成對設計下敏感性，特異性參數的推論與雙敏感性， 雙特異性的簡單強韌概似分析法

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姓名

蔣仁潔(Renjie Jiang) 查詢紙本館藏

畢業系所

統計研究所

論文名稱

成對設計下敏感性，特異性參數的推論與雙敏感性，雙特異性的簡單強韌概似分析法
(A Simple Robust Likelihood Approach for Binocular Sensitivity and Specificity of Screening Tests in Paired Scenarios)

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摘要(中)

在醫藥研究中，通常用敏感性和特異性來描述檢測儀器或藥劑的準確性。而為了比較兩種儀器或藥劑，成對的設計可以減少人與人之間的差異性所造成的偏差。Perera et al. (2017) 提出一個新的測量雙眼（成對器官）的準確性的方法，并介紹了雙眼的敏感性和特異性來描述如何進行篩檢測試。但是他們文中採用的模型過於複雜。在本篇論文中，我們利用只包含了伯努利分佈的簡單模型來分析資料。我們的方法在使用上極為便利，完全不需要上述文章中必須採用的複雜數值方法便可完成。同時，在推論成對器官準確性前需對成對器官個別的準確性參數做相同的檢定。本論文亦提出不需假設相關性的強韌概似推論法。

摘要(英)

In medical research, the accuracy of a machine or a therapy is commonly measured by sensitivity and specificity. In order to compare the accuracy of the machines or therapies, paired design can reduce the effect of heterogeneity among individuals. A new binocular accuracy measurement was proposed by Perera et al. (2017), who introduced the binocular versions of sensitivity and specificity to describe how screening tests are conducted in practice. However, the models they adopted are excessively complicated. In this thesis, we proposed an easier model, which only involves Bernoulli distributions, to accomplish the intended tasks.

關鍵字(中)

★ 相關性資料
★ 敏感性
★ 特異性
★ 雙敏感性
★ 雙特異性
★ 強韌概似推論法

關鍵字(英)

★ correlated data
★ sensitivity
★ specificity
★ binocular sensitivity
★ binocular specificity
★ robust likelihood

論文目次

摘要 ..................................................................................................................................... i
ABSTRACT .............................................................................................................................. ii
致謝辭 ....................................................................................................................................... iii
Table of Contents ..................................................................................................................... iv
List of Tables ............................................................................................................................ vi
Chapter 1 Introduction ............................................................................................................ 1
Chapter 2 Analysis of binocular sensitivity and specificity .................................................. 3
2.1 Notation ........................................................................................................................ 3
2.2 The Gaussian copula probit model ............................................................................... 5
2.3 Our simple Binomial model ....................................................................................... 10
Chapter 3 Comparing two dependent sensitivities and specificities .................................. 12
3.1 Robust likelihood function for sensitivity .................................................................. 13
3.1.1 Fisher information matrix .................................................................................. 15
3.1.2 Variance matrix of the score functions .............................................................. 17
3.1.3 Construction of the robust likelihood function.................................................. 21
3.1.4 Robust score test statistic for 0 0 H：   .......................................................... 27
3.2 Robust likelihood function for specificity .................................................................. 31
3.2.1 Fisher information matrix .................................................................................. 34
3.2.2 Variance matrix of the score functions .............................................................. 35
3.2.3 Construction of the robust likelihood function.................................................. 38
3.2.4 Robust score test statistic for 0 0 H：   .......................................................... 42
Chapter 4 Simulation ............................................................................................................. 47
4.1 Comparisons of two dependent sensitivities and specificities ................................... 47
4.1.1 Simulation layout for sensitivity ....................................................................... 47
4.1.2 Simulation layout for specificity ....................................................................... 50
4.2 Simulation layout for Gaussian copula probit model ................................................. 53
4.3 Simulation results ....................................................................................................... 54
4.3.1 Simulation results for sensitivity ....................................................................... 54
4.3.2 Simulation results for specificity ....................................................................... 67
4.3.3 Simulation results for Gaussian copula probit model ....................................... 79
Chapter 5 Real data analysis ................................................................................................. 82
Example 1 ......................................................................................................................... 82
Example 2 ......................................................................................................................... 85
Chapter 6 Conclusion ............................................................................................................. 93
References ................................................................................................................................ 94
Appendix ................................................................................................................................. 96
The calculation of joint probabilities
l1r1l2r2 P in chapter 2.2 ................................................. 96

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指導教授

鄒宗山(Tsung-Shan Tsou)

審核日期

2018-6-26

推文