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題名 競爭風險下長期存活資料之貝氏分析
Bayesian analysis for long-term survival data作者 蔡佳蓉 貢獻者 陳麗霞
蔡佳蓉關鍵詞 治癒率模式
競爭風險
混合模式
擴充的概似函數
馬可夫鏈蒙地卡羅方法(MCMC)
完全條件後驗分配
Gibbs 抽樣法
條件預測指標(CPO)
對數擬邊際概似函數值(LPML)
cure rate models
competing risks
mixture models
augmented likelihood functions
Markov Chain Monte Carlo method(MCMC)
full conditional posterior distributions
Gibbs samplings
conditional predictive ordinate(CPO)
log of pseudo marginal likelihood(LPML)日期 2009 上傳時間 9-May-2016 15:11:37 (UTC+8) 摘要 當造成失敗的原因不只一種時，若各對象同一時間最多只經歷一種失敗原因，則這些失敗原因稱為競爭風險。然而，有些個體不會失敗或者經過治療之後已痊癒，我們稱這部分的群體為治癒群。本文考慮同時處理競爭風險及治癒率的混合模式，即競爭風險的治癒率模式，亦將解釋變數結合到治癒率、競爭風險的條件失敗機率，或未治癒下競爭風險的條件存活函數中，並以建立在完整資料上之擴充的概似函數為貝氏分析的架構。對於右設限對象則以插補方式決定是否會治癒或會因何種風險而失敗，並推導各參數的完全條件後驗分配及其性質。由於邊際後驗分配的數學形式無法明確呈現，再加上需對右設限者判斷其狀態，所以採用屬於馬可夫鏈蒙地卡羅法的Gibbs抽樣法及適應性拒絕抽樣法(adaptive rejection sampling) ，執行參數之模擬抽樣及設算右設限者之治癒或失敗狀態。實證部分，我們分析Klein and Moeschberger (1997)書中骨髓移植後的血癌病患的資料，並用不同模式之下的參數模擬值計算各對象之條件預測指標(CPO)，換算成各模式的對數擬邊際概似函數值(LPML)，比較不同模式的優劣。
In case that there are more than one possible failure types, if each subject experiences at most one failure type at one time, then these failure types are called competing risks. Moreover, some subjects have been cured or are immune so they never fail, then they are called the cured ones. This dissertation discusses several mixture models containing competing risks and cure rate. Furthermore, covariates are associated with cure rate, conditional failure rate of each risk, or conditional survival function of each risk, and we propose the Bayesian procedure based on the augmented likelihood function of complete data. For right censored subjects, we make use of imputation to determine whether they were cured or failed by which risk and derive full conditional posterior distributions. Since all marginal posterior distributions don’t have closed forms and right censored subjects need to be identified their statuses, we take Gibbs sampling and adaptive rejection sampling of Markov chain Monte Carlo method to simulate parameter values. We illustrate how to conduct Bayesian analysis by using the bone marrow transplant data from the book written by Klein and Moeschberger (1997). To do model selection, we compute the conditional predictive ordinate(CPO) for every subject under each model, then the goodness is determined by the comparing the value of log of pseudo marginal likelihood (LMPL) of each model.參考文獻 Boag, J.W. (1949). Maximum likelihood estimates of the proportion of patients cured by cancer therapy. Journal of the Royal Statistical Society 11, 15-53. Berkson, J. and Gage, R. P. (1952). Survival curve for cancer patients following treatment. Journal of the American Statistical Association 47, 501-515. Betensky, R. A. and Schoenfeld, D. A. (2001). Nonparametric estimation in a cure model with random cure times. Biometrics 57, 282-286. Casella, G. and George, E. I. (1992). Explaining the Gibbs sampler. The American Statistician 46, 167-174. Choa, E. C.(1994). A comparison of models including possibility of cure for survival data. Ph.D. dissertation, University of Michigan, Ann Arbor. Choa, E. C. (1998). Gibbs Sampling for long-term survival data with competing risks. Biometrics 54, 350-366. Cantor, A. B. and Shuster, J. J. (1992). Parametric versus non-parametric methods for estimating cure rates based on censored survival data. Statistics in Medicine 11, 931-937. Farewell, V. T. (1977). A model for a binary variable with time-censored observations. Biometrika 64, 43-46 Farewell, V. T. (1982). The use of mixture models for the analysis of survival data with long-term survivors. Biometrics 38, 1041-1046. Farewell, V. T. (1986). Mixture models in survival analysis: Are they worth the risk? The Canadian Journal of Statistics 14, 257-262. Geman, S. and Geman, D. (1984). Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence 6, 721-741. Gelfand, A. E., Smith, A. F. M. (1990). Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association 87, 523-532. Gelfand, A. E. and Dey, D. K. (1994). Bayesian model choice: asymptotics and exact calculations. Journal of the Royal Statistical Society, Series B 56, 501-514. Ghitany, M. E. and Maller, R. A. (1992). Asymptotic results for exponential mixture models with long-term survivors. Statistics 23, 321-336. Ghitany, M. E., Maller, R. A., and Zhou, S. (1994). Exponential mixture models with long-term survivors and covariates. Journal of Multivariate analysis 49, 218-241. Gilks, W. R., and Wild, P. (1992). Adaptive rejection sampling for Gibbs sampling. Applied Statistics 41, 337-348. Greenhouse, J. B. and Wolfe, R. A. (1984). A competing risks derivation of a mixture model for the analysis of survival data. Communications in Statistics—Theeory and Method 13, 3133-3154. Kalbfleisch, J. D. and Prentice, R. L. (1980). The statistical Analysis of Failure Time Data. New York: Wiley Kuk, A. Y. C. and Chen, C. (1992). A mixture model combining logistic regression with proportional hazards regression. Biometrika 79, 531-541. Larson, M. G. and Dinse, G. E. (1985). A mixture model for the regression analysis of competing risks data. Applied Statistics 34, 201-211 Laska, E. M. and Meisner, M. J. (1992). Nonparametric estimation and testing in a cure model. Biometrics 48, 1223-1234. Ng, S. K. and McLachlan, G. J. (2003). An EM-based semi-parametric mixture model approach to the regression analysis of competing-risks data. Peng, Y. and Dear, K. B. G. (2000) A nonparametric miture model for cure rate estimation. Biometrics 56, 237-243. Taylor, J. M. G. (1995). Semi-parametric estimation in failure time mixture models. Biometrics 51, 899-907. 描述 碩士
國立政治大學
統計學系
96354023資料來源 http://thesis.lib.nccu.edu.tw/record/#G0096354023 資料類型 thesis dc.contributor.advisor 陳麗霞 zh_TW dc.contributor.author (Authors) 蔡佳蓉 zh_TW dc.creator (作者) 蔡佳蓉 zh_TW dc.date (日期) 2009 en_US dc.date.accessioned 9-May-2016 15:11:37 (UTC+8) - dc.date.available 9-May-2016 15:11:37 (UTC+8) - dc.date.issued (上傳時間) 9-May-2016 15:11:37 (UTC+8) - dc.identifier (Other Identifiers) G0096354023 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/95123 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 統計學系 zh_TW dc.description (描述) 96354023 zh_TW dc.description.abstract (摘要) 當造成失敗的原因不只一種時，若各對象同一時間最多只經歷一種失敗原因，則這些失敗原因稱為競爭風險。然而，有些個體不會失敗或者經過治療之後已痊癒，我們稱這部分的群體為治癒群。本文考慮同時處理競爭風險及治癒率的混合模式，即競爭風險的治癒率模式，亦將解釋變數結合到治癒率、競爭風險的條件失敗機率，或未治癒下競爭風險的條件存活函數中，並以建立在完整資料上之擴充的概似函數為貝氏分析的架構。對於右設限對象則以插補方式決定是否會治癒或會因何種風險而失敗，並推導各參數的完全條件後驗分配及其性質。由於邊際後驗分配的數學形式無法明確呈現，再加上需對右設限者判斷其狀態，所以採用屬於馬可夫鏈蒙地卡羅法的Gibbs抽樣法及適應性拒絕抽樣法(adaptive rejection sampling) ，執行參數之模擬抽樣及設算右設限者之治癒或失敗狀態。實證部分，我們分析Klein and Moeschberger (1997)書中骨髓移植後的血癌病患的資料，並用不同模式之下的參數模擬值計算各對象之條件預測指標(CPO)，換算成各模式的對數擬邊際概似函數值(LPML)，比較不同模式的優劣。 