最大概似法分析具有治癒子群的現狀數據。 一些基於具有治癒子群之現狀數據的迴歸方法已被建立 (Kuk and Chen (1992); Tsodikov (2003); Lu and Ying (2004)),但皆是在混合型治癒模型 (Berkson and Gage (1952)) 之下。 相對的,我們考慮比例勝算比治癒模型 (Zeng et al. (2006)),屬於非混合治癒模型。 為了確保模型參數的可辨識性,我們假設所有右設限觀測者中設限時間最大的研究對象為治癒。 我們進行模擬試驗及白內障資料的分析來評估我們所提出的統計方法。
英文摘要 Survival data with a cured subgroup have been extensively studied in the context of right-censored data but less for current status data. Motivated by the cataract dataset from a cross-sectional study, where the occurrences of cataract was current status censored and a fraction of subjects seemed not susceptible to cataract, we describe a maximum likelihood method for analyzing current status data with a cured subgroup. Some regression approaches based on current status data with a cured subgroup have been developed, Kuk and Chen (1992); Tsodikov (2003); Lu and Ying (2004), but all under two-component mixture cure models (Berkson and Gage (1952)). Alternatively, we consider the proportional odds cure model (Zeng et al (2006)), a non-mixture model, in this study. To ensure identifiability of the model, in the estimation, we assume the study unit who has the largest censoring time among all right censored observations is cured. We evaluate the proposed method through simulation studies and illustrate it with the cataract data.
論文目次 目錄
1 緒論 1
2 模型與資料介紹 4
2.1 模型介紹 4
2.2 資料介紹 7
3 估計方法 8
3.1 最大概似估計法 8
3.2 變異數估計 9
4 模擬試驗 11
5 實例分析 21
6 結論 23
參考文獻 24
附錄一 25
附錄二 26
附錄三 28
附錄四 30

表目錄
1 參數參數(α,β,γ_1,γ_2)=(1,1,1,1)之四組模擬樣本在有無假定治癒者下之估計比較 14
2 參數(α,β,γ_1,γ_2)=(1,1,1,1)(治癒率=27%), 檢查時間C∼U(0,1)之模擬結果 15
3 參數(α,β,γ_1,γ_2)=(1,1,1,1)(治癒率=27%), 檢查時間C∼U(0,4)之模擬結果 15
4 參數(α,β,γ_1,γ_2)=(-1,1,1,1)(治癒率=73%), 檢查時間C∼U(0,1)之模擬結果 16
5 參數(α,β,γ_1,γ_2)=(-1,1,1,1)(治癒率=73%), 檢查時間C∼U(0,4)之模擬結果 16
6 白內障資料的摘要 21
7 白內障資料的分析結果 22
8 不同潛在因子個數 N 的分布(期望值E(N)=θ) 所對應的母體存活函數S_pop(t) 25

圖目錄
1 白內障資料根據糖尿病分組的存活函數估計 2
2 模擬試驗(α,β,γ_1,γ_2)=(1,1,1,1)(治癒率=27%), C∼U(0,4), n=900之標準化估計對N(0,1)之 Q-Q Plot 17
3 模擬試驗(α,β,γ_1,γ_2)=(-1,1,1,1)(治癒率=73%), C∼U(0,4), n=900之標準化估計對N(0,1)之 Q-Q Plot 18
4 模擬試驗(α,β,γ_1,γ_2)=(1,1,1,1)(治癒率=27%), C∼U(0,4), n=900之參數估計盒形圖 19
5 模擬試驗(α,β,γ_1,γ_2)=(-1,1,1,1)(治癒率=73%), C∼U(0,4), n=900之參數估計盒形圖 19
6 模擬試驗(α,β,γ_1,γ_2)=(1,1,1,1)(治癒率=27%), C∼U(0,4), n=900之散佈圖 20
7 模擬試驗(α,β,γ_1,γ_2)=(-1,1,1,1)(治癒率=73%), C∼U(0,4), n=900之散佈圖 20
8 罹患糖尿病與否之白內障存活函數估計 22
參考文獻 Arag´on, J. and Eberly, D. (1992), On convergence of convex minorant algorithms for distribution estimation with interval-censored data, Journal of Computational and Graphical Statistics 1, 129-140.
Berkson, J. and Gage, R. P. (1952), Survival curve for cancer patients following treatment, Journal of the American Statistical Association 47, 501-515.
Chen, M. H., Ibrahim, J. G. and Sinha, D. (1999), A new Bayesian model for survival data with a surviving fraction, Journal of the American Statistical Association 94, 909-919.
Cooner, F., Banerjee, S., Carlin, B. P. and Sinha, D. (2007), Flexible cure rate modeling under latent activation schemes, Journal of the American Statistical Association 102, 560-572.
Farewell, V. T. (1982), The use of mixture models for the analysis of survival data with longterm survivors, Biometrics 39, 1041-1046.
Farewell, V. T. (1986), Mixture models in survival analysis: Are they worth the risk? The Canadian Journal of Statistics 14, 257-262.
Gu, Y., Sinha, D. and Banerjee, S. (2011), Analysis of cure rate survival data under proportional odds model, Lifetime Data Analysis 17, 123-134.
Kuk, A. Y. C. and Chen, C.-H. (1992), A mixture model combining logistic regression with proportional hazards regression, Biometrika 79, 531-541.
Lu, W. and Ying, Z. (2004), On semiparametric transformation cure models, Biometrika 91, 331-343.
Maller, R. and Zhou, X. (1996), Survival analysis with long-term survivors, New York, Wiley.
Ortega, E. M.M., Cordeiro, G. M. and Kattan, M. W. (2012), The negative binomial-beta Weibull regression model to predict the cure of prostate cancer, Journal of Applied Statistics 39, 1191-1210.
Tsodikov, A. D., Ibrahim, J. G. and Takovlev, A. Y. (2003), Estimating cure rates from survival data: An alternative to two-component mixture models, Journal of the American Statistical Association 98, 1063-1078.
Takovlev, A. Y. and Tsodikov, A. D. (1996), Stochastic models of tumor latency and their biostatistical applications, Hackensack, NY: World Scientific.
Tsodikov, A. D. (1998), A proportional hazards model taking account of long-term survivors, Biometrics 54, 1508-1516.
Wen, C. C. and Chen, Y. H., Nonparametric maximum likelihood analysis of clustered current status data with the gamma-frailty Cox model, Computational Statistics and Data Analysis 55, 1053-1060.
Zeng, D., Yin, G. and Ibrahim, J. G. (2006), Semiparametric transformation models for survival data with a cure fraction, Journal of the American Statistical Association 101, 670-684.
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