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題名 指數失敗時間模式之條件D-最適設計
Conditional D-optimal Design for Exponential Failure Time Model
作者 葉湘怡
Yeh, Hsiang Yi
貢獻者 丁兆平<br>陳麗霞
Ting, Chao Ping<br>Chen, Li Shya
葉湘怡
Yeh, Hsiang Yi
關鍵詞 指數失敗時間
D-最適設計
穩健分析
穩健效率值
穩健設計
Exponential failure time
D-optimal design
robustness
efficiency
robust design
日期 2013
上傳時間 7-Jul-2014 11:14:07 (UTC+8)
摘要 本論文將最適設計理論應用於指數失敗時間，其期望值之倒數與解釋變數間呈線性關係，且模型中含有兩個解釋變數，一為不可控變數，另一為可控變數。由於在決定最適設計時，實驗單位進入研究的時間及其不可控變數之值均為未知，故必須對此二未知變數給予分配，並將該單位在研究期間內為失敗或設限的可能性納入考慮，方能在各實驗單位進入研究時提供適當之決策。為增進參數估計之效率，本論文採用D-準則，以決定出建立在進入時間及不可控變數之下的條件D-最適設計。本論文並以臨床醫學的例子，在參數值的不同設定下進行電腦計算，除分別找到對應之條件D-最適設計，且進行參數的穩健分析。在本論文考慮的各種情況之下，所得到的穩健效率值均可說明此條件D-最適設計為穩健設計。
Optimal design under the survival analysis models has rarely been considered in the literature. In this article, exponential failure time is assumed and the expected failure time which is inversely related to two explanatory variables, one is controlled variable and the other is uncontrolled variable, through a linear function is considered. Since the time each experimental unit entering into the study is not known, and the corresponding uncontrolled variable is also unknown, assumptions on the distributions of the entering time and the uncontrolled variable are made in order to find optimal designs. Upon entering into the study, an “optimal” decision is made on the experimental unit, and whether the unit will fail or be censored is also considered. To improve efficiency of parameter estimation, D-optimal criterion is employed, and conditional D-optimal designs are found. Under different setting of values of the parameters and with the help of computer programming, conditional D-optimal designs are found and are listed for a clinical medicine problem. Design robustness on unknown parameters is also investigated.
參考文獻 Cook, R.D., and Thibodeau, L.A. (1980). Marginally Restricted D-Optimal Designs. Journal of the American Statistical Association 75, 366-371.
Garcet-Rodríguez, S., López-Fidalgo, J., and Martín-Martín, R. (2008). Some Complexities in Optimal Experimental Designs Introduced by Real Life Problems. Tatra Mountains Mathematical Publications 39, 135-143.
Harville, D.A. (1974). Nearly Optimal Allocation of Experimental Units Using Observed Covariate Values. Technometrics 16, 589-599.
Huang, M.N.L., and Hsu, M.C. (1993). Marginally Restricted Linear-Optimal Designs. Journal of Statistical Planning and Inference 35, 251-266.
Huang, M.N.L., and Chang, H.F. (1995). Marginally Restricted Constrained Optimal Designs. The Indian Journal of Statistics 57, 128-141.
Lee, C.M.-S. (1988). Constrained Optimal Designs. Journal of Statistical Planning and Inference 18, 377-389.
López-Fidalgo, J., and Garcet-Rodríguez, S. (2004). Optimal Experimental Designs when Some Independent Variables are Not Subject to Control. Journal of the American Statistical Association 99, 1190-1199.
López-Fidalgo, J., Rivas-López, M.J., and del Campo, R. (2009). Optimal Designs for Cox Regression. Statistica Neerlandica 63, 135-148.
López-Fidalgo, J., and Garcet-Rodríguez, S. (2011). Optimal Experimental Designs when An Independent Variable is Potentially Censored. Statistics 45, 143-154.
López-Fidalgo, J., and Rivas-López, M.J. (2014). Optimal Experimental Designs for Partial Likelihood Information. Computational Statistics and Data Analysis 71, 859-867.
Martín-Martín, R., Torsney, B., and López-Fidalgo, J. (2007). Construction of Marginally and Conditionally Restricted Designs Using Multiplicative Algorithms. Computational Statistics and Data Analysis 51, 5547-5561.
Nachtsheim, C.J. (1989). On the Design of Experiments in the Presence of Fix Covariates. Journal of Statistical Planning and Inference 22, 203-212.
Varela, G., Cordovilla, R., Jiménez, M.F., and Novoa, N. (2001). Utility of Standardized Exercise Oximetry to Predict Cardiopulmonary Morbidity after Lung Resection. European Journal of Cardio-thoracic Surgery 19, 351-354.