zh_TW dc.description.abstract (摘要) In case that there are more than one possible failure types, if each subject experiences at most one failure type at one time, then these failure types are called competing risks. Moreover, some subjects have been cured or are immune so they never fail, then they are called the cured ones. This dissertation discusses several mixture models containing competing risks and cure rate. Furthermore, covariates are associated with cure rate, conditional failure rate of each risk, or conditional survival function of each risk, and we propose the Bayesian procedure based on the augmented likelihood function of complete data. For right censored subjects, we make use of imputation to determine whether they were cured or failed by which risk and derive full conditional posterior distributions. Since all marginal posterior distributions don’t have closed forms and right censored subjects need to be identified their statuses, we take Gibbs sampling and adaptive rejection sampling of Markov chain Monte Carlo method to simulate parameter values. We illustrate how to conduct Bayesian analysis by using the bone marrow transplant data from the book written by Klein and Moeschberger (1997). To do model selection, we compute the conditional predictive ordinate(CPO) for every subject under each model, then the goodness is determined by the comparing the value of log of pseudo marginal likelihood (LMPL) of each model. en_US dc.description.tableofcontents 第一章 緖論................................................1 第一節 研究動機.............................................1 第二節 研究目的.............................................1 第三節 文獻探討.............................................2 第四節 本文架構.............................................4 第二章 競爭風險的治癒率模式及貝氏分析..........................5 第一節 競爭風險的治癒率模式...................................5 2.1.1 標準治癒率式.....................................5 2.1.2 競爭風險的治癒率式................................5 2.1.3 概似數..........................................7 第二節 Gibbs抽法............................................8 2.2.1 馬可鏈..........................................8 2.2.2 Gibbs抽法.......................................9 第三節 競爭風險治癒率模式的貝氏分析...........................10 2.3.1 失敗時間服從Weibull配...........................10 2.3.2 治癒率及條件失敗率為邏輯斯迴歸式..................12 2.3.3 競爭風險為Weibull迴歸式..........................15 第三章 實證分析............................................18 第一節 失敗時間為Weibull分配的治癒率模式之貝氏析..............19 第二節 治癒率及條件失敗率為邏輯斯迴歸模式的治癒率模式之貝氏分析..23 第三節 模式比較............................................33 第四章 結論與建議...........................................35 參考文獻...................................................37 zh_TW dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0096354023 en_US dc.subject (關鍵詞) 治癒率模式 zh_TW dc.subject (關鍵詞) 競爭風險 zh_TW dc.subject (關鍵詞) 混合模式 zh_TW dc.subject (關鍵詞) 擴充的概似函數 zh_TW dc.subject (關鍵詞) 馬可夫鏈蒙地卡羅方法(MCMC) zh_TW dc.subject (關鍵詞) 完全條件後驗分配 zh_TW dc.subject (關鍵詞) Gibbs 抽樣法 zh_TW dc.subject (關鍵詞) 條件預測指標(CPO) zh_TW dc.subject (關鍵詞) 對數擬邊際概似函數值(LPML) zh_TW dc.subject (關鍵詞) cure rate models en_US dc.subject (關鍵詞) competing risks en_US dc.subject (關鍵詞) mixture models en_US dc.subject (關鍵詞) augmented likelihood functions en_US dc.subject (關鍵詞) Markov Chain Monte Carlo method(MCMC) en_US dc.subject (關鍵詞) full conditional posterior distributions en_US dc.subject (關鍵詞) Gibbs samplings en_US dc.subject (關鍵詞) conditional predictive ordinate(CPO) en_US dc.subject (關鍵詞) log of pseudo marginal