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姓名 黃穎慈(Ying-tzu Huang)  查詢紙本館藏   畢業系所 統計研究所
論文名稱 以聯合模型探討地中海果蠅繁殖力與老化之關係
(Joint modelling fecundity and aging of medfly)
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摘要(中) 在存活分析中,半母數模型通常用 Cox 比例風險模型或加速失敗時間模型來描述變數與存活資訊間的關係,而當變數的資料型態為長期追蹤資料時,可以使用聯合模型做配適,以消除因資料遺失所造成的偏誤。在使用聯合模型的文獻中,大多數都是以 Cox 比例風險模型的風險函數作為架構,搭配混合線性模型組合成聯合模型。但是當資料不符合比例性的假設時,使用 Cox 比例風險模型並不合理,因此 Tseng et al.(2005) 提出可以使用加速失敗時間模型來替換 Cox 比例風險模型。本文引用 Tseng et al.(2005) 提出之加速失敗時間模型架構下的聯合模型,介紹如何使用 EM 演算法估計未知參數與未知的基準風險函數,以及使用拔靴法估計參數的標準差。並將模型應用在 1000 隻雌性地中海果蠅的資料上,其中以果蠅的每日產卵數作為繁殖力的指標,存活時間作為老化程度的指標,以模型探討繁殖力與老化間的關係;此外依照總產卵量大小對果蠅進行分組,用以探討總產卵量的多寡是否會影響參數的估計以及變數與存活時間之間的關係。
摘要(英) In survival analysis, Cox proportional hazard model or accelerated failure time model are used to describe the relationship between variate and survival information in semi-parametric model. When the type of the variate data becomes a longitudinal data, the joint model will be suitable. Most literature would use the Cox proportional hazard model as its basis and then combine it with the mixed linear model to form the joint model. However, it will be unreasonable to use Cox proportional hazard model when the data can’’t fit in the proportionality assumption. Consequently, Tseng et al. (2005) suggests to use the accelerated failure time model instead. This thesis will use the joint model of linera mixed dffdct model and accelerated failure time model that proposed by Tseng et al. (2005), and to introduce how to estimate the unknown parameter and baseline hazard function by using EM algoritme and estimate the standard error by bootstrap as well. Besides, this model can also be applied to the study of 1000 female medflies.As for the method, we can use the reproductiive egg-laying data as the index of fecundity and the longevity as the index of ageing to observe the relationship between the fecundity and ageing. What’’s more, group the medflies according to their total amont of edd-lying data to study if it will affect the estimation of parameter and the relationship between variate and survival time.
關鍵字(中) ★ 隨機效應
★ 加速失敗時間模型
★ 聯合模型
關鍵字(英) ★ Random effect
★ Accelerated failure time model
★ Joint model
論文目次 1 緒論............................................ 1
1.1 資料選擇...................................... 3
1.2 模型配適...................................... 4
1.3 問題敘述...................................... 8
2 統計方法........................................10
2.1 線性混合隨機效應模型..........................11
2.2 加速失敗時間模型..............................12
3 參數估計........................................14
3.1 概似函數......................................14
3.2 EM 演算法.....................................15
3.2.1 E-Step......................................16
3.2.2 M-Step......................................18
3.2.3 估計步驟....................................20
3.3 標準誤的估計..................................21
4 實例分析........................................22
4.1 圖形分析......................................23
4.1.1 事件歷史圖..................................23
4.1.2 趨勢曲線圖..................................28
4.1.3 3D 平滑曲面圖...............................29
4.2 估計值分析....................................33
4.2.1 模型........................................33
4.2.2 AFT 模型參數................................35
4.2.3 混合線性模型參數............................38
4.3 實例分析結論..................................40
5 結論與討論......................................41
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指導教授 曾議寬(Yi-kuan Tseng) 審核日期 2008-6-23
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