描述 碩士
國立政治大學
統計研究所
98354016
102
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0983540161
資料類型 thesis
dc.contributor.advisor 丁兆平<br>陳麗霞zh_TW
dc.contributor.advisor Ting, Chao Ping<br>Chen, Li Shyaen_US
dc.contributor.author (Authors) 葉湘怡zh_TW
dc.contributor.author (Authors) Yeh, Hsiang Yien_US
dc.creator (作者) 葉湘怡zh_TW
dc.creator (作者) Yeh, Hsiang Yien_US
dc.date (日期) 2013en_US
dc.date.accessioned 7-Jul-2014 11:14:07 (UTC+8)-
dc.date.available 7-Jul-2014 11:14:07 (UTC+8)-
dc.date.issued (上傳時間) 7-Jul-2014 11:14:07 (UTC+8)-
dc.identifier (Other Identifiers) G0983540161en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/67337-
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) 98354016zh_TW
dc.description (描述) 102zh_TW
dc.description.abstract (摘要) 本論文將最適設計理論應用於指數失敗時間，其期望值之倒數與解釋變數間呈線性關係，且模型中含有兩個解釋變數，一為不可控變數，另一為可控變數。由於在決定最適設計時，實驗單位進入研究的時間及其不可控變數之值均為未知，故必須對此二未知變數給予分配，並將該單位在研究期間內為失敗或設限的可能性納入考慮，方能在各實驗單位進入研究時提供適當之決策。為增進參數估計之效率，本論文採用D-準則，以決定出建立在進入時間及不可控變數之下的條件D-最適設計。本論文並以臨床醫學的例子，在參數值的不同設定下進行電腦計算，除分別找到對應之條件D-最適設計，且進行參數的穩健分析。在本論文考慮的各種情況之下，所得到的穩健效率值均可說明此條件D-最適設計為穩健設計。zh_TW
dc.description.abstract (摘要) Optimal design under the survival analysis models has rarely been considered in the literature. In this article, exponential failure time is assumed and the expected failure time which is inversely related to two explanatory variables, one is controlled variable and the other is uncontrolled variable, through a linear function is considered. Since the time each experimental unit entering into the study is not known, and the corresponding uncontrolled variable is also unknown, assumptions on the distributions of the entering time and the uncontrolled variable are made in order to find optimal designs. Upon entering into the study, an “optimal” decision is made on the experimental unit, and whether the unit will fail or be censored is also considered. To improve efficiency of parameter estimation, D-optimal criterion is employed, and conditional D-optimal designs are found. Under different setting of values of the parameters and with the help of computer programming, conditional D-optimal designs are found and are listed for a clinical medicine problem. Design robustness on unknown parameters is also investigated.en_US
dc.description.tableofcontents 第一章 緒論 1
第一節 研究背景與動機 1
第二節 研究問題與目的 3
第三節 論文結構 5
第二章 文獻探討 6
第三章 指數失敗時間模式之條件D-最適設計 10
第一節 模型假設與費雪訊息矩陣 10
第二節 D-最適設計 16
第三節 條件D-最適設計 18
3.1 當 γ("c" )="c" ("3" -"c" )⁄"2" 21
3.2 當 γ("c" )="1" ⁄"2" 26
第四節 模擬結果 31
第四章 結論與未來發展方向 42
參考文獻 44		zh_TW
dc.format.extent 1044065 bytes-
dc.format.mimetype application/pdf-
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0983540161en_US
dc.subject (關鍵詞) 指數失敗時間zh_TW
dc.subject (關鍵詞) D-最適設計zh_TW
dc.subject (關鍵詞) 穩健分析zh_TW
dc.subject (關鍵詞) 穩健效率值zh_TW
dc.subject (關鍵詞) 穩健設計zh_TW
dc.subject (關鍵詞) Exponential failure timeen_US
dc.subject (關鍵詞) D-optimal designen_US
dc.subject (關鍵詞) robustnessen_US
dc.subject (關鍵詞) efficiencyen_US
dc.subject (關鍵詞) robust designen_US
dc.title (題名) 指數失敗時間模式之條件D-最適設計zh_TW
dc.title (題名) Conditional D-optimal Design for Exponential Failure Time Modelen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) Cook, R.D., and Thibodeau, L.A. (1980). Marginally Restricted D-Optimal Designs. Journal of the American Statistical Association 75, 366-371.
Garcet-Rodríguez, S., López-Fidalgo, J., and Martín-Martín, R. (2008). Some Complexities in Optimal Experimental Designs Introduced by Real Life Problems. Tatra Mountains Mathematical Publications 39, 135-143.
Harville, D.A. (1974). Nearly Optimal Allocation of Experimental Units Using Observed Covariate Values. Technometrics 16, 589-599.
Huang, M.N.L., and Hsu, M.C. (1993). Marginally Restricted Linear-Optimal Designs. Journal of Statistical Planning and Inference 35, 251-266.
Huang, M.N.L., and Chang, H.F. (1995). Marginally Restricted Constrained Optimal Designs. The Indian Journal of Statistics 57, 128-141.
Lee, C.M.-S. (1988). Constrained Optimal Designs. Journal of Statistical Planning and Inference 18, 377-389.
López-Fidalgo, J., and Garcet-Rodríguez, S. (2004). Optimal Experimental Designs when Some Independent Variables are Not Subject to Control. Journal of the American Statistical Association 99, 1190-1199.
López-Fidalgo, J., Rivas-López, M.J., and del Campo, R. (2009). Optimal Designs for Cox Regression. Statistica Neerlandica 63, 135-148.
López-Fidalgo, J., and Garcet-Rodríguez, S. (2011). Optimal Experimental Designs when An Independent Variable is Potentially Censored. Statistics 45, 143-154.
López-Fidalgo, J., and Rivas-López, M.J. (2014). Optimal Experimental Designs for Partial Likelihood Information. Computational Statistics and Data Analysis 71, 859-867.
Martín-Martín, R., Torsney, B., and López-Fidalgo, J. (2007). Construction of Marginally and Conditionally Restricted Designs Using Multiplicative Algorithms. Computational Statistics and Data Analysis 51, 5547-5561.
Nachtsheim, C.J. (1989). On the Design of Experiments in the Presence of Fix Covariates. Journal of Statistical Planning and Inference 22, 203-212.
Varela, G., Cordovilla, R., Jiménez, M.F., and Novoa, N. (2001). Utility of Standardized Exercise Oximetry to Predict Cardiopulmonary Morbidity after Lung Resection. European Journal of Cardio-thoracic Surgery 19, 351-354.		zh_TW