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系統識別號 U0026-0208201421111000
論文名稱(中文) 兩組中位數存活時間之比的統計推論
論文名稱(英文) Inference on the Ratio of Two Median Survival times
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) 賴冠瑜
研究生(英文) Guan-Yu Lai
學號 R26014056
學位類別 碩士
語文別 中文
論文頁數 49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 中位數之比  變異數估計量  信賴區間  非劣性檢定 
英文關鍵字 ratio of medians  variance estimator  confidence interval  non-inferiority hypotheses 
學科別分類
中文摘要 在右設限資料下,本論文提出了一種樣本存活時間中位數(簡稱中位數)之變異數的估計方法。使用的技巧類似於Tsai et al. (2014)的方法,皆是根據中位數信賴區間的寬度,只是建構信賴區間的方式不同。經模擬發現,本論文提出的估計量之偏誤和均方誤差皆較其他估計量小,漸近於真實值的速度也較其他估計量快,且其所需計算時間也較少。接著,本論文進行兩組中位數之比較。本論文整合了三種檢定方式下,共四種檢定統計量以建立中位數之比的信賴區間及進行非劣性檢定。最後經模擬發現本論文提出的估計量搭配差值轉換統計量,在建立中位數之比的信賴區間時,其涵蓋率較接近名目的信賴水準;在進行非劣性檢定時,此統計量的型I誤差率也較接近名目的顯著水準;此外,此統計量的型式相較其他統計量簡單。故建議研究者採用本論文提出的樣本中位數的變異數之估計量結合差值轉換統計量進行兩組中位數之比的比較。
英文摘要 To make inference about the ratio of two median survival times, four types of test statistics, including two Wald tests based on the ratio of two sample medians with slightly different variance estimators (W1 and W2), the Wald test based on the difference between two sample medians (W3), and the Wald test based on the difference between two logarithm of sample medians (W4). Each test statistic involves the variance of sample median survival time. To avoid estimating the density function in the variance non-parametrically, Tsai et al. (2014) proposed a variance estimator (LB1) based on the length of confidence interval for median. This thesis further suggests an alternative variance estimator (LB2), which constructs the confidence interval for median by inverting the acceptance region of the test proposed by Brookmeyer and Crowley. Simulation results indicate that the proposed estimator has smaller bias and mean square error.

Moreover, extensive simulation studies are conducted to compare the accuracy of the four types of test statistics with two estimated variance of sample median in constructing two-sided confidence intervals. Simulation results show that the Wald test W1 with LB1 as variance estimate outperforms other tests. Nevertheless, the Wald test W3 with LB2 perform well for testing non-inferiority hypotheses. This is due to that the asymptotic distributions of W1 and W2 are left-skewed for small and moderate sample sizes. In conclusion, our simulation results demonstrate that the variance estimator LB2 is recommended for estimating the variance of sample median. Furthermore, the choice of a test statistic will depend on the hypotheses to be tested such as one-sided or two-sided.
論文目次 第一章 緒論 1
第二章 研究背景 3
2.1 符號介紹 3
2.2 存活函數估計量 3
2.3 樣本中位數之變異數估計 5
2.3.1 漸近變異數 (asymptotic variance) 5
2.3.2 自助法 (bootstrap method) 6
2.3.3 信賴區間長度法 (length-based method) 7
第三章 樣本中位數之變異數估計量之比較 8
3.1 新的估計方法 8
3.2 模擬比較 9
第四章 兩組中位數存活時間之比較 14
4.1 兩組中位數存活時間之比的信賴區間 14
4.1.1 比值統計量(一) 14
4.1.2 比值統計量(二) 15
4.1.3 差值轉換統計量 16
4.1.4 對數轉換統計量 17
4.2 模擬比較 18
4.3 兩組中位數存活時間比值之非劣性檢定 28
4.4 模擬比較 29
第五章 建議與結論 38
參考文獻 39
附錄一 41
附錄二 43
附錄三 45
附錄四 46
附錄五 47
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Rothman, M. D., Wiens, B. L. and Chan, I. S. (2012). “Design and analysis of non-  inferiority trials,” 279-283. Boca Raton, FL: Chapman & Hall/CRC.
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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,” Technical   Report, Department of statistics, National Cheng-Kung University.
Walker, E. and Nowacki, A. S. (2011). “Understanding equivalence and noninferiority   testing,” Journal of General Internal Medicine, 26, Issue 2, 192-196.
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