加速壽命模型(AFT model , accelerated failure time model)具有相當直覺性的解釋，因此它是除了 Cox 比例風險模型外另一個常用的統計模型。但當自變數受測量誤差影響時，目前還未能提出具一致性的估計方法。本文考慮在自變數有重複測量的情形下，修正Tsiatis(1990)提出的估計方法以期能找出在自變數受測量誤差影響能具一致性的估計方法。而我們提出的估計方法具一致性的推測不僅可從理論來證明也可從電腦模擬結果中得到驗證。

Accelerated failure time model is an attractive alternative to the Cox proportional hazard model since it is more intuitive in interpretation. When the covariates are measured with errors, there is no consistent estimation method so far. When there are replicate measurements, we modified the estimation in Tsiatis (1990) to account for measurement errors. Our method is expected to be consistent and this conjecture is supported by our simulation results.

1 緒論 1
2 加速壽命模型中使用序數統計量之估計方法 5
2.1 符號的定義 5
2.2 估計方法之簡述 6
3 加速壽命模型中在自變數有重複測量時之估計方法 11
3.1 測量誤差模型 11
3.2 直覺(Naive) 估計法 11
3.3 交替使用重複測量估計法 13
4 參數估計量的變異數之估計方法 18
4.1 參數估計量的變異數估計 18
5 模擬研究 21
5.1 模擬設定 21
5.2 測量誤差之模擬設定 23
5.3 模擬結果比較 24
6 結論與討論 26
參考文獻 27
附錄A : 模擬表格 29

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