| 姓名 |
邱奕慶(Yi-Ching Chiu)
查詢紙本館藏 |
畢業系所 |
統計研究所 |
| 論文名稱 |
分析交叉設計得到的連續資料的強韌概似法
(Robust likelihood inference for crossover designs for continuous data)
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| 相關論文 | |
| 檔案 |
 [Endnote RIS 格式]
[Bibtex 格式]
 [相關文章]  [文章引用]  [完整記錄]  [館藏目錄]  至系統瀏覽論文 (2027-6-30以後開放)
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| 摘要(中) |
在臨床試驗中，實驗者常用的試驗手法為交叉設計 (crossoverdesign)。本文使用獨立常態模型與獨立伽瑪模型作為實作模型 (working model)，並利用強韌概似函數 (robust likelihood function) 方法，使得實作模型強韌化。進一步得到強韌華德檢定統計量 (robust Wald statistics)、強韌分數檢定統計量 (robust score statistics)、強韌概似比檢定統計量 (robust likelihood ratio statistics)，也可
得到各個檢定的信賴區間。
藉由模擬研究與實例分析，比較強韌華德檢定統計量、強韌分數檢定統計
量、強韌概似比檢定統計量、Seen (1994) 提出的 CROS 檢定統計量和 Putt and Chinchilli (2004) 提出的魏克生符號檢定 (Wilcoxon signed rank)。不論實作模型與資料間的假設是否相同，透過強韌概似函數方法可以得出正確的統計推論。 |
| 摘要(英) |
In clinical trials, the experimental technique commonly used by experimenters is a crossover design. In this paper, independent normal model and independent gamma model are used as working model, and the robust likelihood function method is used to robust working model. Further obtain the robust Wald test statistics , the robust score test statistics , the robust likelihood ratio test statistics , and confidence intervals for individual tests are also available.
By using simulation research and real data analysis, we can compare the robust Wald test statistic, robust score test statistic, robust likelihood ratio test statistic, CROS test statistic proposed by Seen (1994), and Putt and Chinchilli (2004) proposed Wilcoxon signed ranked. Regardless of whether the assumption between the working model and the data are the same, robust likelihood function method can obtain correctly statistical inferences. |
| 關鍵字(中) |
★ 交叉設計
★ 強韌概似函數
★ 強韌分數檢定
★ 魏克生符號檢定 |
關鍵字(英) |
★ Crossover design
★ Robust likelihood function
★ Robust score test
★ Wilcoxon signed rank |
| 論文目次 |
摘要 ................................................ i
Abstract ............................................ ii
致謝辭 .............................................. iii
目錄 ................................................ iv
表目錄 ............................................... vii
第一章 緒論........................................... 1
第二章 文獻回顧 ...................................... 3
2.1 CROS 估計量 ..................................... 3
2.2 Wilcoxon Signed Rank ........................... 4
第三章 交叉設計下 AB、BA 常態模型之強韌化 ............. 5
3.1 費雪信息矩陣(Fisher information matrix) ......... 7
3.2 修正項 B ........................................ 9
3.3 常見的三種檢定統計量 ............................. 13
3.3.1 強韌華德檢定統計量.............................. 14
3.3.2 強韌分數檢定統計量.............................. 14
3.3.3 強韌概似比檢定統計量 ........................... 15
第四章 交叉設計下 AB、BA 伽瑪模型之強韌化 .............. 16
4.1 費雪信息矩陣...................................... 18
4.2 修正項 B ......................................... 19
4.3 常見的三種檢定統計量................................ 21
4.3.1 強韌華德檢定統計量................................ 21
4.3.2 強韌分數檢定統計量................................. 21
4.3.3 強韌概似比檢定統計量.............................. 22
第五章 交叉設計下 ABB、AAB 常態模型之強韌化 ............. 23
5.1 費雪信息矩陣....................................... 25
5.2 修正項 B ......................................... 26
5.3 常見的三種檢定統計量............................... 28
5.3.1 強韌華德檢定統計量............................... 28
5.3.2 強韌分數檢定統計量................................ 28
5.3.3 強韌概似比檢定統計量.............................. 29
第六章 交叉設計下 ABB、AAB 伽瑪模型之強韌化 ............. 30
6.1 費雪信息矩陣....................................... 33
6.2 修正項 B ......................................... 34
6.3 常見的三種檢定統計量............................... 35
6.3.1 強韌華德檢定統計量............................... 36
6.3.2 強韌分數檢定統計量............................... 36
6.3.3 強韌概似比檢定統計量............................. 36
第七章 交叉設計下 ABB、BAA 常態模型之強韌化 ............ 38
7.1 費雪信息矩陣...................................... 40
7.2 修正項 B ........................................ 41
