長期追蹤研究期間常會產生遺失值的問題，解決遺失值的問題有許多種方法，其中一種解決遺失值的有效方法為插補法。Demirtas與Hedeker (2007) 利用在多變量常態下具有完整發展架構的多重插補法與應用隨機生成二元反應變數之演算法，以對於二元資料進行轉換，進而提出對於不完整長期追蹤二元資料之插補策略。由於Demirtas與Hedeker (2007)方法無法確保相關性矩陣為正定，以及必須滿足範圍限制使得其相關性才有唯一解。為改善使用Demirtas-Hedeker方法時可能會面臨到的困難，我們提出對Demirtas- Hedeker方法之修改插補程序，並應用標準偏誤 (standardized bias)，覆蓋率(coverage percentage)，和均方誤根(root-mean-squared error)等基準量測，討論在不同的遺失型態與遺失比率下，比較所提出之插補方法與Demirtas-Hedeker方法之表現差異。此外，並使用實例來模擬研究說明如何應用我們所提出的方法。

It is very common for longitudinal studies to involve missing data. The imputation method is one of the effective procedures for handling with the problem of missing data. Based on the well-developed multiple imputation for normal
responses and a random number generation algorithm for binary outcomes, Demirtas and Hedeker (2007) introduced a quasi-imputation strategy for incomplete longitudinal binary data. The shortcomings of Demirtas-Hedeker approach are that positive-definiteness of the correlation matrix cannot be guaranteed and the correlations need to satisfy the constraint for a unique solution. To improve the shortcomings of Demirtas-Hedeker method, the proposed methods can be regarded as the modification of Demirtas-Hedeker method with simpler procedures. The performance of Demirtas-Hedeker method and the proposed procedures is compared in terms of standardized bias, coverage percentage, and root-mean-squared error under various configurations of missing rates and missingness mechanisms. A real data set is used to illustrate the application of the proposed methods.

Contents
1 Introduction 1
2 Description of Methodology 7
2.1 Imputation Method . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Demirtas and Hedeker Approach . . . . . . . . . . . . . . . . . 12
2.3 Proposed Imputation Strategies . . . . . . . . . . . . . . . . . . 13
3 Simulation Study 18
3.1 Missingness Mechanisms . . . . . . . . . . . . . . . . . . . . . . 19
3.2 GEE Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.3 Evaluation Criteria . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4 Conclusion and Discussion 34
i
List of Tables
1 The first ten patients for each center in a trial of respiratory
disease. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2 The parameter estimates of GEE model with independent working
correlation and their standard errors, confidence intervals,
test statistics as well as p-values for respiratory disease data. . 22
3 The parameter estimates of GEE model with exchangeable working
correlation and their standard errors, confidence intervals,
test statistics as well as p-values for respiratory disease data. . 23
4 The parameter estimates of GEE model with unstructured working
correlation and their standard errors, confidence intervals,
test statistics as well as p-values for respiratory disease data. . 24
5 The performance measures of DH, M1 and M2 approaches using
GEE model with independent working correlation under various
missing rates of MCAR. The targeted value is -0.0656. . . . . . 28
6 The performance measures of DH, M1 and M2 approaches using
GEE model with independent working correlation under various
missing rates of MAR. The targeted value is -0.0656. . . . . . . 29
ii
7 The performance measures of DH, M1 and M2 approaches using
GEE model with exchangeable working correlation under
various missing rates of MCAR. The targeted value is -0.0685. . 30
8 The performance measures of DH, M1 and M2 approaches using
GEE model with exchangeable working correlation under
various missing rates of MAR. The targeted value is -0.0685. . . 31
9 The performance measures of DH, M1 and M2 approaches using
GEE model with unstructured working correlation under
various missing rates of MCAR. The targeted value is -0.0954. . 32
10 The performance measures of DH, M1 and M2 approaches using
GEE model with unstructured working correlation under
various missing rates of MAR. The targeted value is -0.0954. . . 33
iii

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