右方設限長期存活資料比率之研究

The Proportion of Long-term Survivor Data in Right Censored Case

蘇秀媛(Hsiu-Yuan Su) ； 蘇志雄(Chih-Hsiung Su) ； 謝鑫能(Hsin-Neng Hsieh)

《作物、環境與生物資訊》 2卷2期 (2005/06) Pp. 95-104

https://doi.org/10.30061/CEB.200506.0001

摘要

自從Boag (1949)提出「治癒資料」的分析方法後，部分學者將此方法成功的應用在醫學資料的分析。本篇文章稱Boag所提的「治癒資料」為「長期存活資料」，亦即在存活資料中，若實驗期間能無限延長下，有部份資料都能永久存活。對於此類資料，我們延用Boag的方法，定義在右方設限資料下概度函數，並假設存活母體為指數分布與Weibull分布，導出「長期存活資料」比率之最大概度估計式及概度比檢定，同時利用Kaplan and Meier的估計方法，提出無母數方法來估計「長期存活資料」比率及檢定方法。本文利用蒙地卡羅統計模擬方法比較在最大概度法及無母數方法不同情形下，觀察「長期存活資料」比率的狀況，發現在中、低設限下，無母數方法在檢定「長期存活資料」比率的檢定力優於最大概度法。

關鍵字

治癒資料 ； 長期存活資料 ； 右方設限 ； 蒙地卡羅統計模擬 ； 最大概度法

並列摘要

Since the method for analyzing the cured data was proposed by Boag in 1949, it has been applied to many medical data successfully by other scholars. The ”cured data” in Boag's paper was renamed as ”long-term survival data” here. The long-term survival data means some of the data can survive in indefinite time. The likelihood function with right-censored data was defined by using Boag's method. The survival population was assumed to be exponential distribution or Weibull distribution. The MLE (maximum likelihood estimator) and LRT (likelihood ratio test) can be derived for long-term survival data. Furthermore, a nonparametric method for estimating proportion of long-term survival data was derived based on Kaplan-Meier's estimation. In this paper, we compare the MLE and non-parametric method by Monte Carlo simulation method for long-term survival data. We find that the performance of non-parametric test is better than that of maximum likelihood ratio test in cases of middle censored rate and low censored rate.

並列關鍵字

Cured data ； Long-term survivor data ； Right-censored ； Monte Carlo simulation ； Maximum likelihood ratio test