7.3 常見的三種檢定統計量............................... 42
7.3.1 強韌華德檢定統計量............................... 43
7.3.2 強韌分數檢定統計量............................... 43
7.3.3 強韌概似比檢定統計量............................. 43
第八章 交叉設計下 ABB、BAA 伽瑪模型之強韌化 ............ 45
8.1 費雪信息矩陣...................................... 48
8.2 修正項 B ........................................ 49
8.3 常見的三種檢定統計量.............................. 50
8.3.1 強韌華德檢定統計量.............................. 50
8.3.2 強韌分數檢定統計量.............................. 51
8.3.3 強韌概似比檢定統計量............................ 51
第九章 交叉設計下 ABC、BCA、CAB 常態模型之強韌化 ...... 53
9.1 費雪信息矩陣..................................... 57
9.2 修正項 B ....................................... 58
9.3 檢定兩個參數的檢定統計量......................... 60
9.3.1 強韌華德檢定統計量............................. 60
9.3.2 強韌分數檢定統計量............................. 60
9.4 單一參數的三種檢定統計量......................... 61
9.4.1 強韌華德檢定統計量............................ 62
9.4.2 強韌分數檢定統計量............................ 62
9.4.3 強韌概似比檢定統計量.......................... 64
第十章 交叉設計下 ABC、BCA、CAB 伽瑪模型之強韌化 ..... 66
10.1 費雪信息矩陣................................... 71
10.2 修正項 B ..................................... 72
10.3 檢定兩個參數的檢定統計量........................ 74
10.3.1 強韌華德檢定統計量............................ 74
10.3.2 強韌分數檢定統計量............................. 74
10.4 單一參數的三種檢定統計量.......................... 75
10.4.1 強韌華德檢定統計量............................. 76
10.4.2 強韌分數檢定統計量............................. 76
10.4.3 強韌概似比檢定統計量........................... 78
第十一章 模擬研究 .................................... 82
11-1 實作模型中參數設定 .............................. 82
11-2 資料來自獨立的分配 .............................. 82
11-3 相關資料的生成 ................................. 83
11-3-1 生成二維相關性資料 ............................ 83
11-3-2 生成三維相關性資料 ........................... 83
11-4 模擬結果 ...................................... 85
第十二章 實例分析 .................................. 211
12.1 實例(一)：AB、BA ............................. 211
12.2 實例(二)：AB、BA ............................. 212
12.3 實例(三)：ABB、BAA ........................... 214
12.4 實例(四)：ABC、BCA、CAB ...................... 216
第十三章 結論...................................... 219
參考文獻........................................... 220
附錄 A ............................................ 221
附錄 B ............................................228
附錄 C ............................................233
附錄 D ............................................239
附錄 E ............................................244
附錄 F ............................................250
附錄 G ............................................261 |
| 參考文獻 |
Bellavance, F., & Tardif, S. (1995). A nonparametric approach to the analysis of threetreatment
three-period crossover designs. Biometrika, 82: 865-875.
Chi, E. M. (1994). M-estimation in cross-over trials. Biometrics, 50: 486-493.
Freeman, P. R. (1989). The performance of the two‐stage analysis of two‐treatment,
two‐period crossover trials. Statistics in medicine, 8:1421-1432.
Nelsen, R. B. (2006). An Introduction to Copulas , 2nd edition. USA: Springer.
Putt, M. E., & Chinchilli, V. M. (2004). Nonparametric approaches to the analysis of crossover studies. Statistical Science, 19: 712-719.
Royall, R. M. and Tsou, T. S. (2003). Interpreting statistical evidence by using imperfect models: robust adjusted likelihood functions. Journal of the Royal
Statistical Society, Series B, 65: 391-404.
Senn, S. (1994). The AB/BA crossover: past, present and future?Statistical methods in medical research, 3: 303-324.
Tsou, T. S. and Chen, C. H. (2008). Comparing several means of dependent populations of count-A parametric robust approach. Statistics in Medicine, 27: 2576-2585.
Wallenstein, S., & Fisher, A. C. (1977). The analysis of the two-period repeated measurements crossover design with application to clinical trials. Biometrics, 33: 261-269. |
| 指導教授 |
鄒宗山(Tsung-Shan Tsou)
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審核日期 |
2022-9-14 |
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