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研究生:鐘俊江
研究生(外文):Zhong, Junjiang
論文名稱:多個實驗處理的三臂臨床試驗下非劣性確認後的優越性檢定
論文名稱(外文):Testing Superiority after the Confirmation of Noninferiority for Three-arm Clinical Trials with Multiple Experimental Treatments
指導教授:温敏杰張紹洪
指導教授(外文):Wen, Miin-JyeCheung, Siu-Hung
口試委員:楊欣洲黃錦輝蘇佩芳
口試委員(外文):Hsin-Chou YangKam-Fai WongPei-Fang Su
口試日期:2017-01-04
學位類別:博士
校院名稱:國立成功大學
系所名稱:統計學系
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2017
畢業學年度:105
語文別:英文
論文頁數:70
中文關鍵詞:三臂試驗非劣性優越性族系誤差率檢測靈敏度檢定力
外文關鍵詞:Three-arm trialNon-inferioritySuperiorityFamilywise error rateAssay sensitivityPower
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在臨床試驗中,透過比較實驗(新)用藥的療效不劣於參考(標準)用藥的療效來證明實驗用藥是具有療效的方式稱為非劣性試驗。通常允許實驗用藥的療效會比參考用藥差一點點,是因為實驗用藥具有參考用藥所沒有的優點,例如:減少副作用、降低成本、引入較簡單的治療方法等。在非劣性試驗中,當研究不同劑量的新藥或幾種藥物的不同組合的療效時,通常都會進行多組實驗用藥。針對包含實驗組、參考組和安慰劑的三臂非劣性試驗,目前已有統計方法用以比較多組實驗用藥療效是否非劣於參考用藥。然而,目前缺乏同時檢驗多組實驗用藥相比參考用藥的非劣性和優越性的檢定程序。

本論文的目的是發展一個檢定程序,該程序用於檢定實驗用藥在非劣性確認後是否優於參考用藥療效。因此,在整個檢定結束時,與標準用藥相比,我們將把實驗用藥分為三類: 劣性組、非劣性組、優越組。相比以前的方法,這裡提出的檢定程序的優點,除了維持相同的非劣性檢定能力外,還有一個附加的能力就是可以識別出優越性用藥。我們提出單步和逐步程序,同是也分別給出各個程序臨界值的詳細計算過程。此外,我們也進行了模擬比較每個檢定方法的優點。為了闡述上述所提出的方法,我們討論了三個臨床試驗例子。最後,我們也給出了檢定力的計算和各組試驗所需的樣本數計算。
The objective of a non-inferiority (NI) trial is to assert the efficacy of an experimental (new) treatment compared with a reference (standard) treatment by showing that the experimental treatment retains a substantial proportion of the efficacy of the reference treatment. The marginal loss of efficacy of adopting the experimental treatment has to be justified by its other benefits, such as the alleviation of side effects, reduction of costs, and introduction of less complicated regimens. In NI trials, it is common to have multiple experimental treatments when the efficacy of different doses of a new drug or different combinations of several new drugs are being investigated. Statistical methods have been developed to test NI of multiple experimental treatments in three-arm NI trials consisting of experimental treatments, a reference treatment and a placebo. However, there is a shortage of procedures that examine both NI and superiority of the new treatments as compared with the reference treatment.

The objective of this thesis is to develop testing procedures which examine the superiority of an experimental treatment after it has been shown to be NI to the reference treatment. Hence, at the end of the entire test procedure, we will be able to classify all the experimental treatments into three groups; namely, inferior, non-inferior and superior to the standard treatment. As compared to previous methods, the advantage of the proposed test procedures is the additional ability to identify superior treatments while retaining an NI testing power comparable to that of existing testing procedures. Both single-step and stepwise procedures are derived and the computational details regarding the required critical values are provided. Further, a comparative study is conducted to investigate the merits of each procedure. To illustrate the proposed procedures, three clinical trial examples are discussed. Finally, the computation of power and the determination of sample size before the onset of an NI study is given.
1 Introduction 1
1.1 Non-inferiority clinical trials 1
1.2 Assay sensitivity and three-arm NI trials 2
1.3 Overview of previous research on three-arm NI trial 4
1.3.1 The fraction approach 5
1.3.2 The difference approach 7
1.4 The objectives of the thesis 8
1.5 Layout of the thesis 10

2 Three-arm non-inferiority studies 12
2.1 The model and the hypotheses 12
2.2 Testing procedures 14
2.2.1 Single-step procedure: KSS 14
2.2.2 Step-up procedure: SU 15

3 Testing superiority after the confirmation of non-inferiority 18
3.1 Clinical examples 18
3.2 The hypotheses and the test statistics 21
3.3 The proposed testing procedures 22
3.3.1 Single-step stagewise test procedure: SSP 22
3.3.2 Step-down stagewise test procedure: SDP 25
3.3.3 Step-up stagewise test procedure: SUP 30

4 Simulation study 33
4.1 Error comparisons 33
4.2 Power comparisons 39

5 Clinical examples 43
5.1 Example 1 43
5.2 Example 2 44
5.3 Example 3 45

6 Sample Size Determination 47
6.1 Definition of power 47
6.2 Sample size determination 48
6.3 A clinical example 50

7 Conclusions and further research 53
7.1 Conclusions 53
7.2 Further research 54

References 56

Appendix A. Evaluation of critical values 64
Appendix B. Evaluation of the power functions of SSP 69
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