在長期追蹤資料(longitudinal data)中，資料的遺失時有所見，此時可以使用多重插補法(multiple imputation)進行插補以解決資料不完整的問題。由於現行的插補法多建立在常態的基礎下，因此Demirtas and Hedeker 在2008年提出了新的插補法配套策略，以處理在不完整長期追蹤順序資料中所發生遺失值的情況。其主要的概念是將原始間斷型的順序尺度轉換成二元型態，接著透過常態下的隨機數生成方式，產生連續型的數值，再針對連續數值進行多重插補法，最後將插補後的資料先轉回二元型態，再轉回順序尺度。
    在本研究論文中，主要是以標準偏誤(standardized bias)、覆蓋率(coverage percentage)以及均方誤根(root-mean-squared-error)，來探討前述多重插補策略在不完整長期追蹤順序資料中遺失型態分別為完全隨機遺失(MCAR)，以及隨機遺失(MAR)的情況下之表現。依據模擬結果顯示，不論在MCAR或MAR遺失型態下，Demirtas and Hedeker所提出之多重插補策略對於分析不完整長期追蹤順序資料有良好的表現。

Missing data are a common occurrence in longitudinal studies. Multiple imputation can be used to solve the problem of missing data. Since the current imputation methods are developed based on the normality, Demirtas and
Hedeker (2008) proposed a multiple imputation strategy for incomplete longitudinal ordinal data, which converts discrete scale to continuous scale by generating normal outcomes and reconvert to binary scale as well as ordinal
one after filling in multiple imputed values. The primary purpose of this article is to evaluate the performance of Demirtas and Hedeker’s method in terms of standardized bias, coverage percentage and root-mean-squared error under
various missing mechanisms such as missing completely at random (MCAR) and missing at random (MAR). According to the simulated results, the plausibility of this imputation strategy is appropriate for analyzing incomplete
longitudinal ordinal data under these two missing mechanisms.

Contents
1 Introduction 1
2 Methodology 7
2.1 Single Imputation 7
2.2 Multiple Imputation 9
2.3 An Imputation Strategy for Ordinal Data 11
3 Simulation Study 17
3.1 Missingness Mechanisms 18
3.2 Criteria 19
3.3 Results 20
4 Conclusion and Discussion 23
List of Tables
1 The first five subjects for each group in a trial of a new drug for treating a skin condition 18
2 Average estimate (AE), standardized bias (SB), root-mean-squared error (RMSE), coverage percentage (CP) and average missing rate(AMR) under six missingness mechanisms 22

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