臺灣博碩士論文加值系統

在人口統計調查或生物醫學研究中，常遇到現狀資料，其中資料的觀測值包含檢查時間及關心的事件是否在檢查時間時已經發生的現狀指標。在本論文中，我們提出了權重逆機率的估計方法來分析現狀指標可能缺失但其替代指標可得的現狀資料。我們的方法建立在正比例存活風險模型及隨機缺失的假設下。模擬結果驗證了我們所提的估計量具有漸進常態性且校正了直接忽略缺失資料的完整資料分析方法所產生的偏誤。除此之外，我們也以骨質疏鬆症的資料分析來作為所提方法的例證說明。

Current status data are commonly encountered in demographic or biomedical studies, in which the observation consists of an examination time and a status indicator for whether or not the event of interest has occurred by the examination time. In this thesis, we propose an inverse probability weighted method for analyzing current status data where the status indicator is subject to missing but a surrogate for status indictor is available instead. Our method is based on the proportional hazards survival model and missing at random mechanism. Simulation results confirm that the proposed estimator is asymptotically normal and it removes the bias resulted from the naive “complete case” analysis discarding subjects with missing value. Besides we illustrate our proposal by analyzing an osteoporosis survey data.

目錄
1 前言.......................1
2 資料，模型和權重逆機率估計.....3
3 大樣本理論與變異數估計........7
4 模擬試驗...................11
5 實例分析...................15
6 結論......................17
參考文獻.....................27

Bickel, P.J., Klaassen, C., Ritov, Y., and Wellner, J.A. (1993). Efficient and Adaptive Estimation for Semiparametric Models, Johns Hopkins University Press, Baltimore.

Cox, D.R. (1972). Regression Models and Life Tables (with Discussion). Journal of the Royal Statistical Society, Series B. 34, 187-220.

Carroll, R.J., Ruppert, D., Crainiceanu, C.M., and Stefanski, L.A. (2006).Measurement Error in Nonlinear Models: A Modern Perspective,Second Edition. Chapman and Hall/CRC Press, Boca Raton.

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

Korosok, M.R. (2008). Introduction to Empirical Processes and Semiparametric Inference. Springer, New York.

Little, R.J.A. and Rubin, D.B. (2002). Statistical Analysis with Missing Data, 2nd ed. Wiley, New York., MR. 1925014.

Robins J.M., Rotnitzky A., and Zhao L.P. (1994). Estimation of regression coefficients when some regressors are not always observed. Journal of the American Statistical Association, 89, 846-866.

van der Vaart, A.W. and Wellner, J.A. (1996). Weak Convergence and Empirical Processes. Springer, New York. 27

van der Vaart, A.W. (1998). Asymptotic Statistics, Cambridge University Press. Cambridge.