不完整長期追蹤資料常見於臨床實驗中，Fitzmaurice et
al.(2001)針對不完整二元資料，考慮遺失型態為MAR(missing
at random)時，比較不同形式GEE參數估計值之影響，其結果顯示
Liang and Zeger(1986)所提出一般GEE方法隨著遺失比率增加會產
生較大偏誤。此外，Spiessens et al.(2003)模擬結果指出，不完
整長期追蹤二元資料且當遺失型態為MAR之群序檢定方法時，邏輯
斯隨機效果模式的型I誤差機率估計值較GEE模式更接近所設定的顯
著水準，而且邏輯斯隨機效果模式比廣義估計方程式模式具有較高的檢定力。

本文著重在討論不同遺失型態為MCAR(missing completely
at random)與MAR之情況下，應用廣義線性混合模式和廣義估計
方程式模式於不完整長期追蹤順序型資料，並以模擬研究來比較在不完整資料下，此兩種模式之型I誤差機率和檢定力之差異。

Longitudinal studies with dropouts are commonly occurred in clinical trials. For the incomplete binary data, Fitzmaurice et al. (2001) discussed the impact on bias of direrent estimating equation methods where missing data follow a MAR (missing at random) process. They pointed out that generalization estimating equations (GEE) proposed by Liang and Zeger (1986) has manifest bias as the MAR dropout rate increases. Spiessens et al. (2003) conducted the group sequential tests for analyzing longitudinal binary data with MAR and MCAR (missing completely at random) dropouts, and compared the performance of logistic random exect models and GEE models in terms of type I error rate and power. The simulation studies indicated that logistic random exect models have noticeably larger power than GEE models for MAR dropouts data.

  In this article, we consider the group sequential tests based on GLMM (generalized linear mixed model) and GEE models for incomplete longitudinal ordinal data, and compare the two methods with respect to type I
error rate and power for various dropout rates by simulation studies.

目錄
1 緒論 1
 1.1 文獻回顧 2 
 1.2 研究動機與目的 5 
 1.3 研究架構 7
2 不完整長期追蹤資料之分析方法 8 
 2.1 完整個案分析 9
 2.2 加權法 10 
 2.3 插補法 11
 2.4 模式建構法 13
3 GLMM與GEE模式之比較 16
 3.1 廣義線性混合模式 18
 3.2 廣義估計方程式模式 19
 3.3 實例分析 22
 3.4 模擬研究 25
4 結論 38
參考文獻 41
表格目錄
表1 在alpha=0.01、不同alpha支配函數與遺失比率下，GLMM和GEE模式之型I誤差估計值 28
表2 在alpha=0.05、不同alpha支配函數與遺失比率下，GLMM和GEE模式之型I誤差估計值 29
表3 在alpha=0.1、不同alpha支配函數與遺失比率下，GLMM和GEE模式之型I誤差估計值 30
表4 在alpha=0.05、不同alpha支配函數與參數beta3下，GLMM之檢定力 31
表5 在alpha=0.05、不同alpha支配函數與參數beta3下，GEE之檢定力 32
表6 在alpha=0.01、GLMM模擬架構下、不同alpha支配函數與遺失比率下，GLMM和GEE模式之型I誤差估計值 33
表7 在alpha=0.05、GLMM模擬架構下、不同alpha支配函數與遺失比率下，GLMM和GEE模式之型I誤差估計值 34
表8 在alpha=0.1、GLMM模擬架構下、不同alpha支配函數與遺失比率下，GLMM和GEE模式之型I誤差估計值 35
表9 在alpha=0.05、GLMM模擬架構下、不同alpha支配函數與參數beta3下，GLMM之檢定力 36
表10 在alpha=0.05、GLMM模擬架構下、不同alpha支配函數與參數beta3下，GEE之檢定力 37

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