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系統識別號 U0026-2507201417392400
論文名稱(中文) 在右設限資料下根據信賴區間長度之K組中位數檢定
論文名稱(英文) A K-sample Median Test Based on the Length of Confidence Interval with the Right-censored Data
校院名稱 成功大學
系所名稱(中) 統計學系
系所名稱(英) Department of Statistics
學年度 102
學期 2
出版年 103
研究生(中文) 李姵宣
研究生(英文) Pei-Syuan Li
學號 R26014022
學位類別 碩士
語文別 中文
論文頁數 37頁
口試委員 指導教授-嵇允嬋
口試委員-陳玉英
口試委員-張升懋
中文關鍵字 右設限資料  K組中位數檢定  中位數存活時間  信賴區間  存活函數 
英文關鍵字 right-censored data  K-sample median test  median survival time  confidence interval  survival function 
學科別分類
中文摘要 在右設限資料下,進行K組母體中位數存活時間相等性的檢定時,Brookmeyer和Crowley (1982b) 提出的檢定統計量,需要K組母體分布之形狀相同或變異數相同,才能推導其在虛無假設成立的漸近抽樣分布。實際上,當K組母體中位數存活時間相同時,其母體分布的變異數未必全然相同,所以Rahbar et al. (2012) 提出之檢定統計量可克服此限制。然而,Rahbar et al. (2012) 的方法需使用自助法估計各組樣本中位數存活時間的變異數。當樣本數大時,以自助法估計之,可能會花費較多時間。因此,Tsai et al. (2014) 根據中位數存活時間的信賴區間長度,估計樣本中位數存活時間之變異數。賴 (2014) 則依據不同的方式推導中位數存活時間之信賴區間,以估計樣本中位數存活時間之變異數。因為Rahbar et al. (2012) 提出的檢定統計量,型I誤判機率會稍偏高,所以本論文沿用Rahbar et al. (2012) 的檢定統計量,再以Tsai et al. (2014) 及賴 (2014) 估計樣本中位數存活時間變異數的方法取代自助法。最後提出調整的檢定統計量,期望能藉此維持型I誤判機率。本論文以模擬來驗證調整統計量的準確性,模擬結果顯示調整統計量的型I誤判機率較Rahbar et al. (2012) 的方法接近名目型I誤判機率。
英文摘要 In clinical trials, researchers usually need to compare the treatment effects of several therapies, the results can be drawn by the K-sample median test. The asymptotic distribution of the test statistic proposed by Brookmeyer and Crowley was derived when the shapes of K populations are the same. To overcome this limitation, Rahbar et al. suggested a nonparametric test statistic which employed the Bootstrap method to estimate the asymptotic variance of the sample median. To provide an explicit formula for the asymptotic variance, Tsai et al. proposed a variance estimator based on the confidence interval for median. Lai further estimated the length of confidence interval for median by another . Because the type I error rates of the test statistic proposed by Rahbar et al. are slightly higher than the nominal level, their test is extended by replacing the bootstrapped variance with the length-based estimator. Simulation studies are conducted to evaluate the type I error rates and powers of the proposed tests. Generally, the proposed test statistics are recommended for the K-sample median test with the right-censored data.
論文目次 第一章 緒論 1
第二章 文獻探討 3
第一節 符號定義 3
第二節 存活函數於右設限資料的估計方法 3
第三節 中位數存活時間於右設限資料的估計方法 5
第四節 樣本中位數存活時間之變異數的估計方法 5
第五節 K組中位數存活時間相等性檢定 9
第三章 根據信賴區間長度之K組中位數檢定 11
第一節 K組中位數存活時間相等性檢定統計量 11
第二節 調整樣本中位數存活時間變異數與檢定統計量 12
第四章 模擬設計與結果 15
第一節 模擬設計 15
第二節 模擬結果與討論 15
第五章 實例分析 26
第六章 結論與建議 29
參考文獻 30
附錄 32
參考文獻 Breslow, N. and Crowley, J. (1974). A large sample study of the life table and product limit estimates under random censorship. The Annals of Statistics, Vol. 2, 437-453.
Brookmeyer, R. and Crowley, J. (1982a). A confidence interval for the median survival time. Biometrics, Vol. 38, 29-41.
Brookmeyer, R. and Crowley, J. (1982b). A k-sample median test for censored data. Journal of the American Statistical Association, Vol. 77, 433-440.
Efron B. (1981). Censored data and the bootstrap. Journal of the American Statistical Association, Vol. 76, 312-319.
Greenwood, M. (1926). The Natural Duration of Cancer. Reports on Public Health and Medical Subjects, Vol. 33, 1-26.
Kaplan, E. L. and Meier, P. (1958). Nonparametric estimation from incomplete observations. Journal of the American statistical association, Vol. 53, 457-481.
Kalbfleisch, J. D. and Prentice, R. L. (2002). The statistical analysis of failure time data. New Jersey: John Wiley & Sons.
Kosorok, M. R. (1999). Two-sample quantile tests under conditions. Biometrika, Vol. 86, 909-921.
Rahbar, M. H., Chen, Z., Jeon, S., Gardiner, J. C., and Ning, J. (2012). A nonparametric test for equality of survival medians. Statistics in Medicine, Vol. 31, 844-854.
Sander, J. M. (1975). The Weak Convergence of Quantiles of the Product-limit Estimator. Stanford University Technical Reports, No. 5.
Tsai, T. H., Tsai, W. Y., Chi, Y. C. and Chang, S. M. (2014). Estimation of the ratio of two median residual lifetimes with left-truncated and right-censored data. National Cheng Kung University Technical Report.
賴冠瑜 (2014)。兩組中位數存活時間的比之推論。國立成功大學統計學系碩士論文。
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