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研究生:呂宗蔚
研究生(外文):Tsung-WeiLu
論文名稱:存活函數之三邊假設檢定
論文名稱(外文):Three-sided Hypothesis Testing of Survival Function
指導教授:馬瀰嘉馬瀰嘉引用關係陳瑞彬陳瑞彬引用關係
指導教授(外文):Mi-Chia MaMi-Chia Ma
學位類別:碩士
校院名稱:國立成功大學
系所名稱:統計學系碩博士班
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:2012
畢業學年度:100
語文別:英文
論文頁數:43
中文關鍵詞:三邊假設檢定型III錯誤
外文關鍵詞:Three-sided hypothesis testingType III error
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在存活分析上,常見到的檢定為兩存活函數是否相等,有分成在固定時間點下存活機率是否相等與整體時間下存活函數是否相等兩種;但是在醫學應用上,則是比較關心檢定於兩存活函數在一個所能容忍的誤差範圍內是否相等,稱之為對等性,若不具對等性,再進一步去探討其較優性與較劣性。Goeman et al. (2010)提出了三邊假設檢定(Three-sided hypothesis testing),控制在型Ⅰ錯誤下,同時檢定較優性、對等性與較劣性,免去重複做兩次假設檢定導致型Ⅰ錯誤的增加。本文將三邊假設檢定的想法用在存活函數上,利用統計模擬計算此假設檢定的型I錯誤、型II錯誤與型III錯誤機率之大小,並應用在兩種不同治療狀況下的存活機率或函數的實例上,檢定他們是否具有對等性、較優性與較劣性。
In survival analysis, it is common to test equality of two different survival functions. It contains two cases: at fixed time point and for all time in survival function. In medical applications, it is considered the equivalent test of the two survival functions in the error range which one can accept. It is called the equivalent test. If two survival functions are not equivalent, the superiority test or the inferiority test will be considered. Goeman et al. (2012) had proposed the three-sided hypothesis testing. It can test the equivalent, superiority and inferiority at the same time when the type I error rate was fixed. It can avoid to increase type I error rate because multiple hypotheses are tested. In this paper, we use the three-sided hypothesis testing on survival analysis. The statistical simulation is conducted to compute type I error rate, type II error rate and type III error rate in this hypothesis testing. Finally, this method is used on real example to compare equivalent, superiority and inferiority of two survival functions.
1. Introduction 1
2. Literature Review 3
2.1 Definition of Notations 3
2.2 Survival function 4
2.3 The hypothesis testing at fixed time point 5
2.4 The hypothesis testing for all time point 7
2.5 Equivalent test, Superiority test and Inferiority test 11
2.6 Three-sided hypothesis testing 13
3. Proposed Methods 15
3.1 Three-sided hypothesis testing at fixed time point 15
3.2 Three-sided hypothesis testing for all time points 16
4. Simulation Study 17
4.1 Simulation Process and Parameter Combination 17
4.2 Simulation Results about at fixed time point 24
4.2.1 Exponential distribution 24
4.2.2 Weibull distribution 27
4.3 Simulation Results about for all time points 31
4.3.1 Exponential distribution 31
4.3.2 Weibull distribution 34
5. Real Example 37
6. Conclusion and Discussion 40
References 42

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2.Fleming T.R. and Harrington D.P. (1981), “A class of hypothesis tests for one and two samples of censored survival data, Communications In Statistics, 10:763-794.
3.Gehan E.A. (1965), “A Generalized Wilcoxon test for comparing arbitrarily singly censored samples., Biometrika, 52:203-223.
4.Gisela Tunes da Silva, Logan B.R. and Klein J.P. (2009), “Methods for Equivalence and Noninferiority Testing, Biology of Blood and Marrow Transplantation, 15(1 Suppl) : 120-127.
5.Goeman J.J. , Solari A. and Stijnen T. (2010),“Three-sided hypothesis testing : Simultaneous testing of superiority, equivalence end inferiority, Statistics in Medicine, 29 : 2117-2125.
6.Hirotsu C. (2007), “A unifying approach to non-inferiority, equivalence and superiority tests via multiple decision processes, Pharmaceutical Statistics, 6 : 193-203.
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9.Kaplan E.L. and Meier P. (1958), “Nonparametric estimation form incomplete observation, Journal of the American Statistical Association, 53:457-481.
10.Klein J.P. and Moeschberger M.L. (2003), Survival Analysis Techniques for Censored ans Truncated Data (Second Edition), Springer, Now York, USA.
11.Klein J.P. , Logan B. , Harhoff M. and Andersen P.K. (2007), Analyzing survival curves at a fixed point in time, Statistics in Medicine, 26:4505–4519.
12.Mantel N. (1966), “Evaluation of survival data and two new rank order statistics arising in its consideration., Cancer Chemotherapy Reports, 50 (3): 163–70.
13.Pepe M.S. and Fleming T.R. (1989), “Weighted Kaplan-Meier Statistic: A Class of Distance Test for Censored Survival data, Biometrics, 45 :497-507.
14.Peto R. and Peto J. (1972), “Asymptotically efficient rank invariant test procedures (with discussion), Journal of the Royal Statistical Society A, 135:185-206.
15.Prentice R.L. and Marek P. (1979), “A qualitative discrepancy between censored data rank tests, Biometrics, 35:861-867.
16.Tarone R.E. and Ware J.H. (1977), “On distribution-free test for equality for survival distributions, Biometrika, 64:156-160.

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