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研究生:蔡宗哲
研究生(外文):Tsai, Tsungche
論文名稱:Cox比例風險模型和Aalen加成模型的適應性模型選擇
論文名稱(外文):Adaptive Model Selection Between Cox Proportional Hazard Model And Aalen Additive Model
指導教授:張玉媚張玉媚引用關係
指導教授(外文):Chang, Yumei
口試委員:沈葆聖陳春樹
口試委員(外文):Shen, PaoshengChen, Chunshu
口試日期:2012-07-11
學位類別:碩士
校院名稱:東海大學
系所名稱:統計學系
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:中文
論文頁數:23
中文關鍵詞:適應性模型選擇資料擾動Kullback-Leibler 損失廣義自由度Cox比例風險模型Aalen加成模型
外文關鍵詞:Adaptive model selectionData perturbationKullback-Leibler lossGenerlized degree of freedomCox proportional hazards modelAalen additive model
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在醫藥的研究中,針對具共變數的右設限存活資料,Cox(1972)比例風險模型(proportional hazards model) 經常被使用來了解病人的存活情形。但實際上,具不同共變數的病人其風險不見得成比例。因此,Aalen’s (1989) 模型變成為另一個被考慮的模型,在此模式,共變數對病人風險的影響是相加(additive)的效果,且允許未知的風險係數跟時間有關,如此,共變數的影響也會隨時間而改變。然而,實務上,資料背後的真實模型一般並無法得知,且Cox模型與Aalen模型在不同的情況下表現亦有所不同。如何在其中選擇一適當的模式,至今尚無相關文獻深入探討。因此,本文嘗試發展一個數據驅動(data-driven)的選模方法,即應用廣義自由度的觀念做模式的選取且透過資料擾動的技巧得到Kullback-Leibler損失的漸近不偏估計式,進而用相對Kullback-Leibler損失做為模型選擇的準則。接著透過電腦模擬的方式驗證此方法的有效性。最後再根據分析原發性膽汁性肝硬化與急性心肌梗塞的資料說明此模型選擇準則的可行性。
In medical studies, Cox proportional hazards model (Cox, 1972) is the most commonly used method to analyze the survivor function of patients when the right-censored survival data are accompany with covariates which are associated with patients’ physiology and conditions. However, the proportional hazards assumption is usually violated in practice. Therefore, the Aalen’s additive model (Aalen, 1989) is an alternative choice under consideration. In this model, the covariates act in an additive manner on an unknown baseline hazard rate. The unknown risk coefficients in the model are allowed to be functions of time so that the effect of a covariate may vary over time. However, the two models generally perform differently under different circumstances, so that neither the Cox model nor the Aalen model is superior in all cases. How to select between them has not been explored in the literature. Therefore, we proposed a data-driven method for making a selection based on a concept of generalized degrees of freedom, resulting in an approximately unbiased estimator of the Kullback-Leibler loss via a data perturbation technique. The effectiveness of the proposed method is justified by a simulation study and also is applied to two real data sets.

第一章、緒論 1
第二章、文獻探討 3
第一節、Cox比例風險模型 3
第二節、Aalen加成模型 4
第三章、研究方法 6
第一節、Kullback-Leibler損失 6
第二節、廣義自由度(Generlized degree of freedom) 8
第三節、資料擾動 9
第四章、統計模擬 11
第一節、模擬步驟 11
第二節、模型選擇結果 12
第五章、資料分析 13
第六章、結論及未來研究方向 15
參考文獻 16
附錄 18

Aalen,O.O.(1975). Statistical inference for a family of countingprocesses. PhD thesis, Univ. of California,Berkeley.
Aalen,O.O.(1978a). Nonparametric estimation of partial transition Probabilities in multiple decrement models. Ann. Statist.6,534-545.
Aalen, O.O.(1989). A linear regression model for the analysis of lifetimes.Statist. Med.8,907-925.
Breslow,N.E.(1975). Analysis of survival data under the proportional hazards model. Int. Statist. Rev. 43,45-58.
Cox,D.R.(1972). Regression models and life tables (with discussion).J. Roy. Statist. Soc. Ser. B 34,187-220
Cox,D.R.(1975). Partial likelihood.Biometrika 62,269-276.
Chen,C.S.,Chang,Y.M.(2011). Model selection for two-sample problems with right-censoreddata:An application of Cox model. Journal of Statistical Planning and Inference,Vol.141,pp.2120-2127.
Huang, H.C., Chen, C.S.(2007). Optimal geostatistical model selection.J.Amer.Statist.Assoc.102,1009-1024.
Lin, D.Y. & Ying, Z.(1994). Semiparametric analysis of general additive Multiplicative hazard models for counting processes.Ann.Statist.23,712-1734
McKeague, I.W. &Sasieni, P.D.(1994). A partly parametric additive risk Model.Biometrika 81,501-514.
Shen, X., Huang, H.C., Ye, J.(2004). Adaptive model selection and assessment for exponential family models. Technometrics 46,306-317.
Shen, X.,Huang, H.C.(2006). Optimal model assessment, selection, and Combination.J.Amer.Statist.Assoc.101,554-568.
Ye, J.(1998). On measuring and correcting the effects of data mining and Model selection.J.Amer.Statist.Assorc.93,120-131.

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