部分成對資料之強韌概似推論

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姓名

鄭宗倫(Chung-Lun Zheng) 查詢紙本館藏

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統計研究所

論文名稱

部分成對資料之強韌概似推論
(Robust likelihood inference for partially paired data)

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摘要(中)

在醫學檢驗疾病並研發新藥時，常使用配對設計來判定此藥是否有效，若此配對設計資料有遺失值時(missing data)，則稱為部分成對資料。本文探討完全隨機遺失(missing completely at random, MCAR)的部分成對資料，此種資料因具相關性使得模型配適變得困難。本文主要的目的是利用強韌概似函數(robust likelihood function)方法，來分析部分成對資料。我們所建立的強韌概似函數，並不需要對該部分成對資料中的相關性建立模型假設，仍可得到正確的統計推論。

摘要(英)

In medical research, the efficacy of the new drug is often decided by the paired design. The data of paired design that has missing values is called partially paired data. This article considers the partially paired data that is missing completely at random. It is hard to find a suitable model to analyze the correlated data.This article utilizes a robust likelihood function method to analyze the partially paired data. Using this robust likelihood function, we obtain correctly statistical inferences without modeling the correlated joint distribution of partially paired data.

關鍵字(中)

★ 強韌概似函數
★ 成對資料
★ 遺失值
★ 完全隨機遺失

關鍵字(英)

★ Robust likelihood function
★ Partially paired data
★ Missing data
★ Missing completely at random

論文目次

摘要............................................... i
Abstract............................................ii
致謝辭 ............................................ iii
目錄 ...............................................iv
表目錄 ..............................................vii
圖目錄 ..............................................x
第一章緒論 ........................................ 1
第二章文獻回顧 ..................................... 3
2.1 Two-sample t-test and Paired t-test ............ 3
2.2 Corrected z-test ............................... 3
2.3 Pooled t-test and Weighted t-test............... 3
2.4 Multiple imputation ............................ 3
2.5 Mixed model .................................... 4
第三章常態模型之強韌化 ............................... 5
3.1 參數之最大概似估計量 .............................. 5
3.2 修正項A之計算 .................................... 8
3.3 修正項B之計算 ................................... 10
3.4 參數θ之檢定統計量 ................................ 19
3.4.1 參數θ之強韌與非強韌Wald 統計量 ................... 20
3.4.2 參數θ之強韌與非強韌score 統計量 .................. 21
3.4.3 參數θ之強韌與非強韌LR 統計量 ..................... 22
第四章常態模型之強韌化() ............................ 25
4.1 修正項A與B之計算 ................................. 26
4.2 參數θ之強韌與非強韌Wald 統計量 ..................... 27
4.3 參數θ之強韌與非強韌score 統計量 .................... 28
4.4 參數θ之強韌與非強韌LR 統計量 ....................... 29
第五章伯努力模型之強韌化 ............................. 31
5.1 參數之最大概似估計量 ............................. 31
5.2 修正項A之計算 ................................... 33
5.3 修正項B之計算 ................................... 35
5.4 參數θ之檢定統計量 ............................... 39
5.4.1 參數θ之強韌與非強韌Wald 統計量 ................. 40
5.4.2 參數θ之強韌與非強韌score 統計量 ................. 41
5.4.3 參數θ之強韌與非強韌LR 統計量 ................... 42
第六章模擬研究 ..................................... 44
6.1 Modified MLE ................................... 44
6.2 Optimal pooled t-test .......................... 45
6.3 資料生成方法 .................................... 46
6.3.1 成對具相關性之常態變數 ......................... 46
6.3.2 成對具相關性之韋伯變數 ......................... 47
6.3.3 成對具相關性之對數常態變數 ...................... 47
6.3.4 成對具相關性之伯努力變數 ........................ 48
6.4 模擬結果 ........................................ 48
第七章實例分析 ...................................... 82
第八章結論 .......................................... 84
參考文獻 ............................................. 85
附錄 ................................................ 87

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指導教授

鄒宗山(Tsung-Shan Tsou)

審核日期

2020-7-15

推文