等比勝算迴歸模型常用來研究順序型反應變數與風險因子之間的關係。本文彙整回溯式研究中等比勝算迴歸模型的參數估計，並擴展Pulkstenis and Robinson(2004)以及Fagerland and Hosmer(2013)的適合度檢定方法。經由模擬研究發現，在回溯式資料中擴展的檢定程序，具有良好的有限樣本的表現。本文建議在回溯式抽樣下，同時使用擴展的數個檢定程序檢驗等比勝算迴歸模型的適合度。

The proportional odds regression model is used popularly for inferring the relationship of ordinal response and risk factors. This paper summarizes the parameter estimation of proportional odds regression models under retrospective sampling. Also, it extends the goodness-of-fit tests proposed by Pulkstenis and Robinson (2004) and Fagerland and Hosmer (2013). For retrospective data simulation studies have found these extended goodness-of-fit tests demonstrate good performance. This paper recommends using the extended tests simultaneously to assess the goodness of-fit of the proportional odds regression model under retrospective sampling.

目錄

第一章 緒論......1
第二章 回溯式研究下等比勝算迴歸模型適合度檢定......9
第三章 模擬研究......13
第一節 型一誤比率......13
第二節 檢定力......18
第四章 實例分析......27
第五章 結論......32
參考文獻......33
附錄一 50筆精神病院收治青少年的部分醫療記錄......34

表目錄

表 1：以兩個二元類別型解釋變數為例的PR檢定觀察次數列聯表......5
表 2：以組數為10組及50筆觀察值為例的HL檢定觀察次數列聯表......7
表 3：HL檢定觀察次數與估計次數列聯表......12
表 4：不同反應變數與兩個解釋變數的RPR、RHL及HL適合度檢定型一誤比率模擬結果......17
表 5：三類反應變數與兩個解釋變數的RPR、RHL及HL方法適合度檢定檢定力模擬結果......25
表 6：不同反應變數與兩個解釋變數的RPR、RHL及HL方法適合度檢定檢定力模擬結果......26
表 7：配適等比勝算迴歸模型(4.1)式結果......28
表 8：配適等比勝算迴歸模型(4.2)式結果......29
表 9：配適等比勝算迴歸模型(4.3)式結果......30

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