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系統識別號 U0002-3107201213373900
中文論文名稱 具共變量測量誤差之現狀數據分析
英文論文名稱 Analysis of Current Status Data with Mismeasured Covariate
校院名稱 淡江大學
系所名稱(中) 數學學系碩士班
系所名稱(英) Department of Mathematics
學年度 100
學期 2
出版年 101
研究生中文姓名 傅婕寧
研究生英文姓名 Chieh-Ning Fu
學號 699190301
學位類別 碩士
語文別 中文
口試日期 2012-06-20
論文頁數 27頁
口試委員 指導教授-温啓仲
委員-黃逸輝
委員-吳裕振
中文關鍵字 條件分數  現狀數據  測量誤差  比例勝算比模型  右設限  篩選法 
英文關鍵字 Conditional score  Current status data  Measurement error  Proportional odds model  Right-censored  Sieve 
學科別分類 學科別自然科學數學
中文摘要 雖然已有相當多的研究工作在右設限存活數據具共變量測量誤差的問題,但具共變量測量誤差現狀數據的迴歸分析近年來才開始。這篇論文中,我們考慮Wen and Chen (2012) 分析具共變量誤差現狀數據的條件分數法。不同於Wen and Chen (2012),我們使用篩選法去近似比例勝算比模型的基線勝算比函數。我們所提方法的優點為條件分數估計的計算更有效率且迴歸係數估計之變異數估計無需估計設限時間分布。所提的方法藉由模擬試驗評量且由一實際數據說明其應用。
英文摘要 While there is considerable work on covariate measurement error problem for right-censored survival data, regression analysis for current status data with mismeasured covariate has just started recently. In this thesis, we consider the conditional score approach of Wen and Chen (2012) for the analysis of errors-in-variable current status data. Distinct from Wen and Chen (2012), we employ a sieve method to approximate the baseline odds ratio function in the proportional odds model. Our proposal has advantages that the computation of conditional score estimates is more efficient and the variance estimation of regression parameter estimate is exempted from estimating the distribution of censoring time. The proposed method is evaluated through simulation studies and illustrated with a real data.
論文目次 目錄
第一節 緒論 1
第二節 模型與數據介紹 4
第三節 條件分數估計 6
第四節 變異數估計 9
第五節 模擬試驗與實例分析 10
5.1 模擬試驗 10
5.2 實例分析 12
第六節 結論 14
參考文獻 24
附錄 26
附錄A 條件概似函數的推導 26
附錄B 矩陣A的明確式 27

表目錄
表1篩選法m=5之模擬試驗 15
表2篩選法m=6之模擬試驗 16
表3篩選法m=7之模擬試驗 17
表4斑馬魚基底細胞癌資料的分析結果 23

圖目錄
圖1根據beta _0 = 0.5 ,sigma _0^2 = 0.7 和n=600模擬試驗: beta之標準化估計對N(0,1)之Q-Q plot(篩選法m=5) 18
圖2根據beta _0 = 0.5 ,sigma _0^2 = 0.7 和n=600模擬試驗: beta之標準化估計對N(0,1)之Q-Q plot(篩選法m=6) 19
圖3根據beta _0 = 0.5 ,sigma _0^2 = 0.7 和n=600模擬試驗: beta之標準化估計對N(0,1)之Q-Q plot(篩選法m=7) 20
圖4標準化後Shh平均的離差對N(0,1)之Q-Q plot 21
圖5條件分數估計法與自然估計法下之基底細胞癌發生的存活曲
線(篩選法m=4且給定共變量為所有重複Shh量測的樣本平均) 22

參考文獻 Carroll, R. J., Ruppert, D., Stefanski, L. A. and Crainiceanu, C. M. (2006). Measurement Error in Nonlinear Models: A Modern Perspective, 2nd edn. Chapman & Hall/CRC Press, Boca Raton.

Chen, Y. H., Wang, Y. H., Yu, T. H., Wu, H. J. and Pai, C. W. (2009). Transgenic zebrafish line with over-expression of Hedgehog on the skin: A useful tool to screen Hedgehog-inhibiting compounds. Transgenic Research, 18, 855-864.

Hu, P., Tsiatis, A. A. and Davidian, M. (1988). Estimating the parameters in the Cox model when covariate variables are measured with error. Biometrica 54, 1407-1419.

Huang, J. (1996). Efficient estimation for the proportional hazards model with interval censoring. The Annals of Statistics, 24, 540-568.

Lin, D. Y., Oakes, D. and Ying, Z. (1998). Additive hazards regression with current status data. Biometrika 85, 289-298.

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

Martinussen, T. and Scheike T. H. (2002). Efficient estimation in additive hazards regression with current status data. Biometrika 89, 649-658.

Rossini, A. J. & 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.

Song, X. and Huang, Y. (2005). On corrected score approach for proportional hazards model with covariate measurement error. Biometrics 61, 702-714.

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

Sun, J. (2006). The Statistical Analysis of Inter-censored Failure Time Data. Springer-Verlag, New York.
Sun, J. and Sun, L. (2005). Semiparametric linear transformation models for current status data. The Canadian Journal of Statistics, 33, 85-96.

Tian, L. and Cai, T. (2006). On the accelerated failure time model for current status and interval censored data. Biometrika 93, 329-342.

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.

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.

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.

Zhang, Z. and Sun, J. (2010). Interval censoring. Statistical Methods in Medical Research, 19, 53-70.
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