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系統識別號 U0002-2007201102583700
中文論文名稱 現狀數據在比例勝算比模型下之概似比檢定
英文論文名稱 Likelihood Ratio Test for Proportional Odds Model with Current Status Data
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 99
學期 2
出版年 100
研究生中文姓名 柯興杰
研究生英文姓名 Hsing-Chen Ke
電子信箱 qazwsxedcaxszscd@yahoo.com.tw
學號 698190302
學位類別 碩士
語文別 中文
口試日期 2011-07-11
論文頁數 23頁
口試委員 指導教授-溫啓仲
委員-黃逸輝
委員-吳裕振
中文關鍵字 現狀數據  概似比檢定統計量  自身一致方程式 
英文關鍵字 Current Status Data  likelihood ratio test statistic  self-consistency equations 
學科別分類 學科別＞自然科學＞數學
中文摘要 現狀數據為一種區間設限資料，其觀察值僅包括檢查時間和事件發生時間是否在檢查時間之前發生。探討事件發生時間和共變量之間的關係之半母數迴歸方法，在現狀數據中已被廣泛地研究。在本論文中，我們考慮在比例勝算比模型下之現狀數據，對於共變量效應之概似比檢定。並提出一個簡單的演算法則來計算此檢定量。此演算法是根據一系列的自身一致方程式且我們利用收縮原理來證明其收斂性。我們進行了模擬計算並分析兩筆真實數據，來說明此概似比檢定量之卡方漸進性的適當性和此演算法的可行性。
英文摘要 Current status data result from a simple form of interval censoring in which the observation consists only of an examination time and knowledge of whether the failure time has occurred before the exam. Semiparametric regression methods which examine the relationship between the failure time and covariates have been studied extensively for current status data. In this thesis, we consider the likelihood ratio test for testing covariate effect under the proportional odds model with current status data and propose an easily implemented algorithm for computing the statistics. The algorithm proposed is based on a set of self-consistency equations and its convergence is proved by contraction principle. The adequacy of the Chi-squared approximation for likelihood ratio statistics and the availability of the algorithm are demonstrated in simulation studies and in the analyses of two real data.
論文目次 致謝.......................................................I

論文中文摘要................................................II

論文英文摘要...............................................III

第一節 前言.................................................1

第二節 資料與模型敘述.........................................2

2.1 資料與模型............................................2

2.2 概似比檢定............................................3

第三節 演算法................................................4

第四節 模擬試驗..............................................8

第五節 實例分析.............................................17

5.1 肺腫瘤數據分析..........................................17

5.2 水晶體鈣化數據分析.......................................18

第六節 結論................................................19

參考文獻...................................................20

附 錄 A..................................................22
附 錄 B..................................................23
參考文獻 Huang, J. (1996). Efficient estimation for the proportional hazards model with interval censoring. The Annals of Statistics, 24, 540-568.

Hoel, D. G. and Walburg, H. E. (1972). Statistical analysis of survival experiments. Journal of National Cancer Institute. 49, 361-372.

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

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

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

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 Statistical Association. 91, 713-721.

Rudin, W. (1973). Functional Analysis. McGraw-Hill, New York.

Sun, J. (2006). The Statistical Analysis of Interval-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.

Xue, H., Lam, K. F. and Li, G. (2004). Sieve maximum likelihood estimation for semiparametric regression models with current status data. Journal of the American Statistical Association. 99, 346-356.

Yu, A. K. F., Kwan, K. Y. W., Chan, D. H. Y. and Fong, D. Y. T. (2001). Clinical features of 46 eyes with calcified hydrogel intraocular lenses. Journal of Cataract and Refractive Surgery. 27, 1596-1606.

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