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    題名: 加速壽命模型有測量誤差時具有一致性之估計方法研究
    其他題名: Consistent Estimations in the Accelerated Failure Model When Covariates Are Subjecto to Measurement Errors
    作者: 黃逸輝
    貢獻者: 淡江大學數學學系
    日期: 2012-08
    上傳時間: 2015-05-13 10:27:23 (UTC+8)
    摘要: 加速壽命模型由於解釋容易、直覺上容易理解,因此是Cox 比例風險模型外另一個 被廣泛使用的統計模型。討論加速壽命模型的文獻很多,多數是沒有測量誤差的情形, 其中跟本計畫有關的是Tsiatis (1990)或是Lin et al.(1998)關於使用序列統計量的 估計概念。然而當測量誤差存在時,加速壽命模型並不像Cox 比例風險模型已有很多的 方法或是討論,加速壽命模型相關的分析方法少之又少,而且都只是一些近似方法。本 計畫假設對於每個真實自變數都有兩個以上的重複觀測,利用其中一個重複觀測“調整 "壽命時間使其有同態分佈,再根據調整後的壽命時間作為排序依據,而另一個重複觀 測值則作為觀測到的自變數,由此似乎可以構造出具有一致性的估計方程式。本計畫會 驗證這個概念,建立相關的統計理論以及進行推廣的工作。
    The accelerated failure time (AFT) model is an attractive alternative to the Cox proportional hazard model. In the accelerated failure time model, the covariate is modeling to expand or contract the life time. Thus the AFT model is more intuitive in interpretation than the Cox proportional hazard model. However, when covariates are subject to measurement errors, much less estimation methods had been developed for the accelerated failure time model than there were for the proportional hazard model. In this paper, we consider the estimation using ranks in the accelerated failure model when covariates are subject to measurement errors. We require two replicates for each covariate to construct our estimating function. The distribution assumption for the unobserved true covariate is not needed. Our estimation function uses one replicate for sorting the observed life time and uses the other one as the observed covariate. The resultant estimating function seems to be 0 unbiased when conditioning on the true covariate. Thus it is expected to yield consistent inference from our proposed method. This project will verify this idea and develop any related statistics inferences. Other applications, extensions or limitations will also be addressed
    顯示於類別:[數學學系暨研究所] 研究報告

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