長期存活資料比率之統計分析

Statistical Analysis of Proportion of Long-term Survivor Data

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》 3卷4期 (2006/12) Pp. 337-344

https://doi.org/10.30061/CEB.200612.0006

摘要

在存活資料中，若試驗期間能無限延長，有部份資料將能永久存活，故稱長期存活資料。本文中長期存活資料為區間設限資料型式，假設存活母體為指數分布與Weibull分布，定義區間設限資料下的概度函數，並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-Meier的估計方法，提出無母數方法來估計「區間設限長期存活資料」比率及其檢定方法。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的表現狀況，結果發現無母數方法在檢定「區間設限長期存活資料」比率的表現優於最大概度法，此與長期存活資料為右方設限資料型式之結果一致。

關鍵字

長期存活資料 ； 區間設限 ； 最大概度估計 ； 概度比檢定

並列摘要

The long-term survival data means some of the data can survive in definite time. The likelihood function with interval-censored data was defined when the survival population was assumed to be exponential or Weibull distribution. The MLE (maximum likelihood estimator) and LRT (likelihood ratio test) can be derived from 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 compared the MLE and nonparametric method by Monte Carlo simulation method for long-term survival data. We found that the performance of nonparametric test was better than maximum likelihood ratio test, which was similar to the results obtained with right-censored data.

並列關鍵字

Long-term survivor data ； Interval-censored ； Maximum likelihood estimator ； Likelihood ratio test