使用伯氏多項式估計存活風險率

本研究將根據右設限資料提出一個具平滑性質之存活風險率，而風險率模型所引進之參數將以最大概似估計法來估計。此估計程序可以提供一個存活風險率的平滑估計。我們根據牛頓法的原理，提出一個有效求取最大概似估計量的演算法。此估計方法的成功，於模擬試驗及對白血病患緩解時間的數據資料之分析結果將被說明。另外，我們的方法與尼爾生-艾倫方法的比較，和伯氏多項式階數之選取亦為本文討論的議題。

關鍵字

右設限資料；伯氏多項式；尼爾生-艾倫；最大概然估計

並列摘要

In this thesis, we study the maximum likelihood estimator for a survival hazard rate with right censored data, in which the hazard rate is specified by the Bernstein polynomial. Our estimation procedure can provide a smooth estimator of the survival hazard rate. We develop an efficient Newton-Raphson based algorithm for the computation of the maximum likelihood estimate. The success of this method is demonstrated in simulation studies and in the analysis of Leukemia remission-time data. In addition, the comparison with Nelson-Aalen method is presented and the selection of the degree for Bernstein polynomial is discussed.

並列關鍵字

Right Censored Data ； Bernstein Polynomial ； Nelson- Aalen ； Maximum Likelihood Estimator

參考文獻

[1]　Chang, I.S., Hsiung, C.A., Wu, Y.J. and Yang, C.C.(2005). Bayesian survival analysis using Bernstein polynomials. Scand. J. Statist. 32 447-466.

[2]　Chang, I.S., Chien, L.C., Hsiung, C.A., Wen, C.C. and Wu, Y.J. (2007). Shape restricted regression with random Bernstein polynomials. In R. Liu, W. Strawderman and C.H. Zhang (eds), Complex Dataset and Inverse Problems. IMS Lecture Notes – Monograph Series. 54 187-202.

[3]　Klein, J.P. and Moeschberger, M.L. (2003). Survival Analysis Techniques for Censored and Truncated Data.

[4]　Lamperti, J.W. (1996). Probability: a Survey of the Mathematical Theory.

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使用伯氏多項式估計存活風險率

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