共變量測量誤差問題在現狀數據近來已被研究(Wen, Huang和Chen 2011; Wen和Chen 2012)，但對具有免疫子群的此類數據卻還未被探討。研究動機源自台灣2005年『國民健康訪問調查』的糖尿病資料，其中糖尿病發生時間是現狀設限的、共變量身體質量指數具有測量誤差且部分受訪者似乎對糖尿病是免疫的，我們在比例勝算比治癒模型下建立條件分數法來分析具共變量測量誤差之部份免疫現狀數據。條件分數法沒有對易有測量誤差的共變量做分佈的假設因而能有更廣泛的應用。我們藉由模擬研究評估所提方法並以糖尿病資料說明其應用。

Covariate measurement error problem has been recently studied in the context of current status data (Wen, Huang, and Chen 2011; Wen and Chen 2012) but not yet for such data with an immune subgroup. Motivated by the diabetes dataset from the 2005 National Health Interview Survey of Taiwan, where the occurrence time of diabetes was current status censored, covariate Body Mass Index was measured with error, and a fraction of participants seemed immune from diabetes, we develop a conditional score method under the proportional odds cure model for analyzing partially immune current status data with mismeasured covariates. The conditional score approach makes no distribu-
tional assumption on the error-prone covariate and hence enjoys wide application. We evaluate the proposed method through simulation studies and illustrate it with the diabetes data.

目錄
第一節 緒論1
第二節 模型與資料介紹5
第三節 條件分數法8
3.1 條件分數估計8
3.2 變異數估計11
第四節 模擬詴驗12
第五節 實例分析15
第六節 結論17
參考文獻23
附錄25
附錄A.1 模型推導25
附錄A.2 條件概似函數推導26
附錄A.3 矩陣A 之明確式27
附錄A.4 毀壞時間的生成方法28

表目錄
表 1 模擬結果18
(a) 參數alpha的估計18
(b) 參數beta的估計19
表 2 糖尿病資料摘要21
表 3 糖尿病資料分析21

圖目錄
圖 1 根據max-min公式，BMI偏高、正常、偏低三組資料各自的糖尿病存活函         數估計2
圖 2 模擬試驗(alpha,beta)=(1,1)(治癒率=0.3),n=600,sigma^2=0.3之alpha與beta標準化估計對N(0,1)之Q-Q plot 20
圖 3 (a)根據max-min公式，BMI偏高、正常、偏低三組資料各自的糖尿病存活函數估計 (b)根據條件分數法，給定BMI 偏高、正常、偏低三組BMI樣本平均值下之糖尿病存活曲線估計(篩選法m=12) 22

1.	Aragόn, J. and Eberly, D. (1992) On convergence of convex minorant algorithms for     
distribution estimation with interval-censored data. Journal of Computational and Graphical Statistics 1, 129-140.

2.	Berkson J. and Gage R. P. (1952) Survival cure for cancer patients following treatment. Journal of the American Statistical Association 47, 501-515.

3.	Carroll, R. J., Ruppert, D., Stefanski, L. A. and Crainiceanu C. M. (2006) Measurement error in nonlinear models. Chapman & Hall, London.

4.	Farewell, V. T. (1982) The use of mixture models for the analysis of survival data with longterm survivors. Biometrics 39, 1041-1046.

5.	Farewell, V. T. (1986) Mixture models in survival analysis: Are they worth the risk?
The Canadian Journal of Statistics 14, 257-262.

6.	Huang, J. (1996) Efficient estimation for the proportional hazards Model with Interval Censoring. The Annals of Statistics 24, 540-568.

7.	Ma, S. (2009) Cure model with current status data. Statistica Sinica 19, 233-249.

8.	Rossini, A. J. and Tsiatis, A. A. (1996) A semiparametric proportional odds regression model for the analysis of current status data. Journal of the American Statistic Association 91, 713-721.

9.	Stefanski, L. A. and Carroll, R. J. (1987) Conditional scores and optimal scores for generalized linear measurement-error models. Biometrika 74, 703-716.

10.	Takovlev, A. Y. and Tsodikov, A. D. (1996) Stochastic models of tumor latency and their biostatistical applications. Hackensack, NY: World Scientific.

11.	Yakovlev, A. Y. (1994) Letter to the editor. Statistics in Medicine 13, 983–986.

12.	Wen, C. C., Huang, Steve Y. H. and Chen, Y. H. (2011) Cox regression for current status data with mismeasured covariates. The Canadian Journal of Statistics 39, 77-88.

13.	Wen, C. C. and Chen, Y. H. (2012) Conditional score approach to errors-in-variable current status data under the proportional odds model. Scandinavian Journal of Statistics, to appear.