此篇論文主要是探討在半母數轉換模型中的模型選擇方法，並且考慮資料為盛行倖存資料，即考量偏差抽樣(Biased sampling)時，該如何利用轉換變數中的隨機誤差項來進行模型選擇。半母數轉換模型為一個彈性的半母數模型，其包含比例風險模型(Proportional hazard model)、比例勝算模型(Proportional odds model)以及其他特殊模式。本文中介紹Chen et al.(2009)所提出的Pseudo-partial likelihood估計手法，再使用其基準函數與自變項參數的估計結果來作模型選擇的推論。本文預想轉換模型中，誤差項的無母數估計量應該會與誤差項的原始設定十分相似，因此考慮比較兩者的倖存函數。在誤差項的估計考慮半母數轉換模型的定義，再使用Wang(1991)所提出對於截斷資料的極限乘積估計量來求得其倖存函數，藉由找到倖存函數差異最小的模型來達到模型選擇的目的。在數值模擬使用本文所提出的方法能尋找到適合資料的隨機誤差母體，並利用此種選模方式，對老年人失智症的資料與女性乳癌患者的資料作模型選擇。根據模型選擇的結果，可以發現結果比較偏向比例勝算模型或其他模式，而非傳統實務上使用比例風險模式。

In this article, we study a model selection method for semiparametric transformation model. We consider the data is prevalent survival data which includes the situation with biased sampling. Semiparametric transformation model is a flexible model including the proportional hazard model and proportional odds model. The selection method's idea is from the random error of semiparametric transformation model. In order to do model selection, we introduce the pseudo-partial likelihood (Chen et al., 2009) to estimate coefficient and baseline function, and use these result to inference the random error by Wang(1991). We expect the estimation for random error's survival function should closed to it's setting. The smallest difference should be chosen as the model selection's result. Simulation shows that this idea can be confirmed by replication. We apply this method to a dementia data and a breast cancer data, form the selection's result we can give a contrary conclusion.

1 緒論1
1.1 倖存資料
1.2 倖存資料處理
1.3 半母數轉換模型(Semiparametric transformation models)
2 文獻回顧
2.1 符號定義以及截斷資料的處理
2.2 模型假設
2.3 Martingale 估計方程
2.4 Pseudo-partial likelihood
3 研究方法
3.1 選模方法推論
3.2 模型選擇
4 數值模擬
4.1 資料設定
4.2 選模結果分析
5 實例分析
5.1 老年人失智症資料分析
5.2 女性乳癌資料分析
6 結論
7 附錄
7.1 樣本數100 的模擬結果
7.2 樣本數500 的模擬結果
7.3 其他模擬結果
參考文獻

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