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研究生:林彥廷
研究生(外文):Lin, Yantin
論文名稱:根據假性觀察值鑑別右設限存活資料之最低有效劑量
論文名稱(外文):Identifying The Minimum Effective Dose Based On Pseudo-value Of Right-censored Data
指導教授:張玉媚張玉媚引用關係
指導教授(外文):Chang, Yumei
口試委員:俞一唐陳春樹
口試委員(外文):Yu, ItangChen, Chunshu
口試日期:20120712
學位類別:碩士
校院名稱:東海大學
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:2012
畢業學年度:100
語文別:中文
論文頁數:27
中文關鍵詞:假性資料
外文關鍵詞:pseudo-value
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藥物劑量反應研究中,為了探討某一種藥物的效果,經常進行數個漸增的劑量水準當作處理組和一個零劑量的對照組來做比較。
此時實驗者主要想研究的問題之一是如何鑑別出優於對照組的最低劑量水準,也稱為最低有效劑量 (Minimum effective dose,簡寫為MED)。
針對右設限存活資料,當兩組存活函數呈現交叉時,通常不會檢定兩組的存活函數有無差異,而是會固定在一些感興趣的時間點上,
比較兩組之存活機率的差異。Klein et al. (2007) 提出在固定時間上比較兩組的存活機率的檢定統計量。
本文推廣Klein et al. (2007) 所建議的檢定統計量,針對多組資料以封閉降階檢定程序 (Closed step-down testing procedure)鑑別最低有效劑量。
接著以模擬方式探討所推廣的檢定統計量,比較其實驗族誤差率、族誤差率、檢定力及偏誤。最後分析實例資料,藉以說明所提方法之應用。

Dose-response studies are frequently conducted to evaluate the treatment effects of a drug in animal experiments or clinical trials for drug development. In these studies, subjects or patients are randomly allocated to groups to receive several increasing dose levels of the drug and a zero-dose control. One factor of interest in such studies is to identify the minimum effective dose (MED) of the drug, which is defined to be the smallest dose level producing a clinically important response that can be declared statistically significantly more effective than the placebo response. For right-censored survival data, we are interest in comparing the difference between two survival functions at a fixed time point rather than comparing the entire survival curves, when the survival functions are crossing. Therefore, Klein et al. (2007) proposed a number of test statistics for comparing two survival functions at a fixed time point for right-censored data. In this thesis, we consider extend their methods to the MED identification problem. We further conduct a Monte Carlo study to investigate the relative error rate, power and bias performances of the competing procedures. Finally, the procedures are illustrated with a right-censored survival data.
1. 研究目的: 1
2. 文獻回顧 3
2.1 封閉降階檢定程序 3
2.2 雙樣本存活函數差異之檢定 4
2.2.1 naïve 5
2.2.2 logarithmic轉換 5
2.2.3 log(-log(.)) 轉換 6
2.2.4 arcsin-square root 轉換 6
2.2.5 Pseudo-Value 7
3 鑑別最低有效劑量之檢定統計量 10
3.1 符號定義 10
3.1.1 naïve 10
3.1.2 logarithmic轉換 11
3.1.3 log(-log(.)) 轉換 11
3.1.4 arcsin-square root 轉換 12
3.1.5 Pseudo-Value 13
4 模擬研究 15
5 實例分析 17
6 結論與建議 19
參考文獻 20
附錄 22

1.Aalen, O.O. (1978b). Nonparametric inference for a family of counting processes.
Annals of Statistics 6, 701-726.
2.Andersen, P. K., Klein, J. P., and Rosthøj, S. (2003). Generalized linear models
for correlated pseudo-observations with applications to multi-state models.
Biometrika 90, 15–27.
3.Bayer, D.P. and Corle, D.K. (1977). Selecting optimal treatment in clinical trials
using covariate information. Journal of Chronic Disease 30, 445-459.
4.Chen, Y.I. (1999). Nonparametric identification of the minimum effective dose.
Biometrics 55, 1236-1240.
5.Chen, Y. I. and Jan, S.L. (2002). Nonparametric identification of the minimum
effective dose for randomized block design. Communications in Statistics —
Simulation & Computation 31, 301-312.
6.Chen, Y. I. and Chang, Y. M. (2007). Identification of the minimum effective dose
for right-censored survival data. Computational Statistics and Data Analysis 51,
3213-3222.
7.Chang, Y. M. and Chen , Y. I. (2011). Identification of the minimum effective dose
based on weighted Kaplan-Meier Statistics. Journal of Statistical Computation
and Simulation 81, 619-634.
8.Fleming, T.R. and Harrington, D.P. (1991). Counting process and survival
analysis. Wiley, New York.
9.Greenwood, M. (1926). The Nature Duration of Cancer. In Reports On Public
Health and Medical Subjects 33, 1-26.
10.Jan, S.L. and Chen, Y.I. (2004). Nonparametric procedures for imultaneous
identification of the minimum effective dose in each of several groups.
Journal of Biopharmaceutical Statistics 14, 781-789.
11.Klein, J. P., Logan, B., Harhoff, M., and Anderson, P. K. (2007). Analyzing
survival curves at a fixed point in time. Statistics in Medicine 26, 4505-4519.
12.Kalbfeisch, J. D. and Prentice, R. L. (1980). The statistical analysis of failure time
data.New York: Wiley.
13.Kaplan, E. L. and Meier, P. (1958). Nonparametric estimation form incomplete
observations. Journal of the American Statistical Association 53, 457-481.
14.Liang, K.Y., Zeger, S.L. (1986) Longitudinal data analysis using generalized
linear models. Biometrika 78, 13-22.
15.Marcus, R., Peritz, E. and Gabriel, K.R. (1976). On closed testing procedures with
special reference to ordered analysis of variance. Biomerrika 63, 655-660。
16.Pepe, M.S. and Fleming, T.R. (1989). Weighted Kaplan-Meier statistics: a class of
distance tests for censored survival data. Biometrics 45, 497-507.
17.Pepe, M.S. and Fleming, T.R. (1991). Weighted Kaplan-Meier statistics: Large
sample and optimality considerations. Journal of the Royal Statistical Society,
Series B 53, 341-352.
18.Ruberg, S.J. (1989). Contrasts for identifying the minimum effective dose.
Journal of the American Statistical Association 84, 816-822.
19.Tamhane, A.C., Hochberg, Y. and Dunnett, C.W. (1996). Multiple test procedures
for dose finding. Biometrics 52, 21-37.

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