likelihood(LPML) en_US dc.title (題名) 競爭風險下長期存活資料之貝氏分析 zh_TW dc.title (題名) Bayesian analysis for long-term survival data en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) Boag, J.W. (1949). Maximum likelihood estimates of the proportion of patients cured by cancer therapy. Journal of the Royal Statistical Society 11, 15-53. Berkson, J. and Gage, R. P. (1952). Survival curve for cancer patients following treatment. Journal of the American Statistical Association 47, 501-515. Betensky, R. A. and Schoenfeld, D. A. (2001). Nonparametric estimation in a cure model with random cure times. Biometrics 57, 282-286. Casella, G. and George, E. I. (1992). Explaining the Gibbs sampler. The American Statistician 46, 167-174. Choa, E. C.(1994). A comparison of models including possibility of cure for survival data. Ph.D. dissertation, University of Michigan, Ann Arbor. Choa, E. C. (1998). Gibbs Sampling for long-term survival data with competing risks. Biometrics 54, 350-366. Cantor, A. B. and Shuster, J. J. (1992). Parametric versus non-parametric methods for estimating cure rates based on censored survival data. Statistics in Medicine 11, 931-937. Farewell, V. T. (1977). A model for a binary variable with time-censored observations. Biometrika 64, 43-46 Farewell, V. T. (1982). The use of mixture models for the analysis of survival data with long-term survivors. Biometrics 38, 1041-1046. Farewell, V. T. (1986). Mixture models in survival analysis: Are they worth the risk? The Canadian Journal of Statistics 14, 257-262. Geman, S. and Geman, D. (1984). Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence 6, 721-741. Gelfand, A. E., Smith, A. F. M. (1990). Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association 87, 523-532. Gelfand, A. E. and Dey, D. K. (1994). Bayesian model choice: asymptotics and exact calculations. Journal of the Royal Statistical Society, Series B 56, 501-514. Ghitany, M. E. and Maller, R. A. (1992). Asymptotic results for exponential mixture models with long-term survivors. Statistics 23, 321-336. Ghitany, M. E., Maller, R. A., and Zhou, S. (1994). Exponential mixture models with long-term survivors and covariates. Journal of Multivariate analysis 49, 218-241. Gilks, W. R., and Wild, P. (1992). Adaptive rejection sampling for Gibbs sampling. Applied Statistics 41, 337-348. Greenhouse, J. B. and Wolfe, R. A. (1984). A competing risks derivation of a mixture model for the analysis of survival data. Communications in Statistics—Theeory and Method 13, 3133-3154. Kalbfleisch, J. D. and Prentice, R. L. (1980). The statistical Analysis of Failure Time Data. New York: Wiley Kuk, A. Y. C. and Chen, C. (1992). A mixture model combining logistic regression with proportional hazards regression. Biometrika 79, 531-541. Larson, M. G. and Dinse, G. E. (1985). A mixture model for the regression analysis of competing risks data. Applied Statistics 34, 201-211 Laska, E. M. and Meisner, M. J. (1992). Nonparametric estimation and testing in a cure model. Biometrics 48, 1223-1234. Ng, S. K. and McLachlan, G. J. (2003). An EM-based semi-parametric mixture model approach to the regression analysis of competing-risks data. Peng, Y. and Dear, K. B. G. (2000) A nonparametric miture model for cure rate estimation. Biometrics 56, 237-243. Taylor, J. M. G. (1995). Semi-parametric estimation in failure time mixture models. Biometrics 51, 899-907. zh_TW
