廣義伽瑪分布加速失敗時間模型之研究

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李克耘(Ke-Yun Li)

指導教授 ： 陳玉英

國立中央大學/理學院/統計研究所/碩士(2008年)

摘要

右設限存活資料分析中的參數化加速失敗時間模型，經常假設其
存活分布為韋伯分布、對數常態分布或對數邏輯司分布，當共變數存
在時，又多展示為對數線性模式。本文考慮的參數化加速失敗時間模
式之存活分布為廣義伽瑪分布，因為此一分布包含韋伯分布、對數常
態分布及伽瑪分布等，所能涵蓋的右偏分布較為廣泛。此外，本文利
用區域概似估計(local likelihood estimation)研究對數線性模式
中共變數的可能轉換。之後本文用模擬研究本文所提比較廣義的模型
在各種不同加速失敗時間模型及存活分布下，估計中位存活時間的偏
誤及均方誤。最後，本文藉一筆資料說明所提模型之應用。

關鍵字

加速失敗時間模型 ； 廣義伽瑪分布 ； 區域槪似估計 ； 右設限存活資料

並列摘要

The parametric accelerated failure time(AFT) model for analyzing the right-censored survival data usually assumes Weibull, lognormal or log-logistic distribution for the lifetime variable of interest. When the covariates are presented, the AFT model is often expressed log-linear
form. In this study, however we consider the parametric accelerated failure time model with lifetime which is distributed for a generalized gamma distribution, including, in particular, Weibull, lognormal and gamma distributions. In addition, we use local likelihood estimation to investigate the possible transformation of the covariates that showing in the log-linear model. A simulation study is further implemented for evaluating the bias and mean squares error of the estimated medians for a
variety of AFT models and survival distributions. Finally, we use a data to illustrate the application of the model, under study.

並列關鍵字

local likelihood estimation ； generalized gamma distribution ； right-censored ； accelerated failure time model

參考文獻

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