在本文中，我們探討Cox比例風險模型中自變數有異質性(heteroscedastic)測量誤差時的迴歸參數估計方法；若量測次數與存活時間相關時，那麼平均量測值的變異數會與存活時間有關，就會造成異質性測量誤差的問題。本文使用小測量誤差的估計方法，它不需在測量誤差上有分配的假設，直接以泰勒展開式來近似含有測量誤差的分數函數；除此之外，再與其它文獻所提過的估計方法一起做比較，這其中還包含新的誤差增量估計方法。最後我們利用電腦模擬在許多不同情況下各種估計方法的表現，並對結果加以討論。

We consider the heteroscedastic measurement error problem in Cox regression model. The heteroscedastic measurement error can happen naturally when the number of replicates is related to the survival time or censoring time. To accommodate the effect of heteroscedastic measurement error in estimation, we consider a small measurement error assumption approach as well as the error augmentation for the conventional corrected score and conditional score. Their performances were evaluate by a simulation study.

1. 緒論...1
2. Cox比例風險模型及自變數有測量誤差時之估計方法簡述...5  
2.1 符號的定義...5
2.2 Cox比例風險模型簡介與其估計方法...6
2.3 自變數含有測量誤差時傳統的估計方法...7
3. 小測量誤差近似估計方法...10
4. 異質性測量誤差的估計方法與誤差增量修正...14
4.1 質性測量誤差下的各種估計方法...14
4.2 誤差增量修正方法...17
5. 模擬研究...20
5.1 模擬條件...20
5.2 模擬結果...23
6. 結論與討論...25
參考文獻...27
附錄A...28
A.1...28
A.2...28
附錄B...30

1.Carroll, R. J., Ruppert, D., Stefanski, L. A., and Crainiceanu, C. M. (2006). Measurement Errors in Nonlinear Models, Chapman & Hall, London.
2.Nakamura, T. (1992). Proportional hazards model with covariates subject to measurement errror. Biometrics 48,829-838.
3.Song, X. and Huang, Y. (2005). On corrected score approach for proportional hazards model with covariate measurement error. Biometrics 61,702-714
4.Tsiatis, A. A. and Davidian, M. (2001). A semiparametric estimator for the proportional hazards model with longitudinal covariates measured with error.Biometrika 88,447-458