具有治癒子群的存活資料在右設限資料上已經被廣泛地研究，但較少對於現狀數據的研究。 我們的研究動機來自於一個關於白內障資料的橫斷面研究，其中白內障的發生是現狀設限的，且似乎有一個比例的研究對象似乎不會罹患白內障。 我們利用最大概似法分析具有治癒子群的現狀數據。 一些基於具有治癒子群之現狀數據的迴歸方法已被建立 (Kuk and Chen (1992); Tsodikov (2003); Lu and Ying (2004))，但皆是在混合型治癒模型 (Berkson and Gage (1952)) 之下。 相對的，我們考慮比例勝算比治癒模型 (Zeng et al. (2006))，屬於非混合治癒模型。 為了確保模型參數的可辨識性，我們假設所有右設限觀測者中設限時間最大的研究對象為治癒。 我們進行模擬試驗及白內障資料的分析來評估我們所提出的統計方法。

Survival data with a cured subgroup have been extensively studied in the context of right-censored data but less for current status data. Motivated by the cataract dataset from a cross-sectional study, where the occurrences of cataract was current status censored and a fraction of subjects seemed not susceptible to cataract, we describe a maximum likelihood method for analyzing current status data with a cured subgroup. Some regression approaches based on current status data with a cured subgroup have been developed, Kuk and Chen (1992); Tsodikov (2003); Lu and Ying (2004), but all under two-component mixture cure models (Berkson and Gage (1952)). Alternatively, we consider the proportional odds cure model (Zeng et al (2006)), a non-mixture model, in this study. To ensure identifiability of the model, in the estimation, we assume the study unit who has the largest censoring time among all right censored observations is cured. We evaluate the proposed method through simulation studies and illustrate it with the cataract data.

目錄
1 緒論  1
2 模型與資料介紹  4
  2.1 模型介紹  4
  2.2 資料介紹  7
3 估計方法  8
  3.1 最大概似估計法  8
  3.2 變異數估計  9
4 模擬試驗 11
5 實例分析 21
6 結論 23
參考文獻 24
附錄一 25
附錄二 26
附錄三 28
附錄四 30

表目錄
1 參數參數(α,β,γ_1,γ_2)=(1,1,1,1)之四組模擬樣本在有無假定治癒者下之估計比較 14
2 參數(α,β,γ_1,γ_2)=(1,1,1,1)(治癒率=27%), 檢查時間C∼U(0,1)之模擬結果 15
3 參數(α,β,γ_1,γ_2)=(1,1,1,1)(治癒率=27%), 檢查時間C∼U(0,4)之模擬結果 15
4 參數(α,β,γ_1,γ_2)=(-1,1,1,1)(治癒率=73%), 檢查時間C∼U(0,1)之模擬結果 16
5 參數(α,β,γ_1,γ_2)=(-1,1,1,1)(治癒率=73%), 檢查時間C∼U(0,4)之模擬結果 16
6 白內障資料的摘要 21
7 白內障資料的分析結果 22
8 不同潛在因子個數 N 的分布(期望值E(N)=θ) 所對應的母體存活函數S_pop(t) 25

圖目錄
1 白內障資料根據糖尿病分組的存活函數估計  2
2 模擬試驗(α,β,γ_1,γ_2)=(1,1,1,1)(治癒率=27%), C∼U(0,4), n=900之標準化估計對N(0,1)之 Q-Q Plot 17
3 模擬試驗(α,β,γ_1,γ_2)=(-1,1,1,1)(治癒率=73%), C∼U(0,4), n=900之標準化估計對N(0,1)之 Q-Q Plot 18
4 模擬試驗(α,β,γ_1,γ_2)=(1,1,1,1)(治癒率=27%), C∼U(0,4), n=900之參數估計盒形圖 19
5 模擬試驗(α,β,γ_1,γ_2)=(-1,1,1,1)(治癒率=73%), C∼U(0,4), n=900之參數估計盒形圖 19
6 模擬試驗(α,β,γ_1,γ_2)=(1,1,1,1)(治癒率=27%), C∼U(0,4), n=900之散佈圖 20
7 模擬試驗(α,β,γ_1,γ_2)=(-1,1,1,1)(治癒率=73%), C∼U(0,4), n=900之散佈圖 20
8 罹患糖尿病與否之白內障存活函數估計 22

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