以動態樣本探討地中海果蠅產卵量與壽命之關係

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廖品璇(Pin-syuan Liao) 查詢紙本館藏

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統計研究所

論文名稱

以動態樣本探討地中海果蠅產卵量與壽命之關係

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摘要(中)

過去在研究地中海果蠅產卵量與壽命之間的關係，通常是依照總產卵量大小對果蠅進行分組，來觀察產卵數與壽命之間的相關性，本研究是以果蠅產卵量因子分成接近連續的方式，將1000隻雌性地中海果蠅產卵量由小至多排序，以累積樣本的方式來觀察產卵量對壽命的影響有什麼樣的變化。在探討時間相依共變數與存活時間之間的關係時，一般較常使用的半母數方法是以部分概似法來估計參數，前提是必須具有完整的共變數資訊及沒有測量誤差，才能夠達到準確地估計。為了減少使用部分概似法對參數的偏誤，可以使用聯合模型來做配適，以Cox比例風險模型與加速失敗模型的風險函數作為架構，主要目的是比較部分概似法與聯合模型對共變數與時間有關之下，其參數估計值的變化與影響，以動態的曲線來探討總產卵量的多寡是否影響參數的估計以及變數與存活時間之間的關係，並尋找果蠅的樣本會造成每日產卵量對存活的效應在Cox模型和AFT模型中有矛盾的結論。

摘要(英)

In the literature, Mediterranean fruit fly is usually classified into a few discrete groups based on the total numbers of eggs laid to observe the relationship of the numbers of eggs and the life expectancy. In our thesis, we adopt semiparametric method for approximately continuous groups according to the total eggs laid, We are interested in the change of impact of daily egg laying when sample size increasing. The semiparametric methods applied including Cox partial likelihood method and full likelihood joint model method. For partial likelihood approach, the complete covariate information and zero measuring error are required, so that we can estimate accurately. If we consider the time-dependent covariates measured with random errors, joint model then is employed with survival described by Cox proportional hazards model or accelerated failure time model. Dynamic curve of regression coefficients as a function of total egg-laying are plotted to identify the change of impact of daily egg-laying on survival. Moreover, from the dynamic curves, we identify specific samples may have contradict conclusions using Cox model or AFT model.

關鍵字(中)

★ 存活分析
★ 部分概似法
★ 聯合模型法
★ 長期追蹤資料
★ Cox比例風險模型
★ 加速失敗模型

關鍵字(英)

論文目次

摘要 i
英文摘要 iii
圖目錄 viii
表目錄 x
1 緒論 1
1.1 地中海果蠅危害 . ......................... 3
1.2 地中海果蠅生物防治 . ....................... 5
1.3 資料選擇與文獻回顧 . ....................... 8
2 統計方法 18
2.1 部分概似法 (partial likelihood)................... 20
2.1.1 Cox 比例風險模型 . .................... 22
2.2 聯合模型 (Joint model)....................... 28
2.3 加速失敗時間模型 (AFT model).................. 31
3 參數估計 33
3.1 概似函數 . ............................. 34
3.2 EM 演算法之 E-step ........................ 37
3.3 EM 演算法之 M-step (Coxmodel)................. 40
3.4 EM 演算法之 M-step (AFTmodel)................. 42
3.5 估計參數過程 . ........................... 44
3.6 參數標準差之估計 . ........................ 46
4 實例分析 48
4.1 資料背景 . ............................. 49
4.2 模型配適 . ............................. 50
4.3 資料分析 . ............................. 52
5 結論與討論 59
參考文獻 61

參考文獻

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指導教授

曾議寬

審核日期

2015-6-30

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