The Correction for Naive Estimation of the Accelerated Failure Time Model with Repeat Measurements

加速壽命模型中自變數有重複觀測時原始分析的偏誤修正

黃逸輝(Yih-Huei Huang)

《統計與資訊評論》 16期 (2014/12) Pp. 33-50

摘要

在加速壽命統計模型中，自變數對壽命的效用很容易解讀，可視為壽命取對數後的分佈的位置參數，具有將壽命直接乘除一個常數的效果。當自變數無法準確觀測而有重複觀測值時，直接使用觀測到的平均值當成真實自變數所進行的統計分析，其推論結果是不正確的，且不論樣本大小其估計量皆具有相當的偏誤。本文檢視上述原始分析具有偏誤的原因並據以提出一個修正的方法，該方法需要有重複觀測值，但對於測量誤差及自變數無需太多的分佈假設。最後我們以模擬分析討論此估計量的表現。

並列摘要

In accelerated failure time (AFT) models, covariate is the location parameter of the distribution of log of life time distribution. It has effect on expanding or contracting the life time. When a covariate is not observed accurately and has repeat measurements, an intuitive way for analysis is to use the average of replicates as the covariate. Such naive analysis yields inconsistent results. We investigate how the naive estimating function is biased which motivate our proposed correction method. The method proposed here is novel and requires no distribution assumptions on covariate or random error. In other words, it is a functional method in the context of measurement error problems. Furthermore, the proposed method is applicable when measurement errors are not identically distributed with unknown variances. We assess the performance of our method by a simulation study.

並列關鍵字

accelerated failure time ； naive estimation ； repeat measurements ； functional method ； measurement error