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中文論文名稱 在不同遺失型態下多重插補法應用於長期追蹤順序資料
英文論文名稱 The Performance of Multiple Imputation for Longitudinal Ordinal Data under MCAR and MAR Dropouts
校院名稱 淡江大學
系所名稱(中) 統計學系碩士班
系所名稱(英) Department of Statistics
學年度 98
學期 2
出版年 99
研究生中文姓名 段力文
研究生英文姓名 Li-Wen Tuan
學號 697650348
學位類別 碩士
語文別 英文
口試日期 2010-06-25
論文頁數 26頁
口試委員 指導教授-陳怡如
委員-林國欽
委員-張春桃
中文關鍵字 長期追蹤順序資料  完全隨機遺失  隨機遺失  多重插補法 
英文關鍵字 Longitudinal ordinal data  MAR  MCAR  Multiple imputation 
學科別分類 學科別自然科學統計
中文摘要 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。
英文摘要 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.
論文目次 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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Davis, C.S. (2002). Statistical Methods for the Analysis of Repeated Measurements, Springer-Verlag: New York.
Demirtas, H. and Hedeker, D. (2007). Gaussianization-based quasi-imputation and expansion strategies for incomplete correlated binary responses, Statistics in Medicine, 26, 782-799.
Demirtas, H. and Hedeker, D. (2008). An imputation strategy for incomplete longitudinal ordinal data, Statistics in Medicine, 27, 4086-4093.
Demirtas, H. and Schafer, J.L. (2003). On the performance of random coefficient pattern-mixture models for nonignorable drop-out, Statistics in Medicine, 22, 2553-2575.
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Fitzmaurice, G.M, Laird, M. and Ware, T. H. (2004). Applied Longitudinal Analysis, Wiley: New Jersey.
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Little, R.J.A. and Rubin, D.B. (2002). Statistical Analysis with Missing Data, 2nd edition, Wiley: New York.
Rubin, D.B. (1978). Multiple Imputation in Sample Surveys, Proc. Survey Res, Meth. Sec. Am. Statist. Assoc, 20-34.
Rubin, D.B. (1987). Multiple Imputation for Nonresponse in Survey, Wiley: New York.
Rubin, D.B. and Schenker, N. (1986). Multiple imputation for interval estimation from simple random samples with ignorable nonresponse, Journal of American Statistical Assocation, 81, 366-374.
Schafer, J.L. (1997). Analysis of Incomplete Multivariate Data, Chapman & Hall: London.
Verbeke, G. and Molenberghs, G. (2000). Linear Mixed Models for Longitudinal Data, Springer: New York.
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