此篇論文主要探討當資料來自長度偏差抽樣(length-biased
sampling) 下，如何對半母數轉換模型(semiparametric transformation
models) 做模式的選取。半母數轉換模型中包含被廣為
使用的比例風險模型(proportional hazard model) 以及比例勝算
模型(proportional odds model)。如何選擇較適合的轉換模型為
研究者所需要考慮的問題。假若資料來自長度偏差抽樣，可以
推得截斷(truncation) 變數服從均勻(uniform) 分配。當資料存
在共變數(covariate)，且具有左截斷(left truncation) 及右設限
(right censored)，推廣Wang (1991) 提出的無母數最大概似估計
法(nonparametric maximum likelihood Estimation) 來估計截斷
時間的分配。由兩者間之最小差異作為模式選取的依據，選擇適
合資料的轉換模式。最後，將此模式選取的方法套用到加拿大健
康與老齡化研究失智症資料中，模式選取的結果以比例勝算模型
作來描述個體倖存時間。

1 緒論1
2 文獻回顧5
2.1 盛行倖存資料 5
2.2 半母數轉換模型 8
2.2.1 符號定義 8
2.2.2 估計方法 9
2.3 長度偏差抽樣資料 14
3 研究方法 16
3.1 條件概似函數法 16
3.2 模型選擇 19
4 數值模擬21
4.1 資料設定 21
4.2 模擬結果 22
5 實例分析27
6 結論29
7 附錄30
參考文獻